Question 18N.2.HL.TZ0.b.i
| Date | November 2018 | Marks available | [Maximum mark: 3] | Reference code | 18N.2.HL.TZ0.b.i |
| Level | HL | Paper | 2 | Time zone | TZ0 |
| Command term | Estimate, Outline | Question number | b.i | Adapted from | N/A |
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.
(i) Estimate the maximum speed of the spacecraft.
(ii) Outline why the answer to (i) is an estimate.
[3]
(i) ALTERNATIVE 1:
(considering the acceleration of the spacecraft)
time for acceleration = = «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» ✔
(ii) as fuel is consumed total mass changes/decreases so acceleration changes/increases
OR
external forces (such as gravitational) can act on the spacecraft so acceleration isn’t constant ✔
