A projectile is fired vertically upwards. It escapes from theearth, wh

1.	A projectile is fired vertically upwards. It escapes from theearth, when fired with velocity v. If it is to be fired at 45° tohorizontal, what should be its velocity to enable it toescape from the gravitational pull of the earth
Answer» 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/Rve = √{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

A projectile is fired vertically upwards. It escapes from theearth, when fired with velocity v. If it is to be fired at 45° tohorizontal, what should be its velocity to enable it toescape from the gravitational pull of the earth

Answer»

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/Rve = √{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

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