Suppose a skydiver (mass =100kg) is falling towards the earth. when the skydiver is 80 m above the earth he is moving at 60 m/s at this point calculate the skydivers total mechanical energy

The total mechanical energy of the skydiver is, E  = 96402.6 J

Explanation:

Given data,

The mass of the skydiver, m = 100 kg

The speed of the skydiver at 80 m height, v = 60 m/s

The initial velocity of the skydiver, u = 0

Using the III equations of motion,

                                  v² = u² + 2gs

                                   s = v²/2g

Substituting the given values,

                                   s = ½ 60²/ 9.8

                                      = 18.37 m

Hence the initial total distance of the skydiver from the ground initially,

                                    h = s + d

                                        = 18.37 + 80

                                         = 98.37 m

Since the total mechanical energy of a system is conserved, the total mechanical energy of the skydiver at height 'h' is equal to the total mechanical energy at height 'd'.

                                        E = P.E + K.E

                                            = mgh + ½ mu²

                                            = 100 x 9.8 x 98.37     ( ∵ u = 0)

                                             = 96402.6 J

Hence, the total mechanical energy of the skydiver is, E  = 96402.6 J

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