A skydiver is at a height of 10,000 m. Assuming no air resistance, how fast is the skydiver travelling at 9,990 m above the ground?

The skydiver has potential energy at the top of his/her jump, which is transferred to kinetic energy when he/she jumps. The difference in height between the start of the jump and the point at which his/her velocity is being measured is: 10,000-9,990 = 10 m This means that the potential energy in a height of 10 m has been transferred to kinetic energy. So:

E_p=E_k=mgh=(1/2)mv²

          =m(9.81)(10)=(1/2)mv²    -->   The mass (m) terms cancel

          =98.1=(1/2)v²  

          =196.2=v²                        -->   Taking the square root of both sides gives the answer below Which means v=14 ms^-1