Question

Hi, can you help me to solve this exercise please

Answer 1

The maximum height reached = 20 feet

The time it takes to reach this height = 1 second

Explanations:

Given the equation that modeled the height of the ball "t" seconds after Susan throws it is expressed as:

`h(t)=-16t^2+32t+4`

At maximum height, the velocity of the ball is zero. Therefore the velocity function is given as:

`h^(\prime)(t)=v(t)=-32t+32`

Substituting v(t) = 0 to get the required time, we will have:

`\begin{gathered} -32t+32=0 \\ -32t=-32 \\ t=1\text{second} \end{gathered}`

Therefore it takes the ball 1 second to reach its maximum height.

Determine the maximum height reached by substituting t = 1 sec into the formula as shown:

`\begin{gathered} h(t)=-16t^2+32t+4 \\ h(1)=-16(1)^2+32(1)+4 \\ h(1)=-16+32+4 \\ h(1)=16+4 \\ h(1)=20\text{feet} \end{gathered}`

Hence the maximum height reached by the ball is 20 feet.