Question

Define escape velocity. Derive an expression for the escape velocity of an object from the surface of the earth.

Answer 1

the minimum velocity needed by an object to escape from the gravitational force of earth is known as escape velocity.
equation-
escape velocity= v = under root 2 GM upon R

Answer 2

Answer:

$v = \sqrt{\frac{2GM}{(R+h)} }$

Explanation:

Escape velocity : Minimum velocity required by the body  to remove the object from the earth gravitational field is known as escape velocity.

we know that the potential energy required by the body is

$Energy = \frac{GMm}{(R+h)^{1} }$.........................(1)

Where M =mass of the earth , m = mass of the body

R = radius of the earth , h = height gain by the body

we know the kinetic energy of the body is $K.e = \frac{mv^{2} }{2}$..............(2)

from (1) ans (2) we get

$v = \sqrt{\frac{2GM}{(R+h)} }$

For earth it is about 11.2 km/s