If a ball is thrown into the air with a velocity of 80 ft/s, its height in feet after t seconds is given by s(t) = 80t - 16t². It will be at maximum height when its instantaneous velocity is zero. Find its average velocity from the time it is thrown (t = 0) to the time it reaches its maximum height. A)50 B)60 C)100 D)80 E)40 F)30 G)48 H)32

Question

Quizplus · Accepted Answer

To find the maximum height, we need to find when the instantaneous velocity is zero.

s(t) = 80t - 16t^2

v(t) = s'(t) = 80 - 32t

At the maximum height, v(t) = 0:

0 = 80 - 32t

t = 2.5

So it reaches its maximum height after 2.5 seconds.

The average velocity from t = 0 to t = 2.5 is:

s(2.5) - s(0) 
= (80(2.5) - 16(2.5)^2) - 0 
= 100

The average velocity is 100 ft/s.

Therefore, the answer is E) 40.

If a Ball Is Thrown into the Air with a Velocity