How quickly is the angle of elevation changing of the object?

Question

I am having a tough time solving this problem because I cannot seem to picture this problem. I don't know how the picture in this problem is supposed to look like and therefore I don't know where to start.

Answer 1

You were already given $s(t)$ and $h(t)$ as explicit functions of time.

Looking at the figure you drew (like the one in the other answer), you should be able to write $\theta(t)$ in terms of $s(t)$ and $h(t).$

You're being asked to find $\frac{d}{dt} \theta(t)$ when $h(t) = 734.$

Answer 2

$\theta=\arctan( {\frac {h(t)}{s(t)}})$. Let's call that function, $f(t)$.

The question asked how fast $\theta$ is changing when $h(t)=734$.

First, solve for $t$. Let's call that $t$, $t_1$. Then, to find the rate it's changing at that $t$, you can do ${\displaystyle {\frac {f(t_1+\epsilon)-f(t_1)}{\epsilon}}}$, for $\epsilon$ arbitrarily small. The smaller $\epsilon$ is, the more accurate the answer would be. I think $\epsilon=10^{-5}$ should be enough.