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.