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Concept explainers
To find: Instantaneous Velocity of a Ball In physics it is shown that the height of a ball thrown straight up with an initial velocity of from ground level is,
where is the elapsed time that the ball is in the air.
a. When does the ball strike the ground? That is, how long is the ball in the air?
![Check Mark](/static/check-mark.png)
Answer to Problem 47AYU
Solution:
a.
Explanation of Solution
Given:
Calculation:
a. The ball strike the ground when
discard the solution , the strikes the ground after .
To find: Instantaneous Velocity of a Ball In physics it is shown that the height of a ball thrown straight up with an initial velocity of from ground level is,
where is the elapsed time that the ball is in the air.
b. What is the average velocity of the ball from ?
![Check Mark](/static/check-mark.png)
Answer to Problem 47AYU
Solution:
b.
Explanation of Solution
Given:
Calculation:
b. The average velocity of the ball from is,
To find: Instantaneous Velocity of a Ball In physics it is shown that the height of a ball thrown straight up with an initial velocity of from ground level is,
where is the elapsed time that the ball is in the air.
c. What is the instantaneous velocity of the ball at time ?
![Check Mark](/static/check-mark.png)
Answer to Problem 47AYU
Solution:
c.
Explanation of Solution
Given:
Calculation:
c. The instantaneous velocity of the ball at time is the derivative : that is,
Replace . the instantaneous velocity of the ball at time is,
To find: Instantaneous Velocity of a Ball In physics it is shown that the height of a ball thrown straight up with an initial velocity of from ground level is,
where is the elapsed time that the ball is in the air.
d. What is the instantaneous velocity of the ball at ?
![Check Mark](/static/check-mark.png)
Answer to Problem 47AYU
Solution:
d.
Explanation of Solution
Given:
Calculation:
d. The instantaneous velocity of the ball at is,
To find: Instantaneous Velocity of a Ball In physics it is shown that the height of a ball thrown straight up with an initial velocity of from ground level is,
where is the elapsed time that the ball is in the air.
e. When is the instantaneous velocity of the ball equal to zero?
![Check Mark](/static/check-mark.png)
Answer to Problem 47AYU
Solution:
e.
Explanation of Solution
Given:
Calculation:
e. The instantaneous velocity of the ball is zero when,
To find: Instantaneous Velocity of a Ball In physics it is shown that the height of a ball thrown straight up with an initial velocity of from ground level is,
where is the elapsed time that the ball is in the air.
f. How high is the ball when its instantaneous velocity equals zero?
![Check Mark](/static/check-mark.png)
Answer to Problem 47AYU
Solution:
f.
Explanation of Solution
Given:
Calculation:
f. How high is the ball when its instantaneous velocity equals zero.
The instantaneous velocity of the ball is zero when,
To find: Instantaneous Velocity of a Ball In physics it is shown that the height of a ball thrown straight up with an initial velocity of from ground level is,
where is the elapsed time that the ball is in the air.
g. What is the instantaneous velocity of the ball when it strikes the ground?
![Check Mark](/static/check-mark.png)
Answer to Problem 47AYU
Solution:
g.
Explanation of Solution
Given:
Calculation:
g. The ball strikes the ground when , the instantaneous velocity when is,
The velocity of the ball at is , the negative value implies that the ball is travelling downward.
Chapter 14 Solutions
Precalculus
Additional Math Textbook Solutions
Calculus: Early Transcendentals (2nd Edition)
Calculus and Its Applications (11th Edition)
University Calculus: Early Transcendentals (3rd Edition)
Single Variable Calculus: Early Transcendentals (2nd Edition) - Standalone book
Thomas' Calculus: Early Transcendentals (14th Edition)
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