EBK COLLEGE PHYSICS
EBK COLLEGE PHYSICS
10th Edition
ISBN: 8220100853050
Author: Vuille
Publisher: CENGAGE L
bartleby

Concept explainers

bartleby

Videos

Textbook Question
Book Icon
Chapter 2, Problem 66AP

Two students air on a balcony a distance h above the street. One student throws a ball vertically down-ward at a speed v0; at the same time, the other student throws a ball vertically upward at the same speed. Answer the following symbolically in terms of v0, g, h, and t. (a) Write the kinematic equation for the y-coordinate of each ball, (b) Set the equations found in part (a) equal to height 0 and solve each for t symbolically using the quadratic formula. What is the difference in the two balls' time in the air? (c) Use the time-independent kinematics equation to find the velocity of each ball as it strikes the ground, (d) How far apart are the balls at a time t after they are released and before the strike the ground?

(a)

Expert Solution
Check Mark
To determine
The kinematic equation of ball thrown downwards.

Answer to Problem 66AP

Solution: The equation is y1=hv0t12gt2 .

Explanation of Solution

Given Info: Initial velocity of ball is v0 .

The displacement and velocity in downward direction is negative and in upward direction is taken as positive. The acceleration due to gravity is acting vertically downwards in both upward and downward motion.

Write the formula to calculate the displacement of ball thrown vertically downwards from the balcony.

y0h=v0t+12(g)t2

  • y1 is the displacement of the ball thrown vertically downwards
  • h is the distance of balcony from the street
  • v0 is the initial velocity of ball
  • g is the acceleration due to gravity
  • t is the time duration for displacement y0

Rearrange the above equation.

y1=hv0t12gt2 (I)

The displacement and velocity in downward direction is negative and in upward direction is taken as positive. The acceleration due to gravity is acting vertically downwards in both upward and downward motion.

Write the formula to calculate the displacement of ball thrown vertically upwards from the balcony.

y2h=v0t+12(g)t2

  • y2 is the displacement of the ball thrown vertically upwards

Rearrange the above equation.

y2=h+v0t12gt2 (II)

Thus, the kinematic equation for ball thrown vertically upwards will be

y2=h+v0t12gt2 .

Conclusion:

Thus, equation for ball thrown in vertically downward and upward directions are y1=hv0t12gt2 and y2=h+v0t12gt2 respectively.

(b)

Expert Solution
Check Mark
To determine
Solve the quadratic equations by setting height equals zero and calculate the time difference of two balls in air.

Answer to Problem 66AP

Solution: the solutions of quadratic equations and the time difference between the balls in air are, t1=v0g+(v0g)2+2hg , t2=v0g+(v0g)2+2hg .and 2v0g respectively

Explanation of Solution

Given Info: Initial velocity of ball is v0 .

Let t1 be the duration of the ball 1 in air.

Write the formula to calculate the displacement of ball thrown vertically downwards from the balcony.

y1=hv0t112gt12

Substitute 0 for y1 in the above equation to find t1 .

0=hv0t112gt12

Multiply each term by 2 and rearrange the above equation in the standard form of a quadratic equation.

gt12+2v0t1+(2h)=0

The solution of above equation can be found using quadratic formula.

t1=2v0±(2v0)24g(2h)2g=v0g±(v0g)2+2hg

Consider only the positive solution of t1 .

t1=v0g+(v0g)2+2hg (III)

Let t2 be the duration of the ball 2 in air.

Write the formula to calculate the displacement of ball thrown vertically upwards from the balcony.

y2=h+v0t112gt12

Substitute 0 for y2 y1 in the above equation to find t2 .

0=h+v0t112gt12

Multiply each term by 2 and rearrange the above equation in the standard form of a quadratic equation.

gt22+(2v0t2)+(2h)=0

The solution of above equation can be found using quadratic formula.

t2=(2v0)±(2v0)24g(2h)2g=v0g±(v0g)2+2hg

Consider only the positive solution of t2 .

t2=v0g+(v0g)2+2hg (IV)

Thus, the value of t2 is v0g+(v0g)2+2hg .

Conclusion:

Write the time difference of two balls in air.

Δt=t2t1

  • Δt is the time difference between two balls in air

Substitute equation (IV) for t2 and equation (III) for t1 in the above equation to find Δt .

Δt=v0g+(v0g)2+2hg(v0g+(v0g)2+2hg)=v0g+v0g+(v0g)2+2hg(v0g)2+2hg=2v0g

Thus, the time difference between the balls in air 2v0g respectively.

(c)

Expert Solution
Check Mark
To determine
The final velocity of balls on touching the ground.

Answer to Problem 66AP

Solution: The velocity of two balls on touching the ground will be v02+2gh .

Explanation of Solution

Given Info: Initial velocity of ball is v0 .

The displacement and velocity in downward direction is negative and in upward direction is taken as positive. The acceleration due to gravity is acting vertically downwards in both upward and downward motion.

Write the formula to calculate the final velocity.

vf1=v02+2(g)(h)

  • vf1 is the final velocity of ball thrown vertically downwards

Rewrite the above equation as follows.

vf1=v02+2gh

The displacement and velocity in downward direction is negative and in upward direction is taken as positive. The acceleration due to gravity is acting vertically downwards in both upward and downward motion.

Write the formula to calculate the velocity of ball thrown upwards on touching the ground.

vf2=v02+2(g)(h)

  • vf2 is the velocity of ball thrown vertically upwards at the moment of touching the ground.

Rewrite the above equation as follows.

vf2=v02+2gh

Conclusion: Thus, the final velocities of two balls are same and the value is v02+2gh .

(d)

Expert Solution
Check Mark
To determine
The separation between balls at time t .

Answer to Problem 66AP

Solution: The separation between balls at time t will be 2v0t .

Explanation of Solution

Given Info: Initial velocity of ball is v0 .

Write the formula to calculate the separation between the balls.

Δy=y2y1

  • Δy is the separation between balls at time t

Substitute equation (II) for y2 and equation (I) for y1 in the above equation.

Δy=(h+v0t212gt22)(hv0t112gt12)=v0(t2+t1)

Substitute t for t1 and t2 in the above equation to find Δy .

Δy=v0(t+t)=2v0t

Conclusion:

Thus, the separation between balls at time t will be 2v0t

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!
Students have asked these similar questions
No chatgpt pls will upvote
No chatgpt pls will upvote
No chatgpt pls will upvote

Chapter 2 Solutions

EBK COLLEGE PHYSICS

Ch. 2 - Math Review Solve the following two equations for...Ch. 2 - A football player runs from his own goal line to...Ch. 2 - A ball is thrown downward from the top of a 40.0 m...Ch. 2 - An arrow is shot straight up in the air at an...Ch. 2 - A red ball is dropped from rest at a height of...Ch. 2 - If the velocity of a particle is nonzero, can the...Ch. 2 - If the velocity of a particle is zero, can the...Ch. 2 - If a car is traveling eastward, can its...Ch. 2 - (a) Can the equations in Table 2.4 be used in a...Ch. 2 - Two cars are moving in the same direction in...Ch. 2 - Figure CQ2.6 shows strobe photographs taken of a...Ch. 2 - (a) Can the instantaneous velocity of an object at...Ch. 2 - A ball is thrown vertically upward. (a) What are...Ch. 2 - Consider the following combinations of signs and...Ch. 2 - A ball rolls in a straight line along the...Ch. 2 - An object moves along the x-axis, its position...Ch. 2 - A ball is thrown straight up in the air. For which...Ch. 2 - A juggler throws a bowling pin straight up in the...Ch. 2 - A racing car starts from rest and reaches a final...Ch. 2 - The speed of a nerve impulse in the human body is...Ch. 2 - Light travels at a speed of about 3 103 m/s. (a)...Ch. 2 - A person travels by car from one city to another...Ch. 2 - The current indoor world record time in the 200-m...Ch. 2 - Two boats start together and race across a...Ch. 2 - A graph of position versus time for a certain...Ch. 2 - A motorist drives for 35.0 minutes at 85.0 km/h...Ch. 2 - A tennis player moves in a straight-line path as...Ch. 2 - A jet plane has a takeoff speed of v0 = 75 m/s and...Ch. 2 - Two cars travel in the same direction along a...Ch. 2 - The cheetah can reach a top speed of 114 km/h (71...Ch. 2 - An athlete swims the length L of a pool in a time...Ch. 2 - A person lakes a trip, driving with a constant...Ch. 2 - A tortoise can run with a speed of 0.10 m/s, and a...Ch. 2 - To qualify for the finals in a racing event, a...Ch. 2 - Prob. 16PCh. 2 - A graph of position versus time for a certain...Ch. 2 - A race car moves such that, its position fits the...Ch. 2 - Runner A is initially 4.0 mi west of a flagpole...Ch. 2 - A particle starts from rest and accelerates as...Ch. 2 - A 50.0-g Super Ball traveling at 25.0 m/s bounces...Ch. 2 - The average person passes out at an acceleration...Ch. 2 - A certain car is capable of accelerating at a rate...Ch. 2 - The velocity vs. time graph for an object moving...Ch. 2 - A steam catapult launches a jet aircraft from the...Ch. 2 - PROBLEM A race car starting from rest accelerates...Ch. 2 - An object moving with uniform acceleration has a...Ch. 2 - In 1865 Jules Verne proposed sending men to the...Ch. 2 - A truck covers 40.0 m in 8.50 s while uniformly...Ch. 2 - A speedboat increases its speed uniformly from vi...Ch. 2 - A Cessna aircraft has a liftoff speed of 120....Ch. 2 - An object moves with constant acceleration 4.00...Ch. 2 - In a test run, a certain car accelerates uniformly...Ch. 2 - A jet plane lands with a speed of 100 m/s and can...Ch. 2 - Speedy Sue, driving at 30.0 m/s, enters a one-lane...Ch. 2 - A record of travel along a straight path is as...Ch. 2 - A train is traveling down a straight track at 20...Ch. 2 - A car accelerates uniformly from rest to a speed...Ch. 2 - A car starts from rest and travels for 5.0 s with...Ch. 2 - A car starts from rest and travels for t1 seconds...Ch. 2 - In the Daytona 500 auto race, a Ford Thunderbird...Ch. 2 - A certain cable car in San Francisco can stop in...Ch. 2 - A hockey player is standing on his skates on a...Ch. 2 - A train 4.00 102 m long is moving on a straight...Ch. 2 - A ball is thrown vertically upward with a speed of...Ch. 2 - A ball is thrown directly downward with an initial...Ch. 2 - A certain freely falling object, released from...Ch. 2 - An attacker at the base of a castle wall 3.65 m...Ch. 2 - Traumatic brain injury such as concussion results...Ch. 2 - A small mailbag is released from a helicopter that...Ch. 2 - A tennis player tosses a tennis ball straight up...Ch. 2 - A package is dropped from a helicopter that is...Ch. 2 - A model rocket is launched straight upward with an...Ch. 2 - A baseball is hit so that it travels straight...Ch. 2 - A truck tractor pulls two trailers, one behind the...Ch. 2 - Colonel John P. Stapp, USAF, participated in...Ch. 2 - A bullet is fired through a board 10.0 cm thick in...Ch. 2 - A speedboat moving at 30.0 m/s approaches a...Ch. 2 - A student throws a set of keys vertically upward...Ch. 2 - A student throws a set of keys vertically upward...Ch. 2 - An insect called the froghopper (Philaenus...Ch. 2 - Prob. 62APCh. 2 - A ball is thrown upward from the ground with an...Ch. 2 - To pass a physical education class at a...Ch. 2 - In Chapter 5 we will define the center of mass of...Ch. 2 - Two students air on a balcony a distance h above...Ch. 2 - You drop a ball from a window on an upper floor of...Ch. 2 - The driver of a truck slams on the brakes when he...Ch. 2 - Emily challenges her husband, David, to catch a 1...Ch. 2 - A mountain climber stands at the top of a 50.0-m...Ch. 2 - An ice sled powered by a rocket engine sum from...Ch. 2 - In Bosnia, the ultimate test of a young nuns...Ch. 2 - Prob. 73APCh. 2 - A glider on an air track carries a flag of length ...Ch. 2 - A stuntman sitting on a tree limb wishes to drop...
Knowledge Booster
Background pattern image
Physics
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.
Similar questions
SEE MORE QUESTIONS
Recommended textbooks for you
Text book image
Principles of Physics: A Calculus-Based Text
Physics
ISBN:9781133104261
Author:Raymond A. Serway, John W. Jewett
Publisher:Cengage Learning
Kinematics Part 3: Projectile Motion; Author: Professor Dave explains;https://www.youtube.com/watch?v=aY8z2qO44WA;License: Standard YouTube License, CC-BY