Question

Question 3 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

Answer 1

uextionn B- Man- 10600 paylond 242 Yocket (o,00 60pe ac 16.238 mf2 15.238X 1X60 = 914.28 V4mls V= 2 momen tum balance Bx .4 D 242xu Bx14 D4 2 hum anity Alay f= m.rw 60-4 -137 X103 rad Te X 56 26. 12 eends .137 G2.1Yminute

Te-enty dusing dariryne-aly larth vi-dhection velociy fr:-resis hance w:- force of gravi