Since the height of the rock after t seconds is given by the formula:
[tex]h(t)=100+30t-5t^2[/tex]
Then, replace t=5 to find the height of the rock after 5 seconds:
[tex]\begin{gathered} h(5)=100+30(5)-5(5)^2 \\ =100+150-5(25) \\ =250-125 \\ =125 \end{gathered}[/tex]
The velocity of the rock after t seconds is given by:
[tex]h^{\prime}(t)=30-10t[/tex]
Replace t=5 to find the velocity of the rock after 5 seconds:
[tex]\begin{gathered} h^{\prime}(5)=30-10(5) \\ =30-50 \\ =-20 \end{gathered}[/tex]
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.
