Physics
Physics
5th Edition
ISBN: 9781260486919
Author: GIAMBATTISTA
Publisher: MCG
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Chapter 4, Problem 167P
To determine

The horizontal distance before the driveway at which J should drop the paper.

Expert Solution & Answer
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Answer to Problem 167P

The horizontal distance before the driveway at which J should drop the paper is 36 m .

Explanation of Solution

Write the equation to find the time taken for the newspaper to hit the ground.

Δy=vt+12gt2

Here, Δy is the height from which the newspaper is dropped, v is the initial velocity of the paper, g is the acceleration due to gravity and t is the time taken for the newspaper to hit the ground

The initial velocity of the newspaper is zero.

Substitute 0 for v in the above equation and rewrite the equation for t .

Δy=0+12gt2=12gt2t=2Δyg (I)

Write the equation for the horizontal distance travelled by the newspaper as it travels through the air.

Δx1=vit (II)

Here, Δx1 is the horizontal distance travelled by the newspaper as it travels through the air and vi is the speed of the newspaper

Write the Newton’s second law.

ΣFx=ma (III)

Here, ΣFx is the net force in x direction, m is the mass of the object and a is the acceleration of the object

Write the equation for the net force in x direction.

ΣFx=fk (IV)

Here, fk is the force of kinetic friction

Write the equation for force of kinetic friction.

fk=μkmg

Here, μk is the coefficient of kinetic friction and g is the acceleration due to gravity

Put the above equation in equation (IV).

ΣFx=μkmg (V)

Equate equations (III) and (V).

ma=μkmga=μkg (VI)

Write the equation of motion to find the horizontal distance travelled by the newspaper after it hits the ground.

vf2vi2=2aΔx2

Here, vf is the final velocity of the newspaper and Δx2 is the horizontal distance travelled by the newspaper after it hits the ground

Put equation (VI) in the above equation.

vf2vi2=2μkgΔx2

The final speed of the newspaper is zero.

Substitute 0 for vf in the above equation and rewrite it for Δx2 .

0vi2=2μkgΔx2vi2=2μkgΔx2Δx2=vi22μkg (VII)

Write the equation for the horizontal distance before the driveway at which J should drop the paper.

d=Δx1+Δx2 (VIII)

Here, d is the horizontal distance before the driveway at which J should drop the paper

Conclusion:

Given that the speed of the vehicle is 15 m/s , the height of the window is 1.00 m and the coefficient of kinetic friction is 0.40 . The value of acceleration due to gravity is 9.8 m/s2 .

Substitute 1.00 m for Δy and 9.8 m/s2 for g in equation (I) to find t .

t=2(1.00 m)9.8 m/s2=0.45 s

Substitute 15 m/s for vi and 0.45 s for t in equation (II) to find Δx1 .

Δx1=(15 m/s)(0.45 s)=6.8 m

Substitute 15 m/s for vi , 0.40 for μk and 9.8 m/s2 for g in equation (VII) to find Δx2 .

Δx2=(15 m/s)22(0.40)(9.8 m/s2)=29 m

Substitute 6.8 m for Δx1 and 29 m for Δx2 in equation (VIII) to find d .

d=6.8 m+29 m=35.8 m36 m

Therefore, the horizontal distance before the driveway at which J should drop the paper is 36 m .

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Chapter 4 Solutions

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