Concept explainers
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)
The time for which the baseball will rise when it is thrown upward with the velocity of
Answer to Problem 39SP
Solution:
Explanation of Solution
Given data:
The initial velocity of the baseball is
Formula used:
The time taken by object to reach the peak altitude is written as (since at peak final velocity becomes 0),
Here,
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
Recall the expression for the time taken by the object to reach the peak altitude.
Substitute
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
(b)
The height for which the baseball will rise if it is thrown upwards with the velocity of
Answer to Problem 39SP
Solution:
Explanation of Solution
Given data:
The initial velocity of the baseball is
Formula used:
The expression for the final velocity of the object in uniformly accelerated motion is written as,
Here,
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
Recall the expression for the final velocity of the object in uniformly accelerated motion.
Rearrange the expression for
Substitute
Conclusion:
Hence, the baseball will rise up to
(c)
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
Answer to Problem 39SP
Solution:
Explanation of Solution
Given data:
The initial velocity of the baseball is
Formula used:
The time taken by an object to reach the peak altitude is written as,
Here,
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),
Here,
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
Recall the expression foe time taken by object to reach the peak altitude.
Substitute
Recall the expression for total time of flight for any object in projectile motion.
Substitute
Conclusion:
Hence, the time taken by the baseball when it leaves the hand and return back to the starting point is
(d)
The time at which the velocity of the baseball will become
Answer to Problem 39SP
Solution:
Explanation of Solution
Given Data:
The initial velocity of the baseball is
Formula used:
The expression for the final velocity is written as,
Here,
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
Write the expression for the final velocity of the baseball when first time its velocity become
Here,
Substitute
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
Here,
Substitute
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
Substitute
Add the time taken to reach the maximum height by the baseball and the time when second time its velocity become
Conclusion:
Hence, the values of time at which the velocity of the baseball will become
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Chapter 2 Solutions
Schaum's Outline of College Physics, Twelfth Edition (Schaum's Outlines)
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