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

b.

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the working equation for the angular size is the product of the physical size and 360 degrees divided by the product of two pi and distance from earth. the minimum size would be 0.559 degrees while the maximum size would be 0.49 degrees.