Question

What is escape velocity? A body is projected out of earth by fabric the escape velocity on earth, Find its speed at infinity

Answer 1

Dear student,
The minimum velocity with which a projectile has to be projected to escape the earth’s gravitational field is called escape velocity.

Let a body of mass ‘m’ be projected with velocity ‘v’.

At the ground, PE = GMm/R

And the KE = ½ mv²

To overcome earth’s gravitational field,

KE>PE

=> ½ mv² > GMm/R

=> v > (2GM/R)^1/2

We know,

g = GM/R²

Therefore,

v > [2(GM/R²)R]^1/2

=> v > [2gR]^1/2

Thus, to escape the earth’s gravitational field, the minimum velocity must be,

v_e = [2gR]^{1/2
At infinity the body will continue to move with escape velocity as it is not under the action of gravity.
Regards}