Question

A ball is thrown upward and its height after t seconds can be described by formula f(t)=−10t2+24t+5.6. Find the maximum height the ball will reach.

Answer 1

The maximum height is 20.

Explanation:

The height of the ball is given by
`f(t)= -10t^(2) +24t+5.6`.

Differentiating the above equation, with respect to t, we get
`(d f(t))/(dt) = -20t + 24`.

At the maximum height the derivative of the function needs to be 0.

Hence,
`(d f(t))/(dt) = 0` gives
`t = (24)/(20) = (6)/(5)`.

The maximum height is
`f((6)/(5) )= -10((6)/(5) )^(2) +24((6)/(5) )+5.6 = 20`