Suppose I am standing at the top of a cliff which is a vertical distance (d) above the ground. Now, if I jump off the slide at an angle beta upwards at an initial velocity (v), I will travel a horizontal distance of (R). I have proved the first part of the question which shows these quantities are related by the equation: Rsin(2beta) + d(1 + cos(2beta))=(R^2)g/v^2 where g is 9.8 meters per second squared. Ok, now here is the relation which I am having problems solving: The condition for maximum range R is tan(2beta)=R/d. I have no idea how to go about showing this. Any ideas or suggestions?