A mother pushes her son in a stroller at a constant speed of 1.52 m/s. The boy tosses a 56.7-g tennis ball straight up at 1.75 m/s and catches it. The boy’s father sits on a bench and watches. a. According to the mother, what are the ball’s initial and final momenta? b. According to the father, what are the ball’s initial and final momenta? c. According to the mother, is the ball’s momentum ever zero? If so, when? If not, why not? d. According to the father, is the ball’s momentum ever zero? If so, when? If not, why not?

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Answer 1

Textbook Question

Chapter 10, Problem 4PQ

A mother pushes her son in a stroller at a constant speed of 1.52 m/s. The boy tosses a 56.7-g tennis ball straight up at 1.75 m/s and catches it. The boy’s father sits on a bench and watches.

a. According to the mother, what are the ball’s initial and final momenta?

b. According to the father, what are the ball’s initial and final momenta?

c. According to the mother, is the ball’s momentum ever zero? If so, when? If not, why not?

d. According to the father, is the ball’s momentum ever zero? If so, when? If not, why not?

(a)

Expert Solution

To determine

The initial and final momentum of ball according to mother’s view.

Answer to Problem 4PQ

The initial momentum is 9.92×10−2j^ kg⋅m/s_, and final momentum is −9.92×10−2j^ kg⋅m/s_.

Explanation of Solution

Consider the figure showing the motion of ball on the basis of mother’s point of view.

Physics for Scientists and Engineers: Foundations and Connections, Chapter 10, Problem 4PQ , additional homework tip 1

According to mother’s point of view, the ball moves vertically upwards and falls vertically downwards with same speed. But initial momentum is in positive y direction and final momentum is in negative y direction.

Write the expression for initial momentum.

(pi→)mot=mvi→ (I)

Here, m is the mass of ball, and vi is the initial velocity.

Write the expression for final momentum.

(pf→)mot=mvf→ (II)

Here, m is the mass of ball, and vf is the final velocity.

Conclusion:

Substitute, 56.7×10−3 kg for m, and 1.75 j^ m/s for vi in equation (I).

(pi→)mot=(56.7×10−3 kg)(1.75 j^ m/s)=9.92×10−2 j^ kg⋅m/s

Substitute, 56.7×10−3 kg for m, and −1.75 j^ m/s for vf in equation (II).

(pi→)mot=(56.7×10−3 kg)(−1.75 j^ m/s)=−9.92×10−2 j^ kg⋅m/s

Therefore, the initial momentum is 9.92×10−2j^ kg⋅m/s_, and final momentum is −9.92×10−2j^ kg⋅m/s_.

(b)

Expert Solution

To determine

The initial and final momentum of ball according to father’s view.

Answer to Problem 4PQ

The initial momentum is (8.62×10−2i^+9.92×10−2j^) kg⋅m/s_, and final momentum is (8.62×10−2i^−9.92×10−2j^) kg⋅m/s_.

Explanation of Solution

Consider the figure showing the motion of ball on the basis of father’s point of view

Physics for Scientists and Engineers: Foundations and Connections, Chapter 10, Problem 4PQ , additional homework tip 2

The path of ball is now parabolic, horizontal velocity is same as those observed by mother, but vertical velocity is equal to the velocity of stroller.

Write the expression for initial momentum.

(pi→)dad=mvi→ (III)

Here, m is the mass of ball, and vi is the initial velocity observed by dad.

Write the expression for final momentum.

(pf→)dad=mvf→ (IV)

Here, m is the mass of ball, and vf is the final velocity observed by dad.

Conclusion:

Substitute, 56.7×10−3 kg for m, and (1.52i^+1.75 j^) m/s for vi in equation (III).

(pi→)dad=(56.7×10−3 kg)(1.52i^+1.75 j^) m/s=(8.62×10−2i^+9.92×10−2 j^) kg⋅m/s

Substitute, 56.7×10−3 kg for m, and (1.52i^−1.75 j^) m/s for vi in equation (IV).

(pi→)dad=(56.7×10−3 kg)(1.52i^−1.75 j^) m/s=(8.62×10−2i^−9.92×10−2 j^) kg⋅m/s

Therefore, the initial momentum is (8.62×10−2i^+9.92×10−2j^) kg⋅m/s_, and final momentum is (8.62×10−2i^−9.92×10−2j^) kg⋅m/s_.

(c)

Expert Solution

To determine

Whether the momentum of ball is zero ever according to mother.

Answer to Problem 4PQ

The momentum will be zero according to mother’s point of view.

Explanation of Solution

According to mother’s view the ball is in vertical motion. At maximum height the kinetic energy is completely converted to potential energy, and velocity of ball is zero, or ball is momentarily at rest.

Momentum is the product of mass and velocity, thus, if velocity is zero, momentum will be zero, at top of flight.

Conclusion:

Therefore, momentum will be zero, at maximum height according to mother’s view.

(d)

Expert Solution

To determine

Whether the momentum of ball is zero ever according to father.

Answer to Problem 4PQ

The momentum is never become zero according to father’s view.

Explanation of Solution

The motion is parabolic according to father’s view, and has two components of velocity, horizontal and vertical. Even though vertical component become zero, at any point, the horizontal component remains same until the ball covers entire parabolic path.

Hence momentum will not be equal to zero.

Conclusion:

The total velocity is the sum of horizontal and vertical velocity, since horizontal velocity remains same as a nonzero value, momentum is never become zero.

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Answer 2

Textbook Question

Chapter 10, Problem 4PQ

A mother pushes her son in a stroller at a constant speed of 1.52 m/s. The boy tosses a 56.7-g tennis ball straight up at 1.75 m/s and catches it. The boy’s father sits on a bench and watches.

a. According to the mother, what are the ball’s initial and final momenta?

b. According to the father, what are the ball’s initial and final momenta?

c. According to the mother, is the ball’s momentum ever zero? If so, when? If not, why not?

d. According to the father, is the ball’s momentum ever zero? If so, when? If not, why not?

(a)

Expert Solution

To determine

The initial and final momentum of ball according to mother’s view.

Answer to Problem 4PQ

The initial momentum is 9.92×10−2j^ kg⋅m/s_, and final momentum is −9.92×10−2j^ kg⋅m/s_.

Explanation of Solution

Consider the figure showing the motion of ball on the basis of mother’s point of view.

Physics for Scientists and Engineers: Foundations and Connections, Chapter 10, Problem 4PQ , additional homework tip 1

According to mother’s point of view, the ball moves vertically upwards and falls vertically downwards with same speed. But initial momentum is in positive y direction and final momentum is in negative y direction.

Write the expression for initial momentum.

(pi→)mot=mvi→ (I)

Here, m is the mass of ball, and vi is the initial velocity.

Write the expression for final momentum.

(pf→)mot=mvf→ (II)

Here, m is the mass of ball, and vf is the final velocity.

Conclusion:

Substitute, 56.7×10−3 kg for m, and 1.75 j^ m/s for vi in equation (I).

(pi→)mot=(56.7×10−3 kg)(1.75 j^ m/s)=9.92×10−2 j^ kg⋅m/s

Substitute, 56.7×10−3 kg for m, and −1.75 j^ m/s for vf in equation (II).

(pi→)mot=(56.7×10−3 kg)(−1.75 j^ m/s)=−9.92×10−2 j^ kg⋅m/s

Therefore, the initial momentum is 9.92×10−2j^ kg⋅m/s_, and final momentum is −9.92×10−2j^ kg⋅m/s_.

(b)

Expert Solution

To determine

The initial and final momentum of ball according to father’s view.

Answer to Problem 4PQ

The initial momentum is (8.62×10−2i^+9.92×10−2j^) kg⋅m/s_, and final momentum is (8.62×10−2i^−9.92×10−2j^) kg⋅m/s_.

Explanation of Solution

Consider the figure showing the motion of ball on the basis of father’s point of view

Physics for Scientists and Engineers: Foundations and Connections, Chapter 10, Problem 4PQ , additional homework tip 2

The path of ball is now parabolic, horizontal velocity is same as those observed by mother, but vertical velocity is equal to the velocity of stroller.

Write the expression for initial momentum.

(pi→)dad=mvi→ (III)

Here, m is the mass of ball, and vi is the initial velocity observed by dad.

Write the expression for final momentum.

(pf→)dad=mvf→ (IV)

Here, m is the mass of ball, and vf is the final velocity observed by dad.

Conclusion:

Substitute, 56.7×10−3 kg for m, and (1.52i^+1.75 j^) m/s for vi in equation (III).

(pi→)dad=(56.7×10−3 kg)(1.52i^+1.75 j^) m/s=(8.62×10−2i^+9.92×10−2 j^) kg⋅m/s

Substitute, 56.7×10−3 kg for m, and (1.52i^−1.75 j^) m/s for vi in equation (IV).

(pi→)dad=(56.7×10−3 kg)(1.52i^−1.75 j^) m/s=(8.62×10−2i^−9.92×10−2 j^) kg⋅m/s

Therefore, the initial momentum is (8.62×10−2i^+9.92×10−2j^) kg⋅m/s_, and final momentum is (8.62×10−2i^−9.92×10−2j^) kg⋅m/s_.

(c)

Expert Solution

To determine

Whether the momentum of ball is zero ever according to mother.

Answer to Problem 4PQ

The momentum will be zero according to mother’s point of view.

Explanation of Solution

According to mother’s view the ball is in vertical motion. At maximum height the kinetic energy is completely converted to potential energy, and velocity of ball is zero, or ball is momentarily at rest.

Momentum is the product of mass and velocity, thus, if velocity is zero, momentum will be zero, at top of flight.

Conclusion:

Therefore, momentum will be zero, at maximum height according to mother’s view.

(d)

Expert Solution

To determine

Whether the momentum of ball is zero ever according to father.

Answer to Problem 4PQ

The momentum is never become zero according to father’s view.

Explanation of Solution

The motion is parabolic according to father’s view, and has two components of velocity, horizontal and vertical. Even though vertical component become zero, at any point, the horizontal component remains same until the ball covers entire parabolic path.

Hence momentum will not be equal to zero.

Conclusion:

The total velocity is the sum of horizontal and vertical velocity, since horizontal velocity remains same as a nonzero value, momentum is never become zero.

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Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 3

Textbook Question

Chapter 10, Problem 4PQ

A mother pushes her son in a stroller at a constant speed of 1.52 m/s. The boy tosses a 56.7-g tennis ball straight up at 1.75 m/s and catches it. The boy’s father sits on a bench and watches.

a. According to the mother, what are the ball’s initial and final momenta?

b. According to the father, what are the ball’s initial and final momenta?

c. According to the mother, is the ball’s momentum ever zero? If so, when? If not, why not?

d. According to the father, is the ball’s momentum ever zero? If so, when? If not, why not?

(a)

Expert Solution

To determine

The initial and final momentum of ball according to mother’s view.

Answer to Problem 4PQ

The initial momentum is 9.92×10−2j^ kg⋅m/s_, and final momentum is −9.92×10−2j^ kg⋅m/s_.

Explanation of Solution

Consider the figure showing the motion of ball on the basis of mother’s point of view.

Physics for Scientists and Engineers: Foundations and Connections, Chapter 10, Problem 4PQ , additional homework tip 1

According to mother’s point of view, the ball moves vertically upwards and falls vertically downwards with same speed. But initial momentum is in positive y direction and final momentum is in negative y direction.

Write the expression for initial momentum.

(pi→)mot=mvi→ (I)

Here, m is the mass of ball, and vi is the initial velocity.

Write the expression for final momentum.

(pf→)mot=mvf→ (II)

Here, m is the mass of ball, and vf is the final velocity.

Conclusion:

Substitute, 56.7×10−3 kg for m, and 1.75 j^ m/s for vi in equation (I).

(pi→)mot=(56.7×10−3 kg)(1.75 j^ m/s)=9.92×10−2 j^ kg⋅m/s

Substitute, 56.7×10−3 kg for m, and −1.75 j^ m/s for vf in equation (II).

(pi→)mot=(56.7×10−3 kg)(−1.75 j^ m/s)=−9.92×10−2 j^ kg⋅m/s

Therefore, the initial momentum is 9.92×10−2j^ kg⋅m/s_, and final momentum is −9.92×10−2j^ kg⋅m/s_.

(b)

Expert Solution

To determine

The initial and final momentum of ball according to father’s view.

Answer to Problem 4PQ

The initial momentum is (8.62×10−2i^+9.92×10−2j^) kg⋅m/s_, and final momentum is (8.62×10−2i^−9.92×10−2j^) kg⋅m/s_.

Explanation of Solution

Consider the figure showing the motion of ball on the basis of father’s point of view

Physics for Scientists and Engineers: Foundations and Connections, Chapter 10, Problem 4PQ , additional homework tip 2

The path of ball is now parabolic, horizontal velocity is same as those observed by mother, but vertical velocity is equal to the velocity of stroller.

Write the expression for initial momentum.

(pi→)dad=mvi→ (III)

Here, m is the mass of ball, and vi is the initial velocity observed by dad.

Write the expression for final momentum.

(pf→)dad=mvf→ (IV)

Here, m is the mass of ball, and vf is the final velocity observed by dad.

Conclusion:

Substitute, 56.7×10−3 kg for m, and (1.52i^+1.75 j^) m/s for vi in equation (III).

(pi→)dad=(56.7×10−3 kg)(1.52i^+1.75 j^) m/s=(8.62×10−2i^+9.92×10−2 j^) kg⋅m/s

Substitute, 56.7×10−3 kg for m, and (1.52i^−1.75 j^) m/s for vi in equation (IV).

(pi→)dad=(56.7×10−3 kg)(1.52i^−1.75 j^) m/s=(8.62×10−2i^−9.92×10−2 j^) kg⋅m/s

Therefore, the initial momentum is (8.62×10−2i^+9.92×10−2j^) kg⋅m/s_, and final momentum is (8.62×10−2i^−9.92×10−2j^) kg⋅m/s_.

(c)

Expert Solution

To determine

Whether the momentum of ball is zero ever according to mother.

Answer to Problem 4PQ

The momentum will be zero according to mother’s point of view.

Explanation of Solution

According to mother’s view the ball is in vertical motion. At maximum height the kinetic energy is completely converted to potential energy, and velocity of ball is zero, or ball is momentarily at rest.

Momentum is the product of mass and velocity, thus, if velocity is zero, momentum will be zero, at top of flight.

Conclusion:

Therefore, momentum will be zero, at maximum height according to mother’s view.

(d)

Expert Solution

To determine

Whether the momentum of ball is zero ever according to father.

Answer to Problem 4PQ

The momentum is never become zero according to father’s view.

Explanation of Solution

The motion is parabolic according to father’s view, and has two components of velocity, horizontal and vertical. Even though vertical component become zero, at any point, the horizontal component remains same until the ball covers entire parabolic path.

Hence momentum will not be equal to zero.

Conclusion:

The total velocity is the sum of horizontal and vertical velocity, since horizontal velocity remains same as a nonzero value, momentum is never become zero.

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Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 4

Textbook Question

Chapter 10, Problem 4PQ

A mother pushes her son in a stroller at a constant speed of 1.52 m/s. The boy tosses a 56.7-g tennis ball straight up at 1.75 m/s and catches it. The boy’s father sits on a bench and watches.

a. According to the mother, what are the ball’s initial and final momenta?

b. According to the father, what are the ball’s initial and final momenta?

c. According to the mother, is the ball’s momentum ever zero? If so, when? If not, why not?

d. According to the father, is the ball’s momentum ever zero? If so, when? If not, why not?

(a)

Expert Solution

To determine

The initial and final momentum of ball according to mother’s view.

Answer to Problem 4PQ

The initial momentum is 9.92×10−2j^ kg⋅m/s_, and final momentum is −9.92×10−2j^ kg⋅m/s_.

Explanation of Solution

Consider the figure showing the motion of ball on the basis of mother’s point of view.

Physics for Scientists and Engineers: Foundations and Connections, Chapter 10, Problem 4PQ , additional homework tip 1

According to mother’s point of view, the ball moves vertically upwards and falls vertically downwards with same speed. But initial momentum is in positive y direction and final momentum is in negative y direction.

Write the expression for initial momentum.

(pi→)mot=mvi→ (I)

Here, m is the mass of ball, and vi is the initial velocity.

Write the expression for final momentum.

(pf→)mot=mvf→ (II)

Here, m is the mass of ball, and vf is the final velocity.

Conclusion:

Substitute, 56.7×10−3 kg for m, and 1.75 j^ m/s for vi in equation (I).

(pi→)mot=(56.7×10−3 kg)(1.75 j^ m/s)=9.92×10−2 j^ kg⋅m/s

Substitute, 56.7×10−3 kg for m, and −1.75 j^ m/s for vf in equation (II).

(pi→)mot=(56.7×10−3 kg)(−1.75 j^ m/s)=−9.92×10−2 j^ kg⋅m/s

Therefore, the initial momentum is 9.92×10−2j^ kg⋅m/s_, and final momentum is −9.92×10−2j^ kg⋅m/s_.

(b)

Expert Solution

To determine

The initial and final momentum of ball according to father’s view.

Answer to Problem 4PQ

The initial momentum is (8.62×10−2i^+9.92×10−2j^) kg⋅m/s_, and final momentum is (8.62×10−2i^−9.92×10−2j^) kg⋅m/s_.

Explanation of Solution

Consider the figure showing the motion of ball on the basis of father’s point of view

Physics for Scientists and Engineers: Foundations and Connections, Chapter 10, Problem 4PQ , additional homework tip 2

The path of ball is now parabolic, horizontal velocity is same as those observed by mother, but vertical velocity is equal to the velocity of stroller.

Write the expression for initial momentum.

(pi→)dad=mvi→ (III)

Here, m is the mass of ball, and vi is the initial velocity observed by dad.

Write the expression for final momentum.

(pf→)dad=mvf→ (IV)

Here, m is the mass of ball, and vf is the final velocity observed by dad.

Conclusion:

Substitute, 56.7×10−3 kg for m, and (1.52i^+1.75 j^) m/s for vi in equation (III).

(pi→)dad=(56.7×10−3 kg)(1.52i^+1.75 j^) m/s=(8.62×10−2i^+9.92×10−2 j^) kg⋅m/s

Substitute, 56.7×10−3 kg for m, and (1.52i^−1.75 j^) m/s for vi in equation (IV).

(pi→)dad=(56.7×10−3 kg)(1.52i^−1.75 j^) m/s=(8.62×10−2i^−9.92×10−2 j^) kg⋅m/s

Therefore, the initial momentum is (8.62×10−2i^+9.92×10−2j^) kg⋅m/s_, and final momentum is (8.62×10−2i^−9.92×10−2j^) kg⋅m/s_.

(c)

Expert Solution

To determine

Whether the momentum of ball is zero ever according to mother.

Answer to Problem 4PQ

The momentum will be zero according to mother’s point of view.

Explanation of Solution

According to mother’s view the ball is in vertical motion. At maximum height the kinetic energy is completely converted to potential energy, and velocity of ball is zero, or ball is momentarily at rest.

Momentum is the product of mass and velocity, thus, if velocity is zero, momentum will be zero, at top of flight.

Conclusion:

Therefore, momentum will be zero, at maximum height according to mother’s view.

(d)

Expert Solution

To determine

Whether the momentum of ball is zero ever according to father.

Answer to Problem 4PQ

The momentum is never become zero according to father’s view.

Explanation of Solution

The motion is parabolic according to father’s view, and has two components of velocity, horizontal and vertical. Even though vertical component become zero, at any point, the horizontal component remains same until the ball covers entire parabolic path.

Hence momentum will not be equal to zero.

Conclusion:

The total velocity is the sum of horizontal and vertical velocity, since horizontal velocity remains same as a nonzero value, momentum is never become zero.

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Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 5

Textbook Question

Answer 6

Textbook Question

Answer 7

(a)

Expert Solution

To determine

The initial and final momentum of ball according to mother’s view.

Answer to Problem 4PQ

The initial momentum is 9.92×10−2j^ kg⋅m/s_, and final momentum is −9.92×10−2j^ kg⋅m/s_.

Explanation of Solution

Consider the figure showing the motion of ball on the basis of mother’s point of view.

Physics for Scientists and Engineers: Foundations and Connections, Chapter 10, Problem 4PQ , additional homework tip 1

According to mother’s point of view, the ball moves vertically upwards and falls vertically downwards with same speed. But initial momentum is in positive y direction and final momentum is in negative y direction.

Write the expression for initial momentum.

(pi→)mot=mvi→ (I)

Here, m is the mass of ball, and vi is the initial velocity.

Write the expression for final momentum.

(pf→)mot=mvf→ (II)

Here, m is the mass of ball, and vf is the final velocity.

Conclusion:

Substitute, 56.7×10−3 kg for m, and 1.75 j^ m/s for vi in equation (I).

(pi→)mot=(56.7×10−3 kg)(1.75 j^ m/s)=9.92×10−2 j^ kg⋅m/s

Substitute, 56.7×10−3 kg for m, and −1.75 j^ m/s for vf in equation (II).

(pi→)mot=(56.7×10−3 kg)(−1.75 j^ m/s)=−9.92×10−2 j^ kg⋅m/s

Therefore, the initial momentum is 9.92×10−2j^ kg⋅m/s_, and final momentum is −9.92×10−2j^ kg⋅m/s_.

(b)

Expert Solution

To determine

The initial and final momentum of ball according to father’s view.

Answer to Problem 4PQ

The initial momentum is (8.62×10−2i^+9.92×10−2j^) kg⋅m/s_, and final momentum is (8.62×10−2i^−9.92×10−2j^) kg⋅m/s_.

Explanation of Solution

Consider the figure showing the motion of ball on the basis of father’s point of view

Physics for Scientists and Engineers: Foundations and Connections, Chapter 10, Problem 4PQ , additional homework tip 2

The path of ball is now parabolic, horizontal velocity is same as those observed by mother, but vertical velocity is equal to the velocity of stroller.

Write the expression for initial momentum.

(pi→)dad=mvi→ (III)

Here, m is the mass of ball, and vi is the initial velocity observed by dad.

Write the expression for final momentum.

(pf→)dad=mvf→ (IV)

Here, m is the mass of ball, and vf is the final velocity observed by dad.

Conclusion:

Substitute, 56.7×10−3 kg for m, and (1.52i^+1.75 j^) m/s for vi in equation (III).

(pi→)dad=(56.7×10−3 kg)(1.52i^+1.75 j^) m/s=(8.62×10−2i^+9.92×10−2 j^) kg⋅m/s

Substitute, 56.7×10−3 kg for m, and (1.52i^−1.75 j^) m/s for vi in equation (IV).

(pi→)dad=(56.7×10−3 kg)(1.52i^−1.75 j^) m/s=(8.62×10−2i^−9.92×10−2 j^) kg⋅m/s

Therefore, the initial momentum is (8.62×10−2i^+9.92×10−2j^) kg⋅m/s_, and final momentum is (8.62×10−2i^−9.92×10−2j^) kg⋅m/s_.

(c)

Expert Solution

To determine

Whether the momentum of ball is zero ever according to mother.

Answer to Problem 4PQ

The momentum will be zero according to mother’s point of view.

Explanation of Solution

According to mother’s view the ball is in vertical motion. At maximum height the kinetic energy is completely converted to potential energy, and velocity of ball is zero, or ball is momentarily at rest.

Momentum is the product of mass and velocity, thus, if velocity is zero, momentum will be zero, at top of flight.

Conclusion:

Therefore, momentum will be zero, at maximum height according to mother’s view.

(d)

Expert Solution

To determine

Whether the momentum of ball is zero ever according to father.

Answer to Problem 4PQ

The momentum is never become zero according to father’s view.

Explanation of Solution

The motion is parabolic according to father’s view, and has two components of velocity, horizontal and vertical. Even though vertical component become zero, at any point, the horizontal component remains same until the ball covers entire parabolic path.

Hence momentum will not be equal to zero.

Conclusion:

The total velocity is the sum of horizontal and vertical velocity, since horizontal velocity remains same as a nonzero value, momentum is never become zero.

Answer 8

(a)

Expert Solution

To determine

The initial and final momentum of ball according to mother’s view.

Answer to Problem 4PQ

The initial momentum is 9.92×10−2j^ kg⋅m/s_, and final momentum is −9.92×10−2j^ kg⋅m/s_.

Explanation of Solution

Consider the figure showing the motion of ball on the basis of mother’s point of view.

Physics for Scientists and Engineers: Foundations and Connections, Chapter 10, Problem 4PQ , additional homework tip 1

According to mother’s point of view, the ball moves vertically upwards and falls vertically downwards with same speed. But initial momentum is in positive y direction and final momentum is in negative y direction.

Write the expression for initial momentum.

(pi→)mot=mvi→ (I)

Here, m is the mass of ball, and vi is the initial velocity.

Write the expression for final momentum.

(pf→)mot=mvf→ (II)

Here, m is the mass of ball, and vf is the final velocity.

Conclusion:

Substitute, 56.7×10−3 kg for m, and 1.75 j^ m/s for vi in equation (I).

(pi→)mot=(56.7×10−3 kg)(1.75 j^ m/s)=9.92×10−2 j^ kg⋅m/s

Substitute, 56.7×10−3 kg for m, and −1.75 j^ m/s for vf in equation (II).

(pi→)mot=(56.7×10−3 kg)(−1.75 j^ m/s)=−9.92×10−2 j^ kg⋅m/s

Therefore, the initial momentum is 9.92×10−2j^ kg⋅m/s_, and final momentum is −9.92×10−2j^ kg⋅m/s_.

Answer 9

(a)

Expert Solution

Answer 10

(a)

Expert Solution

Answer 11

Expert Solution

Answer 12

To determine

The initial and final momentum of ball according to mother’s view.

Answer 13

Answer to Problem 4PQ

The initial momentum is 9.92×10−2j^ kg⋅m/s_, and final momentum is −9.92×10−2j^ kg⋅m/s_.

Answer 14

Explanation of Solution

Consider the figure showing the motion of ball on the basis of mother’s point of view.

Physics for Scientists and Engineers: Foundations and Connections, Chapter 10, Problem 4PQ , additional homework tip 1

According to mother’s point of view, the ball moves vertically upwards and falls vertically downwards with same speed. But initial momentum is in positive y direction and final momentum is in negative y direction.

Write the expression for initial momentum.

(pi→)mot=mvi→ (I)

Here, m is the mass of ball, and vi is the initial velocity.

Write the expression for final momentum.

(pf→)mot=mvf→ (II)

Here, m is the mass of ball, and vf is the final velocity.

Conclusion:

Substitute, 56.7×10−3 kg for m, and 1.75 j^ m/s for vi in equation (I).

(pi→)mot=(56.7×10−3 kg)(1.75 j^ m/s)=9.92×10−2 j^ kg⋅m/s

Substitute, 56.7×10−3 kg for m, and −1.75 j^ m/s for vf in equation (II).

(pi→)mot=(56.7×10−3 kg)(−1.75 j^ m/s)=−9.92×10−2 j^ kg⋅m/s

Therefore, the initial momentum is 9.92×10−2j^ kg⋅m/s_, and final momentum is −9.92×10−2j^ kg⋅m/s_.

Answer 15

(b)

Expert Solution

To determine

The initial and final momentum of ball according to father’s view.

Answer to Problem 4PQ

The initial momentum is (8.62×10−2i^+9.92×10−2j^) kg⋅m/s_, and final momentum is (8.62×10−2i^−9.92×10−2j^) kg⋅m/s_.

Explanation of Solution

Consider the figure showing the motion of ball on the basis of father’s point of view

Physics for Scientists and Engineers: Foundations and Connections, Chapter 10, Problem 4PQ , additional homework tip 2

The path of ball is now parabolic, horizontal velocity is same as those observed by mother, but vertical velocity is equal to the velocity of stroller.

Write the expression for initial momentum.

(pi→)dad=mvi→ (III)

Here, m is the mass of ball, and vi is the initial velocity observed by dad.

Write the expression for final momentum.

(pf→)dad=mvf→ (IV)

Here, m is the mass of ball, and vf is the final velocity observed by dad.

Conclusion:

Substitute, 56.7×10−3 kg for m, and (1.52i^+1.75 j^) m/s for vi in equation (III).

(pi→)dad=(56.7×10−3 kg)(1.52i^+1.75 j^) m/s=(8.62×10−2i^+9.92×10−2 j^) kg⋅m/s

Substitute, 56.7×10−3 kg for m, and (1.52i^−1.75 j^) m/s for vi in equation (IV).

(pi→)dad=(56.7×10−3 kg)(1.52i^−1.75 j^) m/s=(8.62×10−2i^−9.92×10−2 j^) kg⋅m/s

Therefore, the initial momentum is (8.62×10−2i^+9.92×10−2j^) kg⋅m/s_, and final momentum is (8.62×10−2i^−9.92×10−2j^) kg⋅m/s_.

Answer 16

(b)

Expert Solution

Answer 17

(b)

Expert Solution

Answer 18

Expert Solution

Answer 19

To determine

The initial and final momentum of ball according to father’s view.

Answer 20

Answer to Problem 4PQ

The initial momentum is (8.62×10−2i^+9.92×10−2j^) kg⋅m/s_, and final momentum is (8.62×10−2i^−9.92×10−2j^) kg⋅m/s_.

Answer 21

Explanation of Solution

Consider the figure showing the motion of ball on the basis of father’s point of view

Physics for Scientists and Engineers: Foundations and Connections, Chapter 10, Problem 4PQ , additional homework tip 2

The path of ball is now parabolic, horizontal velocity is same as those observed by mother, but vertical velocity is equal to the velocity of stroller.

Write the expression for initial momentum.

(pi→)dad=mvi→ (III)

Here, m is the mass of ball, and vi is the initial velocity observed by dad.

Write the expression for final momentum.

(pf→)dad=mvf→ (IV)

Here, m is the mass of ball, and vf is the final velocity observed by dad.

Conclusion:

Substitute, 56.7×10−3 kg for m, and (1.52i^+1.75 j^) m/s for vi in equation (III).

(pi→)dad=(56.7×10−3 kg)(1.52i^+1.75 j^) m/s=(8.62×10−2i^+9.92×10−2 j^) kg⋅m/s

Substitute, 56.7×10−3 kg for m, and (1.52i^−1.75 j^) m/s for vi in equation (IV).

(pi→)dad=(56.7×10−3 kg)(1.52i^−1.75 j^) m/s=(8.62×10−2i^−9.92×10−2 j^) kg⋅m/s

Therefore, the initial momentum is (8.62×10−2i^+9.92×10−2j^) kg⋅m/s_, and final momentum is (8.62×10−2i^−9.92×10−2j^) kg⋅m/s_.

Answer 22

(c)

Expert Solution

To determine

Whether the momentum of ball is zero ever according to mother.

Answer to Problem 4PQ

The momentum will be zero according to mother’s point of view.

Explanation of Solution

According to mother’s view the ball is in vertical motion. At maximum height the kinetic energy is completely converted to potential energy, and velocity of ball is zero, or ball is momentarily at rest.

Momentum is the product of mass and velocity, thus, if velocity is zero, momentum will be zero, at top of flight.

Conclusion:

Therefore, momentum will be zero, at maximum height according to mother’s view.

Answer 23

(c)

Expert Solution

Answer 24

(c)

Expert Solution

Answer 25

Expert Solution

Answer 26

To determine

Whether the momentum of ball is zero ever according to mother.

Answer 27

Answer to Problem 4PQ

The momentum will be zero according to mother’s point of view.

Answer 28

Explanation of Solution

According to mother’s view the ball is in vertical motion. At maximum height the kinetic energy is completely converted to potential energy, and velocity of ball is zero, or ball is momentarily at rest.

Momentum is the product of mass and velocity, thus, if velocity is zero, momentum will be zero, at top of flight.

Conclusion:

Therefore, momentum will be zero, at maximum height according to mother’s view.

Answer 29

(d)

Expert Solution

To determine

Whether the momentum of ball is zero ever according to father.

Answer to Problem 4PQ

The momentum is never become zero according to father’s view.

Explanation of Solution

The motion is parabolic according to father’s view, and has two components of velocity, horizontal and vertical. Even though vertical component become zero, at any point, the horizontal component remains same until the ball covers entire parabolic path.

Hence momentum will not be equal to zero.

Conclusion:

The total velocity is the sum of horizontal and vertical velocity, since horizontal velocity remains same as a nonzero value, momentum is never become zero.

Answer 30

(d)

Expert Solution

Answer 31

(d)

Expert Solution

Answer 32

Expert Solution

Answer 33

To determine

Whether the momentum of ball is zero ever according to father.

Answer 34

Answer to Problem 4PQ

The momentum is never become zero according to father’s view.

Answer 35

Explanation of Solution

The motion is parabolic according to father’s view, and has two components of velocity, horizontal and vertical. Even though vertical component become zero, at any point, the horizontal component remains same until the ball covers entire parabolic path.

Hence momentum will not be equal to zero.

Conclusion:

The total velocity is the sum of horizontal and vertical velocity, since horizontal velocity remains same as a nonzero value, momentum is never become zero.