(a) A rocket with initial velocity u ms-1 is projected vertically upwards from the surface of a planet. The acceleration due to gravity is 4 ms-2 towards the centre of the planet, where x is the distance in metres from the centre of the planet and k E R . Assume air resistance is negligible. (i) Show that k = gr*, where r is the radius of the planet in metres and g ms-2 is the 1 acceleration due to gravity at the surface of the planet. (ii) Given that the speed of the rocket at a distance x metres from the centre is v ms -1, 2 show that: 2k 12 = uz + 3 (iii) Give an expression for the escape velocity in terms of g and r. 2 (iv) If u2 = 297 find the time taken for the rocket to travel to a point 3r metres above 2 the planet's surface. Give your answer in terms of g and r. (v) If u2 = , find the distance travelled before the rocket returns to the planet. Give 2 your answer in terms of r