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.
express your answer in terms of the variables m, m,h, r and appropriate constants.

Explanation:

The initial mechanical energy of the object, when it is located at height h above the the planet, is just gravitational potential energy:

where

G is the gravitational constant

M is the mass of the planet

m is the mass of the object

R is the radius of the planet

h is the altitude of the object

When the object hits the ground, its mechanical energy will sum of potential energy and kinetic energy:

where

v is the speed of the object at the ground

Since the mechanical energy is conserved, we can write

and solving for v, we find

explanation: in any substance/object, the particles inside it (atoms/molecules) constantly move in random directions and with random speeds (this motion is called brownian motion). as a result, the particles have some kinetic energy (which is proportional to the temperature of the substance).

explanation:

have a great day!

it is the second option.