A body of mass `50 kg` falls on the earth from infinity. What will be its velocity on reaching the earth? What will be its `KE`? Take radius of the earth `= 6.4 xx 10^(6) m , g = 10 ms^(-2)`. Air friction is neglected.

Explanation

Here, `m = 50 kg , R = 6.4 xx 10^(6) m`
As body thrown up escape velocity `upsilon_(e)` reaches infinity, so a body falling from infinity will be reaching the earth with velocity `upsilon_(e)` (=escape velocity).
`upsilon_(e) = sqrt(2gR) = sqrt(2 xx 10 xx 6.4 xx 10^(6)) = 11.31 xx 10^(3) m`
`= 11.31 km//s`
`KE = (1)/(2) m upsilon_(e)^(2) = (1)/(2) xx 50 xx (11.31 xx 10^(3))^(2)`
`= 3.2 xx 10^(9) J`