A child swinging on a swingset with chains of length l wants to swing and jump...
A child swinging on a swingset with chains of length l wants to swing and jump off the swing to get as far as possible. The child isn't being pushed.
At what angle θ should the child let go of the swing to maximize the landing distance and what is the distance jumped as a function of θ?
Hints: Model swinging using simple pendulum and jumping using projectile motion.
Find equations for speed and height as functions of the swing angle and then a range equation.
Note: The answer is not 45 degrees as the launch is from above the ground level!
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