Question

The escape velocity of a body from earth is . If a body is projected with a velocity twice its escape velocity then the velocity of the body at infinity is

Answer 1

apply law of conservation of energy. If ve is escape velocity, then mechanical energy on the surface of the earth, in given condition is

E1= (1/2)m(2ve)^2- GMm/R…………(1)

m is mass of the body to be projected,

M is mass of the earth.

R is radius of the earth.

G is universal gravitational constant.

Now, escape velocity satisfies the relation::

(1/2)mve^2= GMm/R…………..(2).

Using equation (2) in equation (1), we get

E1=(1/2)m(2ve)^2-(1/2)mve^2…………(3)

Now, at infinity potential energy is zero.

If v' is velocity of the body at infinity, it's kinetic energy there will be,

E2=(1/2)mv'^2……………….(4)

Comparing equation (1) with equation (4), and cancelling common factor,

3ve^2=v'^2 or

v'=[ sqrt (3)]ve……………(.5)

The body will continue to move at this velocity at infinity.