Question

A Bullet is fired vertically upwards with velocity v from the surface of a spherical planet. When it reaches its maximum height, its acceleration due to the planet's gravity is 1/4^th of its value at the surface of the planet. If the escape velocity from the planet is v_esc = v√n,  then the value of N is (ignore energy loss due to atmosphere)

Answer 1

When it reaches its maximum height, its acceleration due to the planet's gravity is 1/4th of its value at the surface of the planet.

By conservation of mechanical energy