Q8 · 2022 · Paper 2Complex familiar4 marks
QUESTION 8 (4 marks)
The graph shows the gravitational force experienced by a rocket of mass as it approaches an asteroid.
Determine the mass of the asteroid. Show your working.
WORKED SOLUTION
4 marksQCAA guide · typeset solution
ANSWER
See worked solution below.
Worked solution
Given
2
GMm
F
r
=
, gradient
GMm
=
2
24
8
44
2
1
2
1
13
13
10
10
1
1
16
5.71
0
y
y
gradient
x
x
−
−
×
×
×
−
=
−
−
=
−
=
1
5.71
6.
12
11
10
10
750
2
10
11
10
750
20
1
67
5.71
6.67
.1 10
M
g
gradient
G
M
Mm
k
−
×
×
×
×
×
×
=
=
−
×
=
=
Mass of asteroid = 1.1 × 1020 kg (to two significant figures)
• recognises the scenario relates to Newton’s Law
of Universal Gravitation [1 mark]
• provides appropriate mathematical reasoning
[1 mark]
• determines the gradient [1 mark]
• determines the mass of the asteroid [1 mark]
One QCAA sample method typeset for web; criterion wording is adapted from the official marking guide.
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Compare your working with the guide above.