A small child (m = 20 kg) falls (from rest) from a tree onto a trampoline. Treat the trampoline as a spring with spring constant k = 2 × 104 N/m. The child falls from a height of h = 3 m onto the trampoline which is d = 1 m tall. 

a) (2 marks) Does the conservation of energy apply in this example? Explain. 

b) (6 marks) How far above the ground is the child after the trampoline reaches its maximum compression? 

c) (2 marks) Find the speed of the child after they bounce back up to a half their initial height above the ground.