Question

A) what is the maximum height of the ball ? B) how many seconds does it take until the ball hits the ground ?

Answer 1

Given:

`h(t)=-16t^2+104t+56`

Models the balls height height about the ground.

Required:

To find the maximum height of the ball.

Step-by-step explanation:

Consider

`\begin{gathered} h(t)=-16t^2+104t+56 \\ a=-16 \\ b=104 \\ c=56 \end{gathered}`
`\begin{gathered} t=-(b)/(2a) \\ \\ t=-(104)/(2(-16)) \\ \\ t=(204)/(32) \\ \\ t=3.25 \end{gathered}`

At t = 3.25 the maximum height is

`\begin{gathered} h(3.25)=-16(3.25)^2+104(t)+56 \\ =225 \end{gathered}`

Final Answer:

The maximum height of the ball is 225 feet.