Question

What is the speed with which a space rock, just falling from infinity, will strike the surface of the earth? Neglect all other effects except gravity.

Answer 1

Explanation:

For a body falling from infinity, there will be no gravitational potential energy on it due to Earth. And if we assume, it's initial speed is zero.

Then the body's initial energy is zero.

As it reaches the Earth's surface it gains speed and also gravitational potential energy.

i.e E=

2

1

mv

2

−

R

GMm

From the conservation of energy, this should be equal to the initial total energy of the body.

∴

2

1

mv

2

−

R

GMm

=0

⇒

2

1

mv

2

=

R

GMm

⇒v=

R

2GM

But GM=gR

2

⇒v=

2gR