1. H
Answers are in notes to slide 2

2. 5 13 1 9 17 6 14 2 10 18 H 7 15 3 11 19 8 16
Answers:
5a/2 (June 2006 Q 4(a)(i))
4 N (January Q 1(b))
25.6 ms-1 (velocity: 8i j)
52 cm
1/8
96 2/3 N
5156 J
41.6° (M2 Ex 5D Q 3a)
2000 kg
4a/3 (June 2006 Q 4(a)(ii))
( …)
45 cm (June 2007 Q5)
-100 m
2/3 s
0.414 s
25°
77.2° (velocity 10/3i j)
4.14 ms-1 (a = 7g/16)
1/15 < e ≤ 1
38i + 15j 4 12 20

3. BACK TO THE BLOCKBUSTER GRID1
Find the distance of the centre of mass from AB
C (6m)
D (2m) 2a 3a
Each rod has
mass m A B
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4. BACK TO THE BLOCKBUSTER GRID2
A parcel of mass 2.5 kg is moving at 8 m s-1 on a smooth surface. It is brought to rest in 20 m by a force R.
Find the value of R.
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5. BACK TO THE BLOCKBUSTER GRID3
A ball is projected with velocity (pi + qj) m s-1 at angle q above horizontal from a point 0.9 m up. It lands 5 seconds later, 40 m away horizontally.
Find the initial speed.
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6. BACK TO THE BLOCKBUSTER GRID4
A sign is in the shape of a lamina. Find the distance of the centre of mass from AD. A E D
90 cm
40 cm A C
120 cm
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7. BACK TO THE BLOCKBUSTER GRID5
Jane has a four sided dice numbered from 1 to 4. She rolls it twice. Find the probability that the sum of her scores is 7.
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8. BACK TO THE BLOCKBUSTER GRID6
A car of mass 1000kg is moving up an incline of q, where sin q = 1/15.
The resistance is R.
The engine power is 15 kW, and the speed is 20 ms-1.
Find R.
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9. BACK TO THE BLOCKBUSTER GRID7
Find the kinetic energy gained by a 70 kg skier descending 100 m along a 10° downward slope, where m = 0.1 (ignore air resistance).
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10. BACK TO THE BLOCKBUSTER GRID8
A ladder mass 20 kg rests against a smooth wall. The coefficient of friction at the base is ¾.
10 kg is attached at A, and the ladder is about to slip.
Find the angle between the ladder and the ground.
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11. BACK TO THE BLOCKBUSTER GRID9
A car travels at 25 m/s. The engine produces a power of 30 kW.
Air resistance is 500 N.
The coefficient of friction is 0.35.
Find the mass of the car.
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12. BACK TO THE BLOCKBUSTER GRID10
Find the distance of the centre of mass from AD
C (6m)
D (2m) 2a 3a
Each rod has
mass m
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13. BACK TO THE BLOCKBUSTER GRID11
Find the distance of the centre of mass of the lamina from the centre O… to 5 s.f.
5 cm O
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14. BACK TO THE BLOCKBUSTER GRID12
A 2 kg beam is AB supported horizontally by a free hinge and a rope at C, inclined at 30°. AC = 0.14 m. The tension in the rope is 63 N. Find AB. A C B
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15. BACK TO THE BLOCKBUSTER GRID13
At time t, the velocity of P is given by 𝑣=8𝑡− 3 2 𝑡 2
At time t = 0, s = 0.
Find the displacement after 10 s of motion.
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16. BACK TO THE BLOCKBUSTER GRID14
A particle moves with acceleration (3t + 5) ms-2. When t = 0 velocity is 2 ms-1. Later, when t = T the velocity is 6 ms-1. Find T.
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17. BACK TO THE BLOCKBUSTER GRID15
A particle starts from rest and moves with constant acceleration.
It travels 1 m in 1 s.
How long will it take to travel the next 1 m?
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18. BACK TO THE BLOCKBUSTER GRID16
A toy car goes down a smooth 2 m ramp from rest. It reaches the bottom with velocity 4.07 ms-1.
Find the angle of the ramp.
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19. BACK TO THE BLOCKBUSTER GRID17
A hippo is launched from ground level, and lands 3 seconds later 10 m away.
Modelling the hippo as a particle, find the angle of projection above horizontal.
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20. BACK TO THE BLOCKBUSTER GRID18
Two particles are connected by a smooth pulley. A (3 kg) is on a smooth 30° slope, B (5 kg) hangs freely, 2 m above the ground.
They are released from rest. Find the speed of B when it hits the floor.
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21. BACK TO THE BLOCKBUSTER GRID19
Two particles P and Q collide. The direction of P is reversed. Find the range of possible values for the coefficient of restitution. P
3 kg Q
5 kg
2 ms-1
1 ms-1
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22. BACK TO THE BLOCKBUSTER GRID20
A 0.5 kg particle is acted on by a force
F = (3t2 – 1)i + 2tj.
At time t = 2, the velocity is
v = (2i + 5j) ms-1.
Find the velocity when t = 3.
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