Q9 · 2022 · Paper 2Complex unfamiliar9 marks
QUESTION 9 (9 marks)
A person spins an object 4.3 m above the ground in a horizontal circular path of radius 0.8 m. They release the object horizontally, allowing it to travel to the ground.
a)[4 marks]
Calculate the centripetal acceleration of the object before it is released, given it takes 5 s for the object to complete 12 revolutions. Show your working. Centripetal acceleration = m s−2 (to two significant figures)
b)[5 marks]
Calculate the total horizontal displacement for the object after it is released. Show your working. Total horizontal displacement = m (to two significant figures)
WORKED SOLUTION
9 marksQCAA guide · typeset solution
ANSWER
See worked solution below.
Worked solution
1
2
2
0.8
5
12
12.1
v
m
r
T
s
π
π
=
×
=
=
−
÷
2
2
2
12.1
0.8
180 m s
v
ac
r
=
=
−
=
Centripetal acceleration = 180 m s-2 (to two significant figures)
2
2
1
2
1
4.3
0
2
4.3
4.
9.8
9
0.94
y
y
s
u t
at
t
s
t
=
+
=
+
=
=
×
2
1
2
0.
0
1
2
12
1
94
0
.94
.1
1.4
2
s
t
x
x
u
at
m
=
+
=
=
×
+
× ×
Horizontal displacement = 11 m (to two significant figures)
• recognises the scenario relates to
velocity in circular motion [1 mark]
centripetal acceleration [1 mark]
• provides appropriate mathematical reasoning
[1 mark]
• calculates the centripetal acceleration of the object
[1 mark]
• recognises the scenario relates to vertical
component of projectile motion [1 mark]
• provides appropriate mathematical reasoning
[1 mark]
• determines the time of flight [1 mark]
• recognises the scenario relates to the horizontal
component of projectile motion [1 mark]
• calculates the total horizontal displacement
[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.