# Homework Help: Speed problem

1. Nov 3, 2009

### 5t34lth

1. The problem statement, all variables and given/known data
At what speed would a 70-kg high jumper have to leave the ground in order to raise his body up to a height of 1.60 m

Acceleration due to gravity: 9.8 m/s^2 [down]
2. Relevant equations

Kinetic Energy = 0.5(mass)(velocity^2)
Gravitational Potential Energy = (mass)(accleration due to gravity)(height)

3. The attempt at a solution

2. Nov 3, 2009

### 5t34lth

Answer is 5.6 m/s but i dont know how to get it

3. Nov 3, 2009

### BlueEight

Because only conservative forces are acting upon the system:
Change in Potential Energy + Change in Kinetic Energy = 0
Change in potential energy = mg(hf-hi)
Change in kinetic energy = .5(m)(vf2-vI2)
vf is zero because the jumper just reaches the maximum height of 1.6 meters. hi is also zero because the jumper starts on the ground. hf is 1.6 meters. Substituting, we obtain
-1097.6 + 35vi2 = 0 (Because gravity points down, it has a value of -9.8 m/s20
Solving for v results in the answer of 5.6 m/s.