Questions M1 (1912 questions)

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Edexcel M1 2006 January Q6
16 marks Standard +0.3
  1. \hspace{0pt} [In this question the horizontal unit vectors \(\mathbf { i }\) and \(\mathbf { j }\) are due east and due north respectively.]
A model boat \(A\) moves on a lake with constant velocity \(( - \mathbf { i } + 6 \mathbf { j } ) \mathrm { m } \mathrm { s } ^ { - 1 }\). At time \(t = 0 , A\) is at the point with position vector \(( 2 \mathbf { i } - 10 \mathbf { j } ) \mathrm { m }\). Find
  1. the speed of \(A\),
  2. the direction in which \(A\) is moving, giving your answer as a bearing. At time \(t = 0\), a second boat \(B\) is at the point with position vector \(( - 26 \mathbf { i } + 4 \mathbf { j } ) \mathrm { m }\).
    Given that the velocity of \(B\) is \(( 3 \mathbf { i } + 4 \mathbf { j } ) \mathrm { m } \mathrm { s } ^ { - 1 }\),
  3. show that \(A\) and \(B\) will collide at a point \(P\) and find the position vector of \(P\). Given instead that \(B\) has speed \(8 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) and moves in the direction of the vector \(( 3 \mathbf { i } + 4 \mathbf { j } )\),
  4. find the distance of \(B\) from \(P\) when \(t = 7 \mathrm {~s}\).
Edexcel M1 2006 January Q7
14 marks Standard +0.3
7. \begin{figure}[h]
\captionsetup{labelformat=empty} \caption{Figure 3} \includegraphics[alt={},max width=\textwidth]{8d3635b1-2d01-48c1-a19b-37e44d593112-12_232_647_292_653}
\end{figure} A fixed wedge has two plane faces, each inclined at \(30 ^ { \circ }\) to the horizontal. Two particles \(A\) and \(B\), of mass \(3 m\) and \(m\) respectively, are attached to the ends of a light inextensible string. Each particle moves on one of the plane faces of the wedge. The string passes over a small smooth light pulley fixed at the top of the wedge. The face on which \(A\) moves is smooth. The face on which \(B\) moves is rough. The coefficient of friction between \(B\) and this face is \(\mu\). Particle \(A\) is held at rest with the string taut. The string lies in the same vertical plane as lines of greatest slope on each plane face of the wedge, as shown in Figure 3. The particles are released from rest and start to move. Particle \(A\) moves downwards and \(B\) moves upwards. The accelerations of \(A\) and \(B\) each have magnitude \(\frac { 1 } { 10 } g\).
  1. By considering the motion of \(A\), find, in terms of \(m\) and \(g\), the tension in the string.
  2. By considering the motion of \(B\), find the value of \(\mu\).
  3. Find the resultant force exerted by the string on the pulley, giving its magnitude and direction.
Edexcel M1 2007 January Q1
6 marks Moderate -0.8
1. \begin{figure}[h]
\captionsetup{labelformat=empty} \caption{Figure 1} \includegraphics[alt={},max width=\textwidth]{7edcbe3d-dd90-41b4-9b87-fccae38927c7-02_287_625_310_662}
\end{figure} A particle of weight 24 N is held in equilibrium by two light inextensible strings. One string is horizontal. The other string is inclined at an angle of \(30 ^ { \circ }\) to the horizontal, as shown in Figure 1. The tension in the horizontal string is \(Q\) newtons and the tension in the other string is \(P\) newtons. Find
  1. the value of \(P\),
  2. the value of \(Q\).
Edexcel M1 2007 January Q2
10 marks Moderate -0.8
2. \begin{figure}[h]
\captionsetup{labelformat=empty} \caption{Figure 2} \includegraphics[alt={},max width=\textwidth]{7edcbe3d-dd90-41b4-9b87-fccae38927c7-03_246_652_310_653}
\end{figure} A uniform plank \(A B\) has weight 120 N and length 3 m . The plank rests horizontally in equilibrium on two smooth supports \(C\) and \(D\), where \(A C = 1 \mathrm {~m}\) and \(C D = x \mathrm {~m}\), as shown in Figure 2. The reaction of the support on the plank at \(D\) has magnitude 80 N . Modelling the plank as a rod,
  1. show that \(x = 0.75\) A rock is now placed at \(B\) and the plank is on the point of tilting about \(D\). Modelling the rock as a particle, find
  2. the weight of the rock,
  3. the magnitude of the reaction of the support on the plank at \(D\).
  4. State how you have used the model of the rock as a particle.
Edexcel M1 2007 January Q3
9 marks Moderate -0.8
  1. A particle \(P\) of mass 2 kg is moving under the action of a constant force \(\mathbf { F }\) newtons. When \(t = 0 , P\) has velocity ( \(3 \mathbf { i } + 2 \mathbf { j } ) \mathrm { m } \mathrm { s } ^ { - 1 }\) and at time \(t = 4 \mathrm {~s} , P\) has velocity \(( 15 \mathbf { i } - 4 \mathbf { j } ) \mathrm { m } \mathrm { s } ^ { - 1 }\). Find
    1. the acceleration of \(P\) in terms of \(\mathbf { i }\) and \(\mathbf { j }\),
    2. the magnitude of \(\mathbf { F }\),
    3. the velocity of \(P\) at time \(t = 6 \mathrm {~s}\).
    4. A particle \(P\) of mass 0.3 kg is moving with speed \(u \mathrm {~m} \mathrm {~s} ^ { - 1 }\) in a straight line on a smooth horizontal table. The particle \(P\) collides directly with a particle \(Q\) of mass 0.6 kg , which is at rest on the table. Immediately after the particles collide, \(P\) has speed \(2 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) and \(Q\) has speed \(5 \mathrm {~m} \mathrm {~s} ^ { - 1 }\). The direction of motion of \(P\) is reversed by the collision. Find
    5. the value of \(u\),
    6. the magnitude of the impulse exerted by \(P\) on \(Q\).
    Immediately after the collision, a constant force of magnitude \(R\) newtons is applied to \(Q\) in the direction directly opposite to the direction of motion of \(Q\). As a result \(Q\) is brought to rest in 1.5 s .
  2. Find the value of \(R\).
Edexcel M1 2007 January Q5
10 marks Moderate -0.8
  1. A ball is projected vertically upwards with speed \(21 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) from a point \(A\), which is 1.5 m above the ground. After projection, the ball moves freely under gravity until it reaches the ground. Modelling the ball as a particle, find
    1. the greatest height above \(A\) reached by the ball,
    2. the speed of the ball as it reaches the ground,
    3. the time between the instant when the ball is projected from \(A\) and the instant when the ball reaches the ground.
Edexcel M1 2007 January Q6
14 marks Moderate -0.3
6. \begin{figure}[h]
\captionsetup{labelformat=empty} \caption{Figure 3} \includegraphics[alt={},max width=\textwidth]{7edcbe3d-dd90-41b4-9b87-fccae38927c7-10_230_642_298_659}
\end{figure} A box of mass 30 kg is being pulled along rough horizontal ground at a constant speed using a rope. The rope makes an angle of \(20 ^ { \circ }\) with the ground, as shown in Figure 3. The coefficient of friction between the box and the ground is 0.4 . The box is modelled as a particle and the rope as a light, inextensible string. The tension in the rope is \(P\) newtons.
  1. Find the value of \(P\). The tension in the rope is now increased to 150 N .
  2. Find the acceleration of the box.
Edexcel M1 2007 January Q7
16 marks Standard +0.3
7. \begin{figure}[h]
\captionsetup{labelformat=empty} \caption{Figure 4} \includegraphics[alt={},max width=\textwidth]{7edcbe3d-dd90-41b4-9b87-fccae38927c7-12_465_1182_301_420}
\end{figure} Figure 4 shows two particles \(P\) and \(Q\), of mass 3 kg and 2 kg respectively, connected by a light inextensible string. Initially \(P\) is held at rest on a fixed smooth plane inclined at \(30 ^ { \circ }\) to the horizontal. The string passes over a small smooth light pulley \(A\) fixed at the top of the plane. The part of the string from \(P\) to \(A\) is parallel to a line of greatest slope of the plane. The particle \(Q\) hangs freely below \(A\). The system is released from rest with the string taut.
  1. Write down an equation of motion for \(P\) and an equation of motion for \(Q\).
  2. Hence show that the acceleration of \(Q\) is \(0.98 \mathrm {~m} \mathrm {~s} ^ { - 2 }\).
  3. Find the tension in the string.
  4. State where in your calculations you have used the information that the string is inextensible. On release, \(Q\) is at a height of 0.8 m above the ground. When \(Q\) reaches the ground, it is brought to rest immediately by the impact with the ground and does not rebound. The initial distance of \(P\) from \(A\) is such that in the subsequent motion \(P\) does not reach \(A\). Find
  5. the speed of \(Q\) as it reaches the ground,
  6. the time between the instant when \(Q\) reaches the ground and the instant when the string becomes taut again.
Edexcel M1 2008 January Q1
6 marks Moderate -0.8
  1. Two particles \(A\) and \(B\) have masses 4 kg and \(m \mathrm {~kg}\) respectively. They are moving towards each other in opposite directions on a smooth horizontal table when they collide directly. Immediately before the collision, the speed of \(A\) is \(5 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) and the speed of \(B\) is \(3 \mathrm {~m} \mathrm {~s} ^ { - 1 }\). Immediately after the collision, the direction of motion of \(A\) is unchanged and the speed of \(A\) is \(1 \mathrm {~m} \mathrm {~s} ^ { - 1 }\).
    1. Find the magnitude of the impulse exerted on \(A\) in the collision.
    Immediately after the collision, the speed of \(B\) is \(2 \mathrm {~m} \mathrm {~s} ^ { - 1 }\).
  2. Find the value of \(m\).
Edexcel M1 2008 January Q2
8 marks Moderate -0.8
2. A firework rocket starts from rest at ground level and moves vertically. In the first 3 s of its motion, the rocket rises 27 m . The rocket is modelled as a particle moving with constant acceleration \(a \mathrm {~m} \mathrm {~s} ^ { - 2 }\). Find
  1. the value of \(a\),
  2. the speed of the rocket 3 s after it has left the ground. After 3 s , the rocket burns out. The motion of the rocket is now modelled as that of a particle moving freely under gravity.
  3. Find the height of the rocket above the ground 5 s after it has left the ground.
Edexcel M1 2008 January Q3
11 marks Standard +0.3
3. A car moves along a horizontal straight road, passing two points \(A\) and \(B\). At \(A\) the speed of the car is \(15 \mathrm {~m} \mathrm {~s} ^ { - 1 }\). When the driver passes \(A\), he sees a warning sign \(W\) ahead of him, 120 m away. He immediately applies the brakes and the car decelerates with uniform deceleration, reaching \(W\) with speed \(5 \mathrm {~m} \mathrm {~s} ^ { - 1 }\). At \(W\), the driver sees that the road is clear. He then immediately accelerates the car with uniform acceleration for 16 s to reach a speed of \(V \mathrm {~m} \mathrm {~s} ^ { - 1 } ( V > 15 )\). He then maintains the car at a constant speed of \(V \mathrm {~m} \mathrm {~s} ^ { - 1 }\). Moving at this constant speed, the car passes \(B\) after a further 22 s .
  1. Sketch, in the space below, a speed-time graph to illustrate the motion of the car as it moves from \(A\) to \(B\).
  2. Find the time taken for the car to move from \(A\) to \(B\). The distance from \(A\) to \(B\) is 1 km .
  3. Find the value of \(V\).
Edexcel M1 2008 January Q4
11 marks Standard +0.3
4. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{7ba14d10-1b57-4930-8d65-f21088c5d513-06_305_607_246_701} \captionsetup{labelformat=empty} \caption{Figure 1}
\end{figure} A particle \(P\) of mass 6 kg lies on the surface of a smooth plane. The plane is inclined at an angle of \(30 ^ { \circ }\) to the horizontal. The particle is held in equilibrium by a force of magnitude 49 N , acting at an angle \(\theta\) to the plane, as shown in Figure 1. The force acts in a vertical plane through a line of greatest slope of the plane.
  1. Show that \(\cos \theta = \frac { 3 } { 5 }\).
  2. Find the normal reaction between \(P\) and the plane. The direction of the force of magnitude 49 N is now changed. It is now applied horizontally to \(P\) so that \(P\) moves up the plane. The force again acts in a vertical plane through a line of greatest slope of the plane.
  3. Find the initial acceleration of \(P\). \(\_\_\_\_\)}
Edexcel M1 2008 January Q5
11 marks Standard +0.3
5. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{7ba14d10-1b57-4930-8d65-f21088c5d513-08_315_817_255_587} \captionsetup{labelformat=empty} \caption{Figure 2}
\end{figure} A beam \(A B\) has mass 12 kg and length 5 m . It is held in equilibrium in a horizontal position by two vertical ropes attached to the beam. One rope is attached to \(A\), the other to the point \(C\) on the beam, where \(B C = 1 \mathrm {~m}\), as shown in Figure 2. The beam is modelled as a uniform rod, and the ropes as light strings.
  1. Find
    1. the tension in the rope at \(C\),
    2. the tension in the rope at \(A\). A small load of mass 16 kg is attached to the beam at a point which is \(y\) metres from \(A\). The load is modelled as a particle. Given that the beam remains in equilibrium in a horizontal position,
  2. find, in terms of \(y\), an expression for the tension in the rope at \(C\). The rope at \(C\) will break if its tension exceeds 98 N. The rope at \(A\) cannot break.
  3. Find the range of possible positions on the beam where the load can be attached without the rope at \(C\) breaking.
Edexcel M1 2008 January Q6
13 marks Standard +0.3
6. [In this question, the unit vectors \(\mathbf { i }\) and \(\mathbf { j }\) are due east and due north respectively.] A particle \(P\) is moving with constant velocity \(( - 5 \mathbf { i } + 8 \mathbf { j } ) \mathrm { m } \mathrm { s } ^ { - 1 }\). Find
  1. the speed of \(P\),
  2. the direction of motion of \(P\), giving your answer as a bearing. At time \(t = 0 , P\) is at the point \(A\) with position vector ( \(7 \mathbf { i } - 10 \mathbf { j }\) ) m relative to a fixed origin \(O\). When \(t = 3 \mathrm {~s}\), the velocity of \(P\) changes and it moves with velocity \(( u \mathbf { i } + v \mathbf { j } ) \mathrm { m } \mathrm { s } ^ { - 1 }\), where \(u\) and \(v\) are constants. After a further 4 s , it passes through \(O\) and continues to move with velocity ( \(u \mathbf { i } + v \mathbf { j } ) \mathrm { m } \mathrm { s } ^ { - 1 }\).
  3. Find the values of \(u\) and \(v\).
  4. Find the total time taken for \(P\) to move from \(A\) to a position which is due south of A.
Edexcel M1 2008 January Q7
15 marks Standard +0.3
7. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{7ba14d10-1b57-4930-8d65-f21088c5d513-12_292_897_278_415} \captionsetup{labelformat=empty} \caption{Figure 3}
\end{figure} Two particles \(A\) and \(B\), of mass \(m\) and \(2 m\) respectively, are attached to the ends of a light inextensible string. The particle \(A\) lies on a rough horizontal table. The string passes over a small smooth pulley \(P\) fixed on the edge of the table. The particle \(B\) hangs freely below the pulley, as shown in Figure 3. The coefficient of friction between \(A\) and the table is \(\mu\). The particles are released from rest with the string taut. Immediately after release, the magnitude of the acceleration of \(A\) and \(B\) is \(\frac { 4 } { 9 } g\). By writing down separate equations of motion for \(A\) and \(B\),
  1. find the tension in the string immediately after the particles begin to move,
  2. show that \(\mu = \frac { 2 } { 3 }\). When \(B\) has fallen a distance \(h\), it hits the ground and does not rebound. Particle \(A\) is then a distance \(\frac { 1 } { 3 } h\) from \(P\).
  3. Find the speed of \(A\) as it reaches \(P\).
  4. State how you have used the information that the string is light.
Edexcel M1 2009 January Q1
5 marks Moderate -0.3
  1. A particle \(P\) moves with constant acceleration \(( 2 \mathbf { i } - 5 \mathbf { j } ) \mathrm { m } \mathrm { s } ^ { - 2 }\). At time \(t = 0 , P\) has speed \(u \mathrm {~m} \mathrm {~s} ^ { - 1 }\). At time \(t = 3 \mathrm {~s} , P\) has velocity \(( - 6 \mathbf { i } + \mathbf { j } ) \mathrm { m } \mathrm { s } ^ { - 1 }\).
Find the value of \(u\).
(5)
Edexcel M1 2009 January Q2
5 marks Moderate -0.8
2. A small ball is projected vertically upwards from ground level with speed \(u \mathrm {~m} \mathrm {~s} ^ { - 1 }\). The ball takes 4 s to return to ground level.
  1. Draw, in the space below, a velocity-time graph to represent the motion of the ball during the first 4 s .
  2. The maximum height of the ball above the ground during the first 4 s is 19.6 m . Find the value of \(u\).
Edexcel M1 2009 January Q3
9 marks Moderate -0.3
3. Two particles \(A\) and \(B\) are moving on a smooth horizontal plane. The mass of \(A\) is \(k m\), where \(2 < k < 3\), and the mass of \(B\) is \(m\). The particles are moving along the same straight line, but in opposite directions, and they collide directly. Immediately before they collide the speed of \(A\) is \(2 u\) and the speed of \(B\) is \(4 u\). As a result of the collision the speed of \(A\) is halved and its direction of motion is reversed.
  1. Find, in terms of \(k\) and \(u\), the speed of \(B\) immediately after the collision.
  2. State whether the direction of motion of \(B\) changes as a result of the collision, explaining your answer. Given that \(k = \frac { 7 } { 3 }\),
  3. find, in terms of \(m\) and \(u\), the magnitude of the impulse that \(A\) exerts on \(B\) in the collision.
Edexcel M1 2009 January Q4
13 marks Standard +0.3
4. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{86bb11a4-b409-49b1-bffb-d0e3727d345c-05_349_869_303_532} \captionsetup{labelformat=empty} \caption{Figure 1}
\end{figure} A bench consists of a plank which is resting in a horizontal position on two thin vertical legs. The plank is modelled as a uniform rod \(P S\) of length 2.4 m and mass 20 kg . The legs at \(Q\) and \(R\) are 0.4 m from each end of the plank, as shown in Figure 1. Two pupils, Arthur and Beatrice, sit on the plank. Arthur has mass 60 kg and sits at the middle of the plank and Beatrice has mass 40 kg and sits at the end \(P\). The plank remains horizontal and in equilibrium. By modelling the pupils as particles, find
  1. the magnitude of the normal reaction between the plank and the leg at \(Q\) and the magnitude of the normal reaction between the plank and the leg at \(R\). Beatrice stays sitting at \(P\) but Arthur now moves and sits on the plank at the point \(X\). Given that the plank remains horizontal and in equilibrium, and that the magnitude of the normal reaction between the plank and the leg at \(Q\) is now twice the magnitude of the normal reaction between the plank and the leg at \(R\),
  2. find the distance \(Q X\).
Edexcel M1 2009 January Q5
13 marks Standard +0.3
5.
\includegraphics[max width=\textwidth, alt={}]{86bb11a4-b409-49b1-bffb-d0e3727d345c-07_352_834_300_551}
\section*{Figure 2} A small package of mass 1.1 kg is held in equilibrium on a rough plane by a horizontal force. The plane is inclined at an angle \(\alpha\) to the horizontal, where \(\tan \alpha = \frac { 3 } { 4 }\). The force acts in a vertical plane containing a line of greatest slope of the plane and has magnitude \(P\) newtons, as shown in Figure 2. The coefficient of friction between the package and the plane is 0.5 and the package is modelled as a particle. The package is in equilibrium and on the point of slipping down the plane.
  1. Draw, on Figure 2, all the forces acting on the package, showing their directions clearly.
    1. Find the magnitude of the normal reaction between the package and the plane.
    2. Find the value of \(P\).
Edexcel M1 2009 January Q6
14 marks Standard +0.3
6. Two forces, \(( 4 \mathbf { i } - 5 \mathbf { j } ) \mathrm { N }\) and \(( p \mathbf { i } + q \mathbf { j } ) \mathrm { N }\), act on a particle \(P\) of mass \(m \mathrm {~kg}\). The resultant of the two forces is \(\mathbf { R }\). Given that \(\mathbf { R }\) acts in a direction which is parallel to the vector ( \(\mathbf { i } - 2 \mathbf { j }\) ),
  1. find the angle between \(\mathbf { R }\) and the vector \(\mathbf { j }\),
  2. show that \(2 p + q + 3 = 0\). Given also that \(q = 1\) and that \(P\) moves with an acceleration of magnitude \(8 \sqrt { } 5 \mathrm {~m} \mathrm {~s} ^ { - 2 }\), (c) find the value of \(m\).
Edexcel M1 2009 January Q7
16 marks Standard +0.3
7. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{86bb11a4-b409-49b1-bffb-d0e3727d345c-11_495_892_301_523} \captionsetup{labelformat=empty} \caption{Figure 3}
\end{figure} One end of a light inextensible string is attached to a block \(P\) of mass 5 kg . The block \(P\) is held at rest on a smooth fixed plane which is inclined to the horizontal at an angle \(\alpha\), where \(\sin \alpha = \frac { 3 } { 5 }\). The string lies along a line of greatest slope of the plane and passes over a smooth light pulley which is fixed at the top of the plane. The other end of the string is attached to a light scale pan which carries two blocks \(Q\) and \(R\), with block \(Q\) on top of block \(R\), as shown in Figure 3. The mass of block \(Q\) is 5 kg and the mass of block \(R\) is 10 kg . The scale pan hangs at rest and the system is released from rest. By modelling the blocks as particles, ignoring air resistance and assuming the motion is uninterrupted, find
    1. the acceleration of the scale pan,
    2. the tension in the string,
  2. the magnitude of the force exerted on block \(Q\) by block \(R\),
  3. the magnitude of the force exerted on the pulley by the string.
OCR M1 2005 January Q1
6 marks Standard +0.3
1
\includegraphics[max width=\textwidth, alt={}, center]{5b10afa1-1c45-4370-a0e6-ad8fd626df9a-2_200_537_269_804} A box of weight 100 N rests in equilibrium on a plane inclined at an angle \(\alpha\) to the horizontal. It is given that \(\sin \alpha = 0.28\) and \(\cos \alpha = 0.96\). A force of magnitude \(P \mathrm {~N}\) acts on the box parallel to the plane in the upwards direction (see diagram). The coefficient of friction between the box and the plane is 0.25 .
  1. Find the magnitude of the normal force acting on the box.
  2. Given that the equilibrium is limiting, show that the magnitude of the frictional force acting on the box is 24 N .
  3. Find the value of \(P\) for which the box is on the point of slipping
    (a) down the plane,
    (b) up the plane.
OCR M1 2005 January Q2
8 marks Standard +0.3
2
\includegraphics[max width=\textwidth, alt={}, center]{5b10afa1-1c45-4370-a0e6-ad8fd626df9a-2_221_1153_1340_497} Three small uniform spheres \(A , B\) and \(C\) have masses \(0.4 \mathrm {~kg} , 1.2 \mathrm {~kg}\) and \(m \mathrm {~kg}\) respectively. The spheres move in the same straight line on a smooth horizontal table, with \(B\) between \(A\) and \(C\). Sphere \(A\) is moving towards \(B\) with speed \(6 \mathrm {~ms} ^ { - 1 } , B\) is moving towards \(A\) with speed \(2 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) and \(C\) is moving towards \(B\) with speed \(4 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) (see diagram). Spheres \(A\) and \(B\) collide. After this collision \(B\) moves with speed \(1 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) towards \(C\).
  1. Find the speed with which \(A\) moves after the collision and state the direction of motion of \(A\).
  2. Spheres \(B\) and \(C\) now collide and move away from each other with speeds \(0.5 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) and \(2 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) respectively. Find the value of \(m\).
OCR M1 2005 January Q3
9 marks Moderate -0.8
3
\includegraphics[max width=\textwidth, alt={}, center]{5b10afa1-1c45-4370-a0e6-ad8fd626df9a-3_638_839_269_653} Three coplanar forces of magnitudes \(5 \mathrm {~N} , 8 \mathrm {~N}\) and 8 N act at the origin \(O\) of rectangular coordinate axes. The directions of the forces are as shown in the diagram.
  1. Find the component of the resultant of the three forces in
    (a) the \(x\)-direction,
    (b) the \(y\)-direction.
  2. Find the magnitude and direction of the resultant.