A bungie jumper of mass 50kg is attached to a bungie with a constant of 100Nm. The unstretched length of the bungie is 15m. What is the maxmimum velocity of the jumper

v = 18.5 m /s

Explanation:

The velocity of the jumper will go on increasing until his weight is more than the restoring force created in the bungle.

mg = kx

50 x 9.8 = 100 X

X = 4.9 m

Total fall = 15 + 4.9 = 19.9 m

kinetic energy gained due to fall by 19.9 m

= mgh = 50 x 9.8 x 19.9 = 9751 J

energy lost due to stored elastic energy in bungie

= 1/2 k x²

= .5 x 100 x 4.9²

= 1200.5 J

Remaining kinetic energy = 9751 - 1200.5 = 8550.5 J

1/2 m v² = 8550.5

.5 x 50 x v² = 8550.5

v² = 342

v = 18.5 m /s