With what speed would a person need to leave the ground?

Question

Excellent human jumpers can leap straight up to a height of 1.1 m off the ground. To reach this height, with what speed would a person need to leave the ground? Assume no air resistance (free-fall motion) and give your answer with 2 significant figures.

Answer 1

The work done by the jumper will be equal to the attained gravitational potential energy, GPE. The gravitational potential energy will be equal to the kinetic energy, KE, as the jumper returns to the ground.

So:

W = GPE and GPE = KE

mgh = ½mv² ...solving for v,

v = √2gh

v = √2(9.8)(1.1) = √21.56

v = 4.64327 m/s = 4.6 m/s (sig figs)