Question

How do you do the work on this problem I’ve been stuck in it for a couple hours now.

Answer 1

56.2 m

Explanation:

We can solve for the maximum height by calculating the derivative of y with respect to time and then equating it to zero, i.e.,

`(dy)/(dt) = 0`

then solve for the time t that satisfies the equation above. The expression for the height y is

`y = 60t - 16t^2`

Taking the derivative of this expression, we get

`(dy)/(dt) = 60 - 32t = 0 \Rightarrow t = (60)/(32) = 1.9\:\text{s}`

This means that at t = 1.9 s, the ball would have reached its maximum height. To determine this height, use this value for t in the the equation for y to get

`y = 60(1.9\:\text{s}) - 16(1.9\:\text{s})^2 = 56.2\:\text{m}`