Question

A projectile is fired vertically upwards. it escapes from the earth, when fired with velocity v. if it is to be fired at 45° to the horizontal, what should be its velocity to enable it to escape from the gravitational pull of the earth

Answer 1

Escape velocity is the minimum velocity required for an object to move from Gravitational influence of a massive body .
For example , in case of earth escape velocity , ve :
1/2mve² [ Kinetic energy of body ] = GMm/R [ gravitational potential energy between body and earth ]
ve² = 2GM/R
ve = √{2GM/R} or, √{2gR}

Here you can see that escape velocity of earth = √{2gR} , which is independent from angle of projection.So , escape velocity will be same , when a projectile is fired at 45° to the horizontal .

Hence, answer is v

Answer 2

Answer:

Escape velocity is independent of the angle of projection #fact

So answer is v