A ball is thrown upward from the top of a building 250 feet tall

Question

A ball is thrown upward from the top of a building 250 feet tall. The height of the ball is described by the function h(t)=−16t^2+24t+250 , where t is in seconds and t=0 corresponds to the moment the ball is thrown.

Determine for what value of t the ball reaches the maximum height and determine this maximum height.

Determine when the ball reaches the ground.

Answer 1

I will not do this problem for you, but I will tell you how to do it.

The maximum height will be attained when h'(t) = 0, i.e. when 32t = 24.

The maximum height will he found by plugging the time of the maximum height into the equation for h(t).

The ball will hit the gound when h(t) =0...and remember that the quadratic formula tacitly assumes that the coefficient of the squared term is positive!