In the movie Shrek, Fiona has recently been rescued from a dragon by Shrek. As Shrek is bringing Fiona to Lord Farkwad, Fiona is abducted by Robin Hood. He swings from the trees and scoops Fiona up in a completely inelastic collision. (They move together with the same velocity after the collision).
Click on the analysis below for a close up look of the equations that describe this event.
For a challenge, try to predict their final height as a fraction of Robin Hood's initial height before you look at the solution.
Step 1 (Swing Down) - Robin Hood's potential energy (PE) at the start of his swing is converted to kinetic energy (KE) at the bottom of his swing. Applying conservation of energy, PEtop = KEbottom.
Step 2 (Collision) - Robin Hood collides with Fiona in a completely inelastic collision. Applying conservation of momentum, m1v1 = 2mv3. For simplicity, we'll assume Fiona and Robin Hood have equal masses.
Step 3 (Swing Up) - Their kinetic energy (KE) together after the collision converts to potential energy (PE) at the top of the swing. Applying conservation of energy, KEbottom = PEtop.
Click here to watch the scene (it all happens in the first 8 seconds).