How high can you jump on the Moon?

On the moon the acceleration due to gravity is gm=1.62m/s2. On earth, a person of mass m=75kg can jump 0.5mvertically. let acceleration path of 0.4 meters.  Find the height this person will reach when jumping on the moon, if the person is wearing nothing in both places. 

Kinetic energy at take-off = potential energy at peak height = work done.

On Earth

                        W = m * g * h = 75 * 9.8 * 0.5 = 368 J

           take-off speed: 

                       E = 1/2  m * v ^2     ==>   v =   (2 * 368 / 75) ^0.5 = 3.13 m/s

                      a = v ^2 / (2 s ) = 3.13 ^2 / (2 * 0.4) =  12.26 m/s^2

            this acceleration is net acceleration related to ground, after over come the Gravity g = 9.8.

                    total acceleration = a + g = 12.26 + 9.8 m/s^2  = 22.06 m/s^2

            exerted force: 

                F = m * a = 75 * (22.06) = 1654.5  Newton

We now move the experiment to the Moon

            the moon the acceleration due to gravity  g = 1.62 m/s^2

            exerted force is the same,  mass is the same, acceleration on the jump on the jump is the same : 

                F = m * a = 75 * (22.06) = 1654.5  Newton

            net acceleration related to the moon:

                a = 22.06 - 1.62 = 20.44   m/s^2

                W = m * a * s = 75 * 20.44 * 0.4

                P = m * g * h 

                m * a * s = m * g * h

                h = ( a * s )/ g = (20.44 * 0.4) / 1.62 = 5.04 m

if the person is wearing a spacesuit with mass m=100kg.

                 m * a * s = (m + 100) * g * h

                 75 * (20.44 * 0.4)  / (175 * 1.62) = h

                h =  613.2 / 283.5 =  2.16 m