SOLUTION
Write out the function foir the height
[tex]h(t)=-16t^2+40t+6[/tex]
The speed of an object is the rate of change of distance with time. Since rate of change is also differentiation, hence we diferentiate the function above
Applying the rule of differentiation, we have
Recall the rule for diffentiation
[tex]\begin{gathered} \text{If } \\ y=x^n \\ \text{Then} \\ \frac{dy}{dx}=ny^{n-1} \end{gathered}[/tex]hence, we have
[tex]\begin{gathered} \frac{dh}{dt}=-16\times2t^{2-1}+40\times1t^{1-1} \\ \\ \frac{dh}{dt}=-32t+40 \end{gathered}[/tex]Then the speed of the ball is goven by the function
[tex]V=\frac{dh}{dt}=-32t+40[/tex]
At t= 1, we substitute into the function we obtained for speed
Hence, we have
[tex]\begin{gathered} V=-32(1)+40 \\ Where\text{ t=1} \\ V=-32+40 \\ V=8\text{fts}^{-1} \end{gathered}[/tex]hence
The speed of the ball at t=1s is 8ft/s
