Schaum's Outline of College Physics, Twelfth Edition (Schaum's Outlines)
Schaum's Outline of College Physics, Twelfth Edition (Schaum's Outlines)
12th Edition
ISBN: 9781259587399
Author: Eugene Hecht
Publisher: McGraw-Hill Education
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Chapter 2, Problem 39SP

A baseball is thrown straight upward with a speed of 30 m/s. (a) How long will it

rise? (b) How high will it rise? (c) How long after it leaves the hand will it return to

the starting point? (d) When will its speed be 16 m/s?

(a)

Expert Solution
Check Mark
To determine

The time for which the baseball will rise when it is thrown upward with the velocity of 30 m/s.

Answer to Problem 39SP

Solution:

3.1 s

Explanation of Solution

Given data:

The initial velocity of the baseball is 30 m/s, and it is thrown upward.

Formula used:

The time taken by object to reach the peak altitude is written as (since at peak final velocity becomes 0),

tp=vig

Here, vi is the initial velocity and g is the gravitational acceleration.

Sign convention:Upward and rightward directions are considered as positive, and downward and leftward directions are considered as negative.

Explanation:

Understand that if a motion is under gravity, then the acceleration acting on the body is equal to the acceleration due to gravity. The value of the acceleration due to gravity is 9.8 m/s2.

Recall the expression for the time taken by the object to reach the peak altitude.

tp=vig

Substitute 30 m/s for vi and 9.81 m/s2 for g.

tp=30 m/s9.81 m/s2=3.1 s

The baseball will rise till to its peak altitude. So, the time for this will be equals to the peak time.

Conclusion:

Hence, the time for which the baseball will rise is 3.1 s.

(b)

Expert Solution
Check Mark
To determine

The height for which the baseball will rise if it is thrown upwards with the velocity of 30 m/s.

Answer to Problem 39SP

Solution:

46 m

Explanation of Solution

Given data:

The initial velocity of the baseball is 30 m/s, thrown upwards.

Formula used:

The expression for the final velocity of the object in uniformly accelerated motion is written as,

vf2=vi2+2as

Here, vi is the initial velocity, a is acceleration and s is the displacement.

Explanation:

Understand that if a motion is under gravity, then the acceleration acting on the body is equal to the acceleration due to gravity. The value of the acceleration due to gravity is 9.8 m/s2.

Recall the expression for the final velocity of the object in uniformly accelerated motion.

vf2=vi2+2as

Rearrange the expression for s.

s=vf2vi22a

Substitute 0 m/s for vf as at peak velocity becomes zero temporarily, 30 m/s for vi and 9.81 m/s2 for g.

s=(0 m/s)2(30 m/s)22(9.81 m/s2)=46 m

Conclusion:

Hence, the baseball will rise up to 46 m.

(c)

Expert Solution
Check Mark
To determine

The time taken by the baseball when it leaves the hand and return back to the starting point if it thrown upwards with the initial speed of 30 m/s.

Answer to Problem 39SP

Solution:

6.1 s

Explanation of Solution

Given data:

The initial velocity of the baseball is 30 m/s, thrown upward.

Formula used:

The time taken by an object to reach the peak altitude is written as,

tp=vig

Here, vi is the initial velocity and g is the gravitational acceleration.

The total time of flight for any object in projectile motion is written as(since the motion will be symmetrical due to the application of same acceleration),

tT=2tp

Here, tp is the time taken by object to reach the peak altitude.

Explanation:

Understand that if a motion is under gravity, then the acceleration acting on the body is equal to the acceleration due to gravity. The value of the acceleration due to gravity is 9.8 m/s2.

Recall the expression foe time taken by object to reach the peak altitude.

tp=vig

Substitute 30 m/s for vi and 9.81 m/s2 for g.

tp=30 m/s9.81 m/s2=3.06 s

Recall the expression for total time of flight for any object in projectile motion.

tT=2tp

Substitute 3.06 s for tp.

tT=2(3.06 s)=6.1 s

Conclusion:

Hence, the time taken by the baseball when it leaves the hand and return back to the starting point is 6.1 s.

(d)

Expert Solution
Check Mark
To determine

The time at which the velocity of the baseball will become 16 m/s, when it is thrown upwards with the velocity of 30 m/s.

Answer to Problem 39SP

Solution:

1.4 s and 4.7 s.

Explanation of Solution

Given Data:

The initial velocity of the baseball is 30 m/s, thrown upward.

Formula used:

The expression for the final velocity is written as,

vf=vi+at

Here, u is the initial velocity and a is the acceleration and t is the time.

Explanation:

Understand that if a motion is under gravity, then the acceleration acting on the body is equal to the acceleration due to gravity. The value of the acceleration due to gravity is 9.8 m/s2.

Write the expression for the final velocity of the baseball when first time its velocity become 16 m/s.

vf=vi+at1

Here, t1 is the time at which first time velocity of baseball will become 16 m/s.

Substitute 16 m/s for vf, 9.81 m/s2 for a and 30 m/s for vi.

16 m/s=30 m/s+(9.81 m/s2)t1t1=16 m/s30 m/s9.81 m/s2=1.4 s

This time is found when the baseball moves in upward direction opposite to gravity. So, the value of gravitational acceleration is taken negative.

Write the expression for the final velocity of the baseball when second time its velocity becomes 16 m/s(during the downward motion of the ball),

vf=vi+at2

Here, t2 is the time at which second time velocity of baseball will become 16 m/s.

Substitute 16 m/s for vf, 9.81 m/s2 for a and 0 m/s for vi.

16 m/s=0 m/s+(9.81 m/s2)t2t2=16 m/s9.81 m/s2=1.6 s

This time is found when the baseball moves in downward direction from the top of the height in the direction of gravitational acceleration. So, the value of gravitational acceleration and the final velocity both will be negative.

Write the expression for the total time, from the starting, when the velocity of baseball become 16 m/s for the second time.

T2=tp+t2

Substitute 3.1 s for tp and 1.6 s for t2.

T2=3.1 s+1.6 s=4.7 s

Add the time taken to reach the maximum height by the baseball and the time when second time its velocity become 16 m/s from the maximum height to calculate the total time when second time velocity of baseball become 16 m/s.

Conclusion:

Hence, the values of time at which the velocity of the baseball will become 16 m/s is 1.4 s and 4.7 s.

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Students have asked these similar questions
A baseball is thrown vertically upward with a speed, as it leaves the hand of 30m/s. (a) How long will it rise? (b) How high will it rise? (c) How long after it leaves the hand will it return to the starting point? (d) When will its speed be 20 m/s?(Free-fall)
A ball is thrown straight upward with a speed of 30 m/s. (a) how long will it rise? (b) how high will it rise? (c) how long after it leaves the hand will it return to the starting point? (d) when will its speed be 16 m/s?
A ball is dropped (from rest) from a window and hits the ground with a speed of 7.0m/s. If the ball were dropped from double the height, what would be its speed (in m/s) when it hits the ground?   Your Answer:

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Schaum's Outline of College Physics, Twelfth Edition (Schaum's Outlines)

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