Question

What is it high after five seconds? what is is velocity after five seconds?

Answer 1

Since the height of the rock after t seconds is given by the formula:

`h(t)=100+30t-5t^2`

Then, replace t=5 to find the height of the rock after 5 seconds:

`\begin{gathered} h(5)=100+30(5)-5(5)^2 \\ =100+150-5(25) \\ =250-125 \\ =125 \end{gathered}`

The velocity of the rock after t seconds is given by:

`h^(\prime)(t)=30-10t`

Replace t=5 to find the velocity of the rock after 5 seconds:

`\begin{gathered} h^(\prime)(5)=30-10(5) \\ =30-50 \\ =-20 \end{gathered}`

Therefore, the height of the rock after 5 seconds is equal to 125 ft. The velocity of the rock after 5 seconds is -20 ft/s.