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Question 18N.2.SL.TZ0.1b.i

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Date November 2018 Marks available [Maximum mark: 2] Reference code 18N.2.SL.TZ0.1b.i
Level SL Paper 2 Time zone TZ0
Command term Estimate Question number b.i Adapted from N/A
b.i.
[Maximum mark: 2]
18N.2.SL.TZ0.1b.i

Ion-thrust engines can power spacecraft. In this type of engine, ions are created in a chamber and expelled from the spacecraft. The spacecraft is in outer space when the propulsion system is turned on. The spacecraft starts from rest.

The mass of ions ejected each second is 6.6 × 10–6 kg and the speed of each ion is 5.2 × 104 m s–1. The initial total mass of the spacecraft and its fuel is 740 kg. Assume that the ions travel away from the spacecraft parallel to its direction of motion.

An initial mass of 60 kg of fuel is in the spacecraft for a journey to a planet. Half of the fuel will be required to slow down the spacecraft before arrival at the destination planet.

(b.i)

Estimate the maximum speed of the spacecraft.

[2]

Markscheme

ALTERNATIVE 1:

(considering the acceleration of the spacecraft)

time for acceleration =  30 6.6 × 10 − 6 = «4.6 × 106» «s» ✔

max speed = «answer to (a) × 4.6 × 106 =» 2.1 × 103 «m s−1» ✔

 

ALTERNATIVE 2:

(considering the conservation of momentum)

(momentum of 30 kg of fuel ions = change of momentum of spacecraft)

30 × 5.2 × 104 = 710 × max speed ✔

max speed = 2.2 × 103 «m s−1» ✔

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