Finding Maximum Range R for Jumping from Cliff: Mechanics Question

[Ed Quanta]

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?

 

[chroot]

http://hyperphysics.phy-astr.gsu.edu/hbase/traj.html

- Warren

 

[Doc Al]

Start by taking the derivative with respect to beta of your first relation.