Question

Sam hits a golf ball from a elevated tee

Answer 1

First take a derivative,

$\frac{d}{dx}-5t^2+10t+30=-10t+10=-10(t-1)$

Now compute the critical point where the slope is 0,

$-10(t-1)=0\implies t-1=0\implies t=1$

And done.

The maximum height is at $t=1$ of $h(1)=-5+10+30=35$.

Hope this helps :)