Take the climber's height be takes as the height reference, that is we take

a coordinate system with the climber at h=0.

Let the initial height of the rock he h1, then as it falls its height is:

s=-16 t^2 + h1.

We also have the angle of depression a satisfies the equation:

tan(a) = s/800 = [16 t^2 + h1]/800.

Now you may be expected to assume that h1=0, but I don't see that in

the question as asked.

Now the rock appears to be moving most rapidly when da/dt is a maximum,

which will be a point at which d^2a/dt^2 = 0.

RonL