If a ball is thrown vertically upward from the roof of 32 foot building with a velocity of 80 ft/sec, its height after t seconds is s(t)=32+80t–16t2. What is the maximum height the ball reaches?

Question

What is the velocity of the ball when it hits the ground (height 0)?

for max height I put 80-32t
and for velocity i put 32...which are wrong..

Answer 1

The building height is not the velocity.

For the max height, rewrite
s(t) = -16t^2 +80t +32 as
-16(t^2 - 5t + 25/4) +132
= -16(t -5/2)^2 + 132

The highest possible value of the function is 132 feet, and it occurs when t = 2.5 seconds.

For the velocity when it hits the ground, first solve for t when s = 0.

Then use the equation for velocity vs time:

V = 80 - 32 t ft/s