The initial velocity v_i required to project a body vertically upward from the surface of the earth to reach a height of 10R, where R is the radius of the earth, may be described in terms of escape velocity v_e such that $${v_i} = \sqrt {{x \over y}} \times {v_e}$$. The value of x will be ____________.

An asteroid is moving directly towards the centre of the earth. When at a distance of 10R (R is the radius of the earth) from the earths centre, it has a speed of 12 km/s. Neglecting the effect of earths atmosphere, what will be the speed of the asteroid when it hits the surface of the earth (escape velocity from the earth is 11.2 km/s) ? Give your answer to the nearest integer in kilometer/s _____.

A ball is dropped from the top of a 100 m high tower on a planet. In the last $${1 \over 2}s$$ before hitting the ground, it covers a distance of 19 m. Acceleration due to gravity (in ms^–2) near the surface on that planet is _____.