Concept explainers
Projectile Motion Alice throws a ball straight up with an initial speed of 40 feet per second from a height of 5 feet.
a. Find parametric equations that model the motion of the ball as a function of time.
b. How long is the ball in the air?
c. When is the ball at its maximum height? Determine the maximum height of the ball.
d. Simulate the motion of the ball by graphing the equations found in part (a).
To find:
a. Find parametric equations that model the motion of the ball as a function of time.
Answer to Problem 50AYU
a.
Explanation of Solution
Given:
Alice throws a ball straight up with an initial speed of 40 feet per second from a height of 5 feet.
Formula used:
Calculation:
, , ,
a.
To find:
b. How long is the ball in the air?
Answer to Problem 50AYU
b. The ball is in the air for secs.
Explanation of Solution
Given:
Alice throws a ball straight up with an initial speed of 40 feet per second from a height of 5 feet.
Formula used:
Calculation:
, , ,
b. When the ball is in the air .
Solving the equation ,
or
Hence, the ball is in the air for secs.
To find:
c. When is the ball at its maximum height? Determine the maximum height of the ball.
Answer to Problem 50AYU
c. Maximum height feet.
Explanation of Solution
Given:
Alice throws a ball straight up with an initial speed of 40 feet per second from a height of 5 feet.
Formula used:
Calculation:
, , ,
c. The maximum height occurs at the vertex.
seconds
Maximum height is when sec.
Maximum height feet.
To find:
d. Simulate the motion of the ball by graphing the equations found in part a.
Answer to Problem 50AYU
d.
Explanation of Solution
Given:
Alice throws a ball straight up with an initial speed of 40 feet per second from a height of 5 feet.
Formula used:
Calculation:
, , ,
d. We have plotted the graph above with so that the line is not on the top of .
Chapter 10 Solutions
Precalculus Enhanced with Graphing Utilities
Additional Math Textbook Solutions
Single Variable Calculus: Early Transcendentals (2nd Edition) - Standalone book
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Thomas' Calculus: Early Transcendentals (14th Edition)
University Calculus: Early Transcendentals (4th Edition)
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