Q4 · 2021 · Paper 2Complex unfamiliar4 marks
QUESTION 4 (4 marks)
A spacecraft is located between two large asteroids, Asteroid A and Asteroid B, that are 120 km apart. Asteroid A’s mass is approximately four times the mass of Asteroid B. Determine the distance of the spacecraft from Asteroid B if it experiences no net gravitational force from the two asteroids.
Distance from Asteroid B = km (to the nearest whole number)
WORKED SOLUTION
4 marksQCAA guide · typeset solution
ANSWER
See worked solution below.
Worked solution
𝐹𝑔,𝑛𝑒𝑡= 0
Therefore |𝐹𝑔,𝐴 | = |𝐹𝑔,𝐵 |
𝐺𝑚𝑠𝑀𝐴
𝑟𝐴
2
= 𝐺𝑚𝑠𝑀𝐵
𝑟𝐵
2
4𝑀𝐵
𝑟𝐴
2 = 𝑀𝐵
𝑟𝐵
2
4𝑀𝐵 × 𝑟𝐵
2 = 𝑟𝐴
2 × 𝑀𝐵
4𝑀𝐵 × 𝑟𝐵
2
𝑀𝐵
= 𝑟𝐴
2
𝑟𝐴
2 = 4𝑟𝐵
2
𝑟𝐴= 2𝑟𝐵
120 = 𝑟𝐴+ 𝑟𝐵
120 = 3𝑟𝐵
𝑟𝐵= 40
Distance from Asteroid B = 40 km (to the nearest whole
number).
• recognises the scenario relates to Newton’s law of
universal gravitation [1 mark]
• recognises that no net force occurs when the
forces are equivalent [1 mark]
• provides appropriate mathematical reasoning
[1 mark]
• determines distance from the asteroid [1 mark]
One QCAA sample method typeset for web; criterion wording is adapted from the official marking guide.
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