Question

9. A 55 kg athlete leaps into the air from a crouching position. Her center of mass rises 60 cm as her feet leave the ground and then it continues another 80 cm to the top of the leap. What is the average power she develops, assuming the force on the ground is constant? The answer key says that the answer is 1.42 kW but I cannot figure out how to solve it.

Answer 1

conserving energy is the method of this problem

she has crouched by 60 cm = 0.6 m

she rises to 80cm = 0.8 m

hence the velocity at which her foot is off the ground is v = sqrt(2g*(0.8-0.6)) = 1.98 m/s

now assuming she applies a constant average force F

work done = F*0.6

conserving energy -55*g*0.6 + F*0.6 = 55*g*0.2

F = 719.4 N

Now the

Power = F*v = 719.4*1.98 = 1424.412 W = 1.42 kW

Please upvote if you like the answer!!