Question

An object of mass m is dropped from height h above a planet of mass M and radius R.Find an expression for the object's speed as it hits the ground

Answer 1

Step-by-step explanation:

Mass of object = m

Height above planet = h

Mass of planet = M

Radius of planet = R

As we have to find out velocity, so let's apply the law of conservation of energies on initial( when the object was at height) and final( when object hit the surface points.

Initial energy = Final energy

`K_(i) + U_(i) = K_(f) + U_(f)`

`(1)/(2)mv_(i) ^(2)  - (GMm)/(h+R) = (1)/(2)mv_(f) ^(2)  - (GMm)/(R)\\v_(i) = 0\\v_(f) ^(2) = 2(GM)/(R) - 2 (GM)/(h+R)`

`v_(f) =\sqrt{(2GMh)/(R(R+h)) }`