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AQA M1 2014 June Q2
5 marks Moderate -0.8
2 Three forces are in equilibrium in a vertical plane, as shown in the diagram. There is a vertical force of magnitude 40 N and a horizontal force of magnitude 60 N . The third force has magnitude \(F\) newtons and acts at an angle \(\theta\) above the horizontal. \includegraphics[max width=\textwidth, alt={}, center]{788534a5-abbb-4d6a-87b2-c54e859a128a-04_490_894_456_571}
  1. \(\quad\) Find \(F\).
  2. \(\quad\) Find \(\theta\).
AQA M1 2014 June Q3
15 marks Moderate -0.8
3 A skip, of mass 800 kg , is at rest on a rough horizontal surface. The coefficient of friction between the skip and the ground is 0.4 . A rope is attached to the skip and then the rope is pulled by a van so that the rope is horizontal while it is taut, as shown in the diagram. \includegraphics[max width=\textwidth, alt={}, center]{788534a5-abbb-4d6a-87b2-c54e859a128a-06_237_1118_497_463} The mass of the van is 1700 kg . A constant horizontal forward driving force of magnitude \(P\) newtons acts on the van. The skip and the van accelerate at \(0.05 \mathrm {~ms} ^ { - 2 }\). Model both the van and the skip as particles connected by a light inextensible rope. Assume that there is no air resistance acting on the skip or on the van.
  1. Find the speed of the van and the skip when they have moved 6 metres.
  2. Draw a diagram to show the forces acting on the skip while it is accelerating.
  3. Draw a diagram to show the forces acting on the van while it is accelerating. State one advantage of modelling the van as a particle when considering the vertical forces.
  4. Find the magnitude of the friction force acting on the skip.
  5. Find the tension in the rope.
  6. \(\quad\) Find \(P\).
    \includegraphics[max width=\textwidth, alt={}]{788534a5-abbb-4d6a-87b2-c54e859a128a-06_771_1703_1932_155}
AQA M1 2014 June Q4
10 marks Standard +0.3
4 A boat is crossing a river, which has two parallel banks. The width of the river is 20 metres. The water in the river is flowing at a speed of \(V \mathrm {~m} \mathrm {~s} ^ { - 1 }\). The boat sets off from the point \(O\) on one bank. The point \(A\) is directly opposite \(O\) on the other bank. The velocity of the boat relative to the water is \(2 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) at an angle of \(70 ^ { \circ }\) to the bank. The boat lands at the point \(B\) which is 3 metres from \(A\). The angle between the actual path of the boat and the bank is \(\alpha ^ { \circ }\). The river and the velocities are shown in the diagram. \includegraphics[max width=\textwidth, alt={}, center]{788534a5-abbb-4d6a-87b2-c54e859a128a-10_490_1307_641_370}
  1. Find the time that it takes for the boat to cross the river.
  2. Find \(\alpha\).
  3. \(\quad\) Find \(V\).
AQA M1 2014 June Q5
5 marks Moderate -0.3
5 Two particles, \(A\) and \(B\), have masses of \(m\) and \(k m\) respectively, where \(k\) is a constant. The particles are moving on a smooth horizontal plane when they collide and coalesce to form a single particle. Just before the collision the velocities of \(A\) and \(B\) are \(( 4 \mathbf { i } + 2 \mathbf { j } ) \mathrm { m } \mathrm { s } ^ { - 1 }\) and \(( 6 \mathbf { i } - 2 \mathbf { j } ) \mathrm { m } \mathrm { s } ^ { - 1 }\) respectively. Immediately after the collision the combined particle has velocity \(( 5.2 \mathbf { i } - 0.4 \mathbf { j } ) \mathrm { m } \mathrm { s } ^ { - 1 }\). Find \(k\).
[0pt] [5 marks]
AQA M1 2014 June Q6
8 marks Standard +0.3
6 A bullet is fired from a rifle at a target, which is at a distance of 420 metres from the rifle. The bullet leaves the rifle travelling at \(V \mathrm {~m} \mathrm {~s} ^ { - 1 }\) and at an angle of \(2 ^ { \circ }\) above the horizontal. The centre of the target, \(C\), is at the same horizontal level as the rifle. The bullet hits the target at the point \(A\), which is on a vertical line through \(C\). The bullet takes 1.8 seconds to reach the point \(A\).
  1. Find \(V\), showing clearly how you obtain your answer.
  2. Find the distance between \(A\) and \(C\).
  3. State one assumption that you have made about the forces acting on the bullet.
    [0pt] [1 mark]
AQA M1 2014 June Q7
11 marks Standard +0.3
7 Two particles, \(A\) and \(B\), move on a horizontal surface with constant accelerations of \(- 0.4 \mathbf { i } \mathrm {~m} \mathrm {~s} ^ { - 2 }\) and \(0.2 \mathbf { j } \mathrm {~m} \mathrm {~s} ^ { - 2 }\) respectively. At time \(t = 0\), particle \(A\) starts at the origin with velocity \(( 4 \mathbf { i } + 2 \mathbf { j } ) \mathrm { m } \mathrm { s } ^ { - 1 }\). At time \(t = 0\), particle \(B\) starts at the point with position vector \(11.2 \mathbf { i }\) metres, with velocity \(( 0.4 \mathbf { i } + 0.6 \mathbf { j } ) \mathrm { m } \mathrm { s } ^ { - 1 }\).
  1. Find the position vector of \(A , 10\) seconds after it leaves the origin.
    [0pt] [2 marks]
  2. Show that the two particles collide, and find the position vector of the point where they collide.
    [0pt] [9 marks]
    \includegraphics[max width=\textwidth, alt={}]{788534a5-abbb-4d6a-87b2-c54e859a128a-16_1881_1707_822_153}
    \includegraphics[max width=\textwidth, alt={}]{788534a5-abbb-4d6a-87b2-c54e859a128a-17_2484_1707_221_153}
AQA M1 2014 June Q8
12 marks Standard +0.3
8 A crate, of mass 40 kg , is initially at rest on a rough slope inclined at \(30 ^ { \circ }\) to the horizontal, as shown in the diagram. \includegraphics[max width=\textwidth, alt={}, center]{788534a5-abbb-4d6a-87b2-c54e859a128a-18_355_882_411_587} The coefficient of friction between the crate and the slope is \(\mu\).
  1. Given that the crate is on the point of slipping down the slope, find \(\mu\).
  2. A horizontal force of magnitude \(X\) newtons is now applied to the crate, as shown in the diagram. \includegraphics[max width=\textwidth, alt={}, center]{788534a5-abbb-4d6a-87b2-c54e859a128a-18_357_881_1208_575}
    1. Find the normal reaction on the crate in terms of \(X\).
    2. Given that the crate accelerates up the slope at \(0.2 \mathrm {~m} \mathrm {~s} ^ { - 2 }\), find \(X\).
      [0pt] [5 marks]
      \includegraphics[max width=\textwidth, alt={}]{788534a5-abbb-4d6a-87b2-c54e859a128a-19_2484_1707_221_153}
AQA M1 2015 June Q1
3 marks Easy -1.2
1 A child, of mass 48 kg , is initially standing at rest on a stationary skateboard. The child jumps off the skateboard and initially moves horizontally with a speed of \(1.2 \mathrm {~m} \mathrm {~s} ^ { - 1 }\). The skateboard moves with a speed of \(16 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) in the opposite direction to the direction of motion of the child. Find the mass of the skateboard.
[0pt] [3 marks]
AQA M1 2015 June Q2
5 marks Moderate -0.3
2 A yacht is sailing through water that is flowing due west at \(2 \mathrm {~m} \mathrm {~s} ^ { - 1 }\). The velocity of the yacht relative to the water is \(6 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) due south. The yacht has a resultant velocity of \(V \mathrm {~m} \mathrm {~s} ^ { - 1 }\) on a bearing of \(\theta\).
  1. \(\quad\) Find \(V\).
  2. Find \(\theta\), giving your answer to the nearest degree.
AQA M1 2015 June Q3
7 marks Moderate -0.3
3 A ship has a mass of 500 tonnes. Two tugs are used to pull the ship using cables that are horizontal. One tug exerts a force of 100000 N at an angle of \(25 ^ { \circ }\) to the centre line of the ship. The other tug exerts a force of \(T \mathrm {~N}\) at an angle of \(20 ^ { \circ }\) to the centre line of the ship. The diagram shows the ship and forces as viewed from above. \includegraphics[max width=\textwidth, alt={}, center]{01338c87-302c-420f-a473-39b0796ccaed-06_279_844_539_664} The ship accelerates in a straight line along its centre line.
  1. \(\quad\) Find \(T\).
  2. A resistance force of magnitude 20000 N directly opposes the motion of the ship. Find the acceleration of the ship.
    [0pt] [4 marks]
    \includegraphics[max width=\textwidth, alt={}]{01338c87-302c-420f-a473-39b0796ccaed-06_1419_1714_1288_153}
AQA M1 2015 June Q4
10 marks Moderate -0.8
4 A particle moves with constant acceleration between the points \(A\) and \(B\). At \(A\), it has velocity \(( 4 \mathbf { i } + 2 \mathbf { j } ) \mathrm { m } \mathrm { s } ^ { - 1 }\). At \(B\), it has velocity \(( 7 \mathbf { i } + 6 \mathbf { j } ) \mathrm { m } \mathrm { s } ^ { - 1 }\). It takes 10 seconds to move from \(A\) to \(B\).
  1. Find the acceleration of the particle.
  2. Find the distance between \(A\) and \(B\).
  3. Find the average velocity as the particle moves from \(A\) to \(B\).
AQA M1 2015 June Q5
16 marks Standard +0.3
5 A block, of mass \(3 m\), is placed on a horizontal surface at a point \(A\). A light inextensible string is attached to the block and passes over a smooth peg. The string is horizontal between the block and the peg. A particle, of mass \(2 m\), is attached to the other end of the string. The block is released from rest with the string taut and the string between the peg and the particle vertical, as shown in the diagram. \includegraphics[max width=\textwidth, alt={}, center]{01338c87-302c-420f-a473-39b0796ccaed-10_170_726_536_657} Assume that there is no air resistance acting on either the block or the particle, and that the size of the block is negligible. The horizontal surface is smooth between the points \(A\) and \(B\), but rough between the points \(B\) and \(C\). Between \(B\) and \(C\), the coefficient of friction between the block and the surface is 0.8 .
  1. By forming equations of motion for both the block and the particle, find the acceleration of the block between \(A\) and \(B\).
  2. Given that the distance between the points \(A\) and \(B\) is 1.2 metres, find the speed of the block when it reaches \(B\).
  3. By forming equations of motion for both the block and the particle, find the acceleration of the block between \(B\) and \(C\).
  4. Given that the distance between the points \(B\) and \(C\) is 0.9 metres, find the speed of the block when it reaches \(C\).
  5. Explain why it is important to assume that the size of the block is negligible.
    [0pt] [1 mark]
AQA M1 2015 June Q6
12 marks Standard +0.3
6 Emma is in a park with her dog, Roxy. Emma throws a ball and Roxy catches it in her mouth. The ground in the park is horizontal. Emma throws the ball from a point at a height of 1.2 metres above the ground and Roxy catches the ball when it is at a height of 0.5 metres above the ground. Emma throws the ball with an initial velocity of \(8 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) at an angle of \(30 ^ { \circ }\) above the horizontal.
  1. Find the time that the ball takes to travel from Emma's hand to Roxy's mouth.
  2. Find the horizontal distance travelled by the ball during its flight.
  3. During the flight, the speed of the ball is a maximum when it is at a height of \(h\) metres above the ground. Write down the value of \(h\).
  4. Find the maximum speed of the ball during its flight.
    [0pt] [4 marks]
    \includegraphics[max width=\textwidth, alt={}]{01338c87-302c-420f-a473-39b0796ccaed-14_1566_1707_1137_153}
AQA M1 2015 June Q7
11 marks Standard +0.3
7 Two forces, which act in a vertical plane, are applied to a crate. The crate has mass 50 kg , and is initially at rest on a rough horizontal surface. One force has magnitude 80 N and acts at an angle of \(30 ^ { \circ }\) to the horizontal and the other has magnitude 40 N and acts at an angle of \(20 ^ { \circ }\) to the horizontal. The forces are shown in the diagram. \includegraphics[max width=\textwidth, alt={}, center]{01338c87-302c-420f-a473-39b0796ccaed-16_241_999_493_523} The coefficient of friction between the crate and the surface is 0.6 . Model the crate as a particle.
  1. Draw a diagram to show the forces acting on the crate.
  2. Find the magnitude of the normal reaction force acting on the crate.
  3. Does the crate start to move when the two forces are applied to the crate? Show all your working.
  4. State one aspect of the possible motion of the crate that is ignored by modelling it as a particle.
    [0pt] [1 mark]
AQA M1 2015 June Q8
11 marks Standard +0.3
8 Two trains, \(A\) and \(B\), are moving on straight horizontal tracks which run alongside each other and are parallel. The trains both move with constant acceleration. At time \(t = 0\), the fronts of the trains pass a signal. The velocities of the trains are shown in the graph below. \includegraphics[max width=\textwidth, alt={}, center]{01338c87-302c-420f-a473-39b0796ccaed-18_633_1077_475_424}
  1. Find the distance between the fronts of the two trains when they have the same velocity and state which train has travelled further from the signal.
  2. Find the time when \(A\) has travelled 9 metres further than \(B\).
    \includegraphics[max width=\textwidth, alt={}]{01338c87-302c-420f-a473-39b0796ccaed-20_2288_1707_221_153}
AQA M1 2016 June Q2
3 marks Moderate -0.8
2 Three forces \(( 4 \mathbf { i } + 7 \mathbf { j } ) \mathrm { N } , ( p \mathbf { i } + 5 \mathbf { j } ) \mathrm { N }\) and \(( - 8 \mathbf { i } + q \mathbf { j } ) \mathrm { N }\) act on a particle of mass 5 kg to produce an acceleration of \(( 2 \mathbf { i } - \mathbf { j } ) \mathrm { m } \mathrm { s } ^ { - 2 }\). No other forces act on the particle.
  1. Find the resultant force acting on the particle in terms of \(p\) and \(q\).
  2. \(\quad\) Find \(p\) and \(q\).
  3. Given that the particle is initially at rest, find the displacement of the particle from its initial position when these forces have been acting for 4 seconds.
    [0pt] [3 marks]
AQA M1 2016 June Q3
4 marks Moderate -0.8
3 A toy car is placed at the top of a ramp. After the car has been released from rest, it travels a distance of 1.08 metres down the ramp, in a time of 1.2 seconds. Assume that there is no resistance to the motion of the car.
  1. Find the magnitude of the acceleration of the car while it is moving down the ramp.
  2. Find the speed of the car, when it has travelled 1.08 metres down the ramp.
  3. Find the angle between the ramp and the horizontal, giving your answer to the nearest degree.
    [0pt] [4 marks]
AQA M1 2016 June Q4
3 marks Moderate -0.8
4 An aeroplane is flying in air that is moving due east at \(V \mathrm {~m} \mathrm {~s} ^ { - 1 }\). Relative to the air, the aeroplane has a velocity of \(90 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) due north. During a 20 second period, the motion of the air causes the aeroplane to move 240 metres to the east.
  1. \(\quad\) Find \(V\).
  2. Find the magnitude of the resultant velocity of the aeroplane.
  3. Find the direction of the resultant velocity, giving your answer as a three-figure bearing, correct to the nearest degree.
    [0pt] [3 marks]
AQA M1 2016 June Q5
4 marks Moderate -0.3
5 Two particles, of masses 3 kg and 7 kg , are connected by a light inextensible string that passes over a smooth peg. The 3 kg particle is held at ground level with the string above it taut and vertical. The 7 kg particle is at a height of 80 cm above ground level, as shown in the diagram. \includegraphics[max width=\textwidth, alt={}, center]{5dd17095-18a6-470b-a24a-4456c8e3ed31-10_469_600_486_721} The 3 kg particle is then released from rest.
  1. By forming two equations of motion, show that the magnitude of the acceleration of the particles is \(3.92 \mathrm {~m} \mathrm {~s} ^ { - 2 }\).
  2. Find the speed of the 7 kg particle just before it hits the ground.
  3. When the 7 kg particle hits the ground, the string becomes slack and in the subsequent motion the 3 kg particle does not hit the peg. Find the maximum height of the 3 kg particle above the ground.
    [0pt] [4 marks]
AQA M1 2016 June Q6
6 marks Standard +0.3
6 A floor polisher consists of a heavy metal block with a polishing cloth attached to the underside. A light rod is also attached to the block and is used to push the block across the floor that is to be polished. The block has mass 5 kg . Assume that the floor is horizontal. Model the block as a particle. The coefficient of friction between the cloth and the floor is 0.2 .
A person pushes the rod to exert a force on the block. The force is at an angle of \(60 ^ { \circ }\) to the horizontal and the block accelerates at \(0.9 \mathrm {~m} \mathrm {~s} ^ { - 2 }\). The diagram shows the block and the force exerted by the rod in this situation. \includegraphics[max width=\textwidth, alt={}, center]{5dd17095-18a6-470b-a24a-4456c8e3ed31-14_309_205_772_1009} The rod exerts a force of magnitude \(T\) newtons on the block.
  1. Find, in terms of \(T\), the magnitude of the normal reaction force acting on the block.
  2. \(\quad\) Find \(T\).
    [0pt] [6 marks]
AQA M1 2016 June Q7
11 marks Moderate -0.3
7 At a school fair, there is a competition in which people try to kick a football so that it lands in a large rectangular box. The height of the top of the box is 1 metre and its width is 3 metres. One student kicks a football so that it initially moves at \(12 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) at an angle of \(50 ^ { \circ }\) above the horizontal. It hits the top front edge of the box, as shown in the diagram below. \includegraphics[max width=\textwidth, alt={}, center]{5dd17095-18a6-470b-a24a-4456c8e3ed31-16_465_1342_625_351} Model the football as a particle that is not subject to any resistance forces as it moves.
  1. Find the time taken for the football to move from the point where it was kicked to the box.
  2. Find the horizontal distance from the point where the football is kicked to the front of the box.
  3. If the same student kicks the football at the same angle from the same initial position, what is the speed at which the student should kick the football if it is to hit the top back edge of the box?
  4. Explain the significance of modelling the football as a particle in this context.
    [0pt] [1 mark]
    \includegraphics[max width=\textwidth, alt={}]{5dd17095-18a6-470b-a24a-4456c8e3ed31-23_2488_1709_219_153}
    \section*{DO NOT WRITE ON THIS PAGE ANSWER IN THE SPACES PROVIDED}
Edexcel M1 Q1
6 marks Moderate -0.8
  1. A bee flies in a straight line from \(A\) to \(B\), where \(\overrightarrow { A B } = \left( 3 \frac { 1 } { 2 } \mathbf { i } - 12 \mathbf { j } \right) \mathrm { m }\), in 5 seconds at a constant speed. Find
    1. the straight-line distance \(A B\),
    2. the speed of the bee,
    3. the velocity vector of the bee.
    4. A small ball \(B\), of mass 0.8 kg , is suspended from a horizontal ceiling by two light inextensible strings. \(B\) is in equilibrium under gravity with both strings inclined at \(30 ^ { \circ }\) to the horizontal, as shown. \includegraphics[max width=\textwidth, alt={}, center]{3e495748-ccb7-4c99-8387-160c4f0f9d4f-1_163_438_758_1480}
    5. Find the tension, in N , in either string.
    6. Calculate the magnitude of the least horizontal force that must be applied to \(B\) in this position to cause one string to become slack.
    7. A particle \(P\) moves in a straight line through a fixed point \(O\) with constant acceleration \(a \mathrm {~ms} ^ { - 2 }\). 3 seconds after passing through \(O , P\) is 6 m from \(O\).
      After a further 6 seconds, \(P\) has travelled a further 33 m in the same direction. Calculate
    8. the value of \(a\),
    9. the speed with which \(P\) passed through \(O\).
    10. A force of magnitude \(F \mathrm {~N}\) is applied to a block of mass \(M \mathrm {~kg}\) which is initially at rest on a horizontal plane. The block starts to move with acceleration \(3 \mathrm {~ms} ^ { - 2 }\). Modelling the block as a particle, \includegraphics[max width=\textwidth, alt={}, center]{3e495748-ccb7-4c99-8387-160c4f0f9d4f-1_134_405_1672_1540}
    11. if the plane is smooth, find an expression for \(F\) in terms of \(M\).
    If the plane is rough, and the coefficient of friction between the block and the plane is \(\mu\),
  2. express \(F\) in terms of \(M , \mu\) and \(g\).
  3. Calculate the value of \(\mu\) if \(F = \frac { 1 } { 2 } M g\).
Edexcel M1 Q5
12 marks Standard +0.3
5. Two metal weights \(A\) and \(B\), of masses 2.4 kg and 1.8 kg respectively, are attached to the ends of a light inextensible string which passes over a smooth fixed pulley so that the string hangs vertically on each side. The system is released from rest with the string taut.
  1. Calculate the acceleration of each weight and the tension in the string. \(A\) is now replaced by a different weight of mass \(m \mathrm {~kg}\), where \(m < 1 \cdot 8\), and the system is again released from rest. The magnitude of the acceleration has half of its previous value.
  2. Calculate the value of \(m\).
    (6 marks) \section*{MECHANICS 1 (A)TEST PAPER 1 Page 2}
Edexcel M1 Q6
12 marks Standard +0.3
  1. The diagram shows the speed-time graph for a particle during a period of \(9 T\) seconds. \includegraphics[max width=\textwidth, alt={}, center]{3e495748-ccb7-4c99-8387-160c4f0f9d4f-2_406_1162_319_351}
    1. If \(T = 5\), find
      1. the acceleration for each section of the motion,
      2. the total distance travelled by the particle.
    2. Sketch, for this motion,
      1. an acceleration-time graph,
      2. a displacement-time graph.
    3. Calculate the value of \(T\) for which the distance travelled over the \(9 T\) seconds is 3.708 km .
    4. Two smooth spheres \(A\) and \(B\), of masses 60 grams and 90 grams respectively, are at rest on a smooth horizontal table. \(A\) is projected towards \(B\) with speed \(4 \mathrm {~ms} ^ { - 1 }\) and the particles collide. After the collision, \(A\) and \(B\) move in the same direction as each other, with speeds \(u \mathrm {~ms} ^ { - 1 }\) and \(6 u \mathrm {~ms} ^ { - 1 }\) respectively. Calculate
    5. the value of \(u\),
    6. the magnitude of the impulse exerted by \(A\) on \(B\), stating the units of your answer.
      (3 marks) \(A\) and \(B\) are now replaced in their original positions and projected towards each other with speeds \(2 \mathrm {~ms} ^ { - 1 }\) and \(8 \mathrm {~ms} ^ { - 1 }\) respectively. They collide again, after which \(A\) moves with speed \(7 \mathrm {~ms} ^ { - 1 }\), its direction of motion being reversed.
    7. Find the speed of \(B\) after this collision and state whether its direction of motion has been reversed.
    8. In a theatre, three lights \(A , B\) and \(C\) are suspended from a horizontal beam \(X Y\) of length \(4.5 \mathrm {~m} . A\) and \(C\) are each of mass 8 kg and \(B\) is of mass 6 kg . The beam \(X Y\) is held in place by vertical ropes \(P X\) and \(Q Y\), as shown. \includegraphics[max width=\textwidth, alt={}, center]{3e495748-ccb7-4c99-8387-160c4f0f9d4f-2_282_643_2104_1316}
    In a simple mathematical model of this situation, \(X Y\) is modelled as a light rod.
  2. Calculate the tension in each of \(P X\) and \(Q Y\). In a refined model, \(X Y\) is modelled as a uniform rod of mass \(m \mathrm {~kg}\).
  3. If the tension in \(P X\) is 1.5 times that in \(Q Y\), calculate the value of \(m\).
Edexcel M1 Q1
5 marks Moderate -0.8
  1. A plank of wood \(A B\), of mass 8 kg and length 6 m , rests on a support at \(P\), where \(A P = 4 \mathrm {~m}\). When particles of mass 1 kg and \(k \mathrm {~kg}\) are suspended from \(A\) and \(B\) respectively, the plank rests horizontally in equilibrium.
    Modelling the plank as a uniform rod, find
    1. the value of \(k\),
    2. the magnitude of the force exerted by the support on the plank at \(P\).
    3. Forces of magnitude 4 N and 6 N act in directions which make an angle of \(40 ^ { \circ }\) with each other, as shown. Calculate \includegraphics[max width=\textwidth, alt={}, center]{9c9b6087-d5a1-4fb0-b771-5ccc13a04bc4-1_209_478_840_1348}
    4. the magnitude of the resultant of the two forces,
    5. the angle, in degrees, between the resultant and the 4 N force.
    6. A stone is dropped from rest at a height of 7 m above horizontal ground. It falls vertically, hits the ground and rebounds vertically upwards with half the speed with which it hit the ground. Calculate
    7. the time taken for the stone to fall to the ground,
    8. the speed with which the stone hits the ground,
    9. the height to which the stone rises before it comes to instantaneous rest.
    State two modelling assumptions that you have made.