Derive a general equation for the time of flight of the banana en route to the monkey in terms of only the velocity, distance, and height

Question

hint: if you are doing everything right, there should be a lot of cancellations resulting in a relatively simple solution
Okay, this is confusing to me. I have looked at projectile equations for time, range, and velocity. However, this question is asking for one equation like T= V, D, H? I am not even sure if this is possible. The graph it gave me contained no numbers just labeled height, velocity, and distance leading me to believe that it wants me to come up with an equation for time that if given velocity, distance, and height you can plug it into that one equation and come up with time. How the heck do I combine 3 separate equations into one? Am I approaching this wrong?
F.W.I. The banana is not present on the graph

Answer 1

If the initial velocity V has components Vi
and u
then d = u t or t = d/u
and
at time t the banana must be at height h
so
h = Vi t - 4.8 t^2
so
h = Vi d/u - 4.9 d^2/u^2