Question

A very light basket (its mass is negligible) hangs from a long stretchy rope 3 meters above the surface of a pond. Three boys equal mass carefully climb into the basket one after the other and the rope stretches one additional meter for each boy, so that all three aboard make the basket just touch the water. They climb out and the basket returns to its initial position. One boy now steps off a tower and falls into the basket, causing the rope to stretch until the basket just touches the water again, for an instant. From what height above the water surface did the boy step?

Answer 1

Force:
F = -k x = -k (3) = -3 m g
k = m g

Energy:
(1/2) k x^2 = m g h
stretched rope = initial potential energy

(1/2)(m g) (3)^2 = m g h
(1/2)(9) = h
h = 4.5 meters

Answer 2

But where does the first part come from? The "-k (3) = -3 m g" part