If a ball is thrown vertically upward with a velocity of 160 ft/s, then its height after t seconds is s = 160t − 16t2. (a) What is the maximum height reached by the ball?

s = 400 ft

The maximum height reached by the ball is 400 ft

Explanation:

Given;

Initial vertical velocity v = 160 ft/s

Height function s = 160t - 16t^2 1

The maximum height is reached when the change in height with respect to time is zero.

ds/dt = 0

Differentiating the height function;

ds/dt = 160 - 32t = 0

160 - 32t = 0

Solving for t;

32t = 160

t = 160/32

t = 5 seconds

Therefore, the maximum height is at t = 5;

Substituting into equation 1 (the height function)

s = 160(5) - 16(5^2)

s = 800 - 400

s = 400 ft

The maximum height reached by the ball is 400 ft

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