On 21 january 2018, rocket lab launched a 10 500 kg rocket from the mahia penin- sula. it carried a 250 kg payload that included the 8 kg humanity star, which is like a large disco ball in size and shape. (a) on the launchpad, the rocket has a mass of 10 500 kg and produces 160 kn of vertical thrust. assuming that the acceleration is constant and motion is in a straight line, find the speed of the rocket after 1 minute [2 marks] (b) the rocket burns fuel and ejects material until it reaches space and eventually releases its payload. assuming that this 250 kg payload is initially at rest and then the 8 kg humanity star is ejected the remaining payload. speed of 1.4 ms, find the speed of [2 marks] at a (c) the humanity star settles into a circular orbit at a radius of 5800 km from the centre of earth. if the centripetal force acting on the humanity star is 60.1 n, find: (i) the angular velocity, and [6 marks] (ii) the orbital period of the humanity star, to the nearest minute. (d) during re-entry, the humanity star experiences air resistance while travelling in a near-circular orbit around the earth. draw a free-body diagram indicating the directions of the forces acting on the humanity star, and the approximate direc- tion of the net force. [3 marks] humanity star earth