Alexandra is tossing a softball into the air with an underhand motion. The distance of the ball above her hand at any time is given by the formula: h ( t ) = 80 t − 16 t 2 for 0 ≤ t ≤ 5

Question

Where  is the height of the ball (in feet) and  is the time (in seconds).At what times, , is the ball in her hands? Note: there are 2 different times.

The ball is in her hands at __ seconds. 

At what time, t is the ball at it's maximum height?

The ball is at it's max height after ___ seconds.

How high, h, is the ball at it's maximum height?

The ball's max height is ___ feet.

Answer 1

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

h'(t) = 80-32t = 0

t = 80/32 = 5/2 = 2.5 seconds to reach max height

h(2,5) = 80(2.5) -16(2.5)^2 = 120 -100= 20 feet = max height

in 2(2.5) = 5 seconds it's at her hand level again, also t=0 seconds