On 21 January 2018, Rocket Lab launched a 10 500 kg rocket from the Mahia Peninsula. It carried a 250 kg payload that included the 8 kg Humanity Star, which is like a large disco ball in size and shape.  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.  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 at a speed of 1.4 m s−1, find the speed of the remaining payload.

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On 21 January 2018, Rocket Lab launched a 10 500 kg rocket from the Mahia Peninsula. It carried a 250 kg payload that included the 8 kg Humanity Star, which is like a large disco ball in size and shape. 

  1. 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. 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 at a speed of 1.4 m s−1, find the speed of the remaining payload.
  3. The Humanity Star settles into a circular orbit at a radius of 6800 km from the centre of Earth. If the centripetal force acting on the Humanity Star is 60.1 N, find: 
    1. the angular velocity, and 
    2. the orbital period of the Humanity Star, in hours and minutes to the nearest minute.
  4. 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 direction of the net force.

 

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Earth
Transcribed Image Text:Humanity star Earth
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