Calculating Speed for High Jump of 1.60m

[5t34lth]

Homework Statement

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]

Homework Equations

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

The Attempt at a Solution

 

[5t34lth]

Answer is 5.6 m/s but i don't know how to get it

 

[BlueEight]

Because only conservative forces are acting upon the system:
Change in Potential Energy + Change in Kinetic Energy = 0
Change in potential energy = mg(h_f-h_i)
Change in kinetic energy = .5(m)(v_f²-v_I²)
v_f is zero because the jumper just reaches the maximum height of 1.6 meters. h_i is also zero because the jumper starts on the ground. h_f is 1.6 meters. Substituting, we obtain
-1097.6 + 35v_i² = 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.