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Calculus (MindTap Course List)

8th Edition
James Stewart
ISBN: 9781285740621

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Calculus (MindTap Course List)

8th Edition
James Stewart
ISBN: 9781285740621
Textbook Problem

If a ball is thrown vertically upward with a velocity of 80 ft/s, then its height after t seconds is s = 80 t 16 t 2 .

(a) What is the maximum height reached by the ball?

(b) What is the velocity of the ball when it is 96 ft above the ground on its way up? On its way down?

To determine

Part (a)

To find: Maximum height reached by the ball

Explanation

1) Concept: Velocity is rate of change of position with respect to time t.

2) Formula:

v=dsdt

3) Given: A ball is thrown vertically upward with the velocity of 80 ft/s  and its height after t second is s=80t-16t2

4) Calculation:

The ball reaches the maximum height when its velocity becomes 0

Therefore,

v=dsdt=ddt80t-16t2=80-32t

When v = 0, 80-32t=0 32t=80t=2

To determine

Part (b)

To find: Velocity of the ball when it is 96 feet above the ground on its way up and on its way down

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