A ball is thrown upward from the roof of a school, 16 m high, with an initial velocity of 20 m/s. The height of the ball above the ground at time t is given by the function h(t) = -4.9t² + 20t + 16, t≥ 0 a) Find the height of the ball at t = 1 and t = 2. b) Find the rate of change of the height of the ball at 1 s and 2 s. c) What is the maximum height of the ball?

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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A ball is thrown upward from the roof of a school, 16 m high, with an initial velocity of 20 m/s.
The height of the ball above the ground at time t is given by the function h(t) = −4.9t² + 20t + 16, t≥ 0.
a) Find the height of the ball at t = 1 and t = 2.
b) Find the rate of change of the height of the ball at 1 s and 2 s.
c) What is the maximum height of the ball?
d) How fast was the ball travelling when it hit the ground?
e) Determine the equation of the tangent to the curve h(t) = -4.9t² + 20t + 16 at t =5 s.
Transcribed Image Text:A ball is thrown upward from the roof of a school, 16 m high, with an initial velocity of 20 m/s. The height of the ball above the ground at time t is given by the function h(t) = −4.9t² + 20t + 16, t≥ 0. a) Find the height of the ball at t = 1 and t = 2. b) Find the rate of change of the height of the ball at 1 s and 2 s. c) What is the maximum height of the ball? d) How fast was the ball travelling when it hit the ground? e) Determine the equation of the tangent to the curve h(t) = -4.9t² + 20t + 16 at t =5 s.
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