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CAIE M1 2024 November Q1
4 marks Moderate -0.8
1 Two particles, of masses 1.8 kg and 1.2 kg , are connected by a light inextensible string that passes over a fixed smooth pulley. The particles hang vertically. The system is released from rest. Find the magnitude of the acceleration of the particles and find the tension in the string. \includegraphics[max width=\textwidth, alt={}, center]{404b5565-d76f-430e-a956-e8ce569aae6a-03_2717_29_105_22}
CAIE M1 2024 November Q2
5 marks Moderate -0.3
2 \includegraphics[max width=\textwidth, alt={}, center]{404b5565-d76f-430e-a956-e8ce569aae6a-03_293_638_258_717} A particle of mass 7.5 kg , starting from rest at \(A\), slides down an inclined plane \(A B\). The point \(B\) is 12.5 metres vertically below the level of \(A\), as shown in the diagram.
  1. Given that the plane is smooth, use an energy method to find the speed of the particle at \(B\).
  2. It is given instead that the plane is rough and the particle reaches \(B\) with a speed of \(8 \mathrm {~ms} ^ { - 1 }\). The plane is 25 m long and the constant frictional force has magnitude \(F \mathrm {~N}\). Find the value of \(F\). \includegraphics[max width=\textwidth, alt={}, center]{404b5565-d76f-430e-a956-e8ce569aae6a-04_725_655_251_641} Coplanar forces of magnitudes \(52 \mathrm {~N} , 39 \mathrm {~N}\) and \(P \mathrm {~N}\) act at a point in the directions shown in the diagram. The system is in equilibrium. Find the values of \(P\) and \(\theta\). \includegraphics[max width=\textwidth, alt={}, center]{404b5565-d76f-430e-a956-e8ce569aae6a-04_2716_38_109_2012} \includegraphics[max width=\textwidth, alt={}, center]{404b5565-d76f-430e-a956-e8ce569aae6a-05_2716_29_107_22}
CAIE M1 2024 November Q4
6 marks Standard +0.3
4 A bus travels between two stops, \(A\) and \(B\). The bus starts from rest at \(A\) and accelerates at a constant rate of \(a \mathrm {~m} \mathrm {~s} ^ { - 2 }\) until it reaches a speed of \(16 \mathrm {~ms} ^ { - 1 }\). It then travels at this constant speed before decelerating at a constant rate of \(0.75 a \mathrm {~m} \mathrm {~s} ^ { - 2 }\), coming to rest at \(B\). The total time for the journey is 240 s .
  1. Sketch the velocity-time graph for the bus's journey from \(A\) to \(B\). \includegraphics[max width=\textwidth, alt={}, center]{404b5565-d76f-430e-a956-e8ce569aae6a-05_401_1198_479_434}
  2. Find an expression, in terms of \(a\), for the length of time that the bus is travelling with constant speed.
  3. Given that the distance from \(A\) to \(B\) is 3000 m , find the value of \(a\).
CAIE M1 2024 November Q5
10 marks Standard +0.3
5 A particle, \(A\), is projected vertically upwards from a point \(O\) with a speed of \(80 \mathrm {~ms} ^ { - 1 }\). One second later a second particle, \(B\), with the same mass as \(A\), is projected vertically upwards from \(O\) with a speed of \(100 \mathrm {~m} \mathrm {~s} ^ { - 1 }\). At time \(T\) s after the first particle is projected, the two particles collide and coalesce to form a particle \(C\).
  1. Show that \(T = 3.5\).
  2. Find the height above \(O\) at which the particles collide. \includegraphics[max width=\textwidth, alt={}, center]{404b5565-d76f-430e-a956-e8ce569aae6a-07_2723_33_99_22}
  3. Find the time from \(A\) being projected until \(C\) returns to \(O\). \includegraphics[max width=\textwidth, alt={}, center]{404b5565-d76f-430e-a956-e8ce569aae6a-08_415_912_246_580} A particle of mass 1.2 kg is placed on a rough plane which is inclined at an angle \(\theta\) to the horizontal, where \(\sin \theta = \frac { 7 } { 25 }\). The particle is kept in equilibrium by a horizontal force of magnitude \(P \mathrm {~N}\) acting in a vertical plane containing a line of greatest slope (see diagram). The coefficient of friction between the particle and the plane is 0.15 . Find the least possible value of \(P\). \includegraphics[max width=\textwidth, alt={}, center]{404b5565-d76f-430e-a956-e8ce569aae6a-08_2714_38_109_2010} \includegraphics[max width=\textwidth, alt={}, center]{404b5565-d76f-430e-a956-e8ce569aae6a-09_2726_35_97_20}
CAIE M1 2024 November Q7
8 marks Moderate -0.3
7 A car has mass 1200 kg . When the car is travelling at a speed of \(v \mathrm {~m} \mathrm {~s} ^ { - 1 }\), there is a resistive force of magnitude \(k v \mathrm {~N}\). The maximum power of the car's engine is 92.16 kW .
  1. The car travels along a straight level road.
    1. The car has a greatest possible constant speed of \(48 \mathrm {~ms} ^ { - 1 }\). Show that \(k = 40\).
    2. At an instant when its speed is \(45 \mathrm {~m} \mathrm {~s} ^ { - 1 }\), find the greatest possible acceleration of the car. [3] \includegraphics[max width=\textwidth, alt={}, center]{404b5565-d76f-430e-a956-e8ce569aae6a-10_2716_40_109_2009}
  2. The car now travels at a constant speed up a hill inclined at an angle of \(\sin ^ { - 1 } 0.15\) to the horizontal. Find the greatest possible speed of the car going up the hill.
CAIE M1 2024 November Q8
7 marks Standard +0.8
8 A particle \(P\) moves in a straight line, passing through a point \(O\) with velocity \(4.2 \mathrm {~ms} ^ { - 1 }\). At time \(t \mathrm {~s}\) after \(P\) passes \(O\), the acceleration, \(a \mathrm {~m} \mathrm {~s} ^ { - 2 }\), of \(P\) is given by \(a = 0.6 t - 2.7\). Find the distance \(P\) travels between the times at which it is at instantaneous rest. \includegraphics[max width=\textwidth, alt={}, center]{404b5565-d76f-430e-a956-e8ce569aae6a-12_2715_38_109_2009}
If you use the following page to complete the answer to any question, the question number must be clearly shown. \includegraphics[max width=\textwidth, alt={}, center]{404b5565-d76f-430e-a956-e8ce569aae6a-14_2716_37_108_2010}
CAIE M1 2024 November Q2
4 marks Moderate -0.3
2 A block of mass 20 kg is held at rest at the top of a plane inclined at \(30 ^ { \circ }\) to the horizontal. The block is projected with speed \(5 \mathrm {~ms} ^ { - 1 }\) down a line of greatest slope of the plane. There is a resistance force acting on the block. As the block moves 2 m down the plane from its point of projection, the work done against this resistance force is 50 J . Find the speed of the block when it has moved 2 m down the plane. \includegraphics[max width=\textwidth, alt={}, center]{145d93bd-7f56-4e8c-a646-938330511347-04_2716_38_109_2012}
CAIE M1 2024 November Q3
5 marks Standard +0.3
3 A cyclist is riding along a straight horizontal road. The total mass of the cyclist and his bicycle is 90 kg . The power exerted by the cyclist is 250 W . At an instant when the cyclist's speed is \(5 \mathrm {~m} \mathrm {~s} ^ { - 1 }\), his acceleration is \(0.1 \mathrm {~ms} ^ { - 2 }\).
  1. Find the value of the constant resistance to motion acting on the cyclist.
    The cyclist comes to the bottom of a hill inclined at \(2 ^ { \circ }\) to the horizontal.
  2. Given that the power and resistance to motion are unchanged, find the steady speed which the cyclist could maintain when riding up the hill.
CAIE M1 2024 November Q4
6 marks Standard +0.3
4 \includegraphics[max width=\textwidth, alt={}, center]{145d93bd-7f56-4e8c-a646-938330511347-06_389_1134_258_468} The diagram shows two particles, \(A\) and \(B\), of masses 0.2 kg and 0.1 kg respectively. The particles are suspended below a horizontal ceiling by two strings, \(A P\) and \(B Q\), attached to fixed points \(P\) and \(Q\) on the ceiling. The particles are connected by a horizontal string, \(A B\). Angle \(A P Q = 45 ^ { \circ }\) and \(B Q P = \theta ^ { \circ }\). Each string is light and inextensible. The particles are in equilibrium.
  1. Find the value of the tension in the string \(A B\). \includegraphics[max width=\textwidth, alt={}, center]{145d93bd-7f56-4e8c-a646-938330511347-06_2715_44_110_2006} \includegraphics[max width=\textwidth, alt={}, center]{145d93bd-7f56-4e8c-a646-938330511347-07_2721_34_101_20}
  2. Find the value of \(\theta\) and the tension in the string \(B Q\).
CAIE M1 2024 November Q5
9 marks Standard +0.8
5 Two particles, \(P\) and \(Q\), of masses \(2 m \mathrm {~kg}\) and \(m \mathrm {~kg}\) respectively, are held at rest in the same vertical line. The heights of \(P\) and \(Q\) above horizontal ground are 1 m and 2 m respectively. \(P\) is projected vertically upwards with speed \(2 \mathrm {~ms} ^ { - 1 }\). At the same instant, \(Q\) is released from rest.
  1. Find the speed of each particle immediately before they collide.
  2. It is given that immediately after the collision the downward speed of \(Q\) is \(3.5 \mathrm {~ms} ^ { - 1 }\). Find the speed of \(P\) at the instant that it reaches the ground.
CAIE M1 2024 November Q6
10 marks Challenging +1.2
6 A particle, \(P\), travels in a straight line, starting from a point \(O\) with velocity \(6 \mathrm {~ms} ^ { - 1 }\). The acceleration of \(P\) at time \(t \mathrm {~s}\) after leaving \(O\) is \(a \mathrm {~m} \mathrm {~s} ^ { - 2 }\), where $$\begin{array} { l l } a = - 1.5 t ^ { \frac { 1 } { 2 } } & \text { for } 0 \leqslant t \leqslant 1 , \\ a = 1.5 t ^ { \frac { 1 } { 2 } } - 3 t ^ { - \frac { 1 } { 2 } } & \text { for } t > 1 . \end{array}$$
  1. Find the velocity of \(P\) at \(t = 1\).
  2. Given that there is no change in the velocity of \(P\) when \(t = 1\), find an expression for the velocity of \(P\) for \(t > 1\). \includegraphics[max width=\textwidth, alt={}, center]{145d93bd-7f56-4e8c-a646-938330511347-11_2725_35_99_20}
  3. Given that the velocity of \(P\) is positive for \(t \leqslant 4\), find the total distance travelled between \(t = 0\) and \(t = 4\). \includegraphics[max width=\textwidth, alt={}, center]{145d93bd-7f56-4e8c-a646-938330511347-12_723_762_248_653} Two particles, \(A\) and \(B\), of masses 0.2 kg and 0.3 kg respectively, are attached to the ends of a light inextensible string. The string passes over a small fixed smooth pulley which is attached to the bottom of a rough plane inclined at an angle \(\theta\) to the horizontal where \(\sin \theta = 0.6\). Particle \(A\) lies on the plane, and particle \(B\) hangs vertically below the pulley, 0.25 m above horizontal ground. The string between \(A\) and the pulley is parallel to a line of greatest slope of the plane (see diagram). The coefficient of friction between \(A\) and the plane is 1.125 . Particle \(A\) is released from rest.
  4. Find the tension in the string and the magnitude of the acceleration of the particles. \includegraphics[max width=\textwidth, alt={}, center]{145d93bd-7f56-4e8c-a646-938330511347-12_2716_38_109_2012}
  5. When \(B\) reaches the ground, it comes to rest. Find the total distance that \(A\) travels down the plane from when it is released until it comes to rest. You may assume that \(A\) does not reach the pulley.
    If you use the following page to complete the answer to any question, the question number must be clearly shown. \includegraphics[max width=\textwidth, alt={}, center]{145d93bd-7f56-4e8c-a646-938330511347-14_2715_31_106_2016}
CAIE M1 2024 November Q1
4 marks Moderate -0.3
1 An athlete has mass \(m \mathrm {~kg}\) .The athlete runs along a horizontal road against a constant resistance force of magnitude 24 N .The total work done by the athlete in increasing his speed from \(5 \mathrm {~ms} ^ { - 1 }\) to \(6 \mathrm {~ms} ^ { - 1 }\) while running a distance of 50 metres is 1541 J . Find the value of \(m\) . \includegraphics[max width=\textwidth, alt={}, center]{3a6ecf05-127f-4ddf-959e-233f6bae9171-04_464_1116_247_478} Coplanar forces of magnitudes \(16 \mathrm {~N} , 12 \mathrm {~N} , 24 \mathrm {~N}\) and 8 N act at a point in the directions shown in the diagram. Find the magnitude and direction of the single additional force acting at the same point which will produce equilibrium.
CAIE M1 2024 November Q3
6 marks Moderate -0.3
3 A car of mass 1600 kg travels up a slope inclined at an angle of \(\sin ^ { - 1 } 0.08\) to the horizontal. There is a constant resistance of magnitude 240 N acting on the car.
  1. It is given that the car travels at a constant speed of \(32 \mathrm {~ms} ^ { - 1 }\). Find the power of the engine of the car.
  2. Find the acceleration of the car when its speed is \(24 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) and the engine is working at 95\% of the power found in (a).
CAIE M1 2024 November Q4
6 marks Standard +0.3
4 Two particles, \(A\) and \(B\), of masses 3 kg and 6 kg respectively, lie on a smooth horizontal plane. Initially, \(B\) is at rest and \(A\) is moving towards \(B\) with speed \(8 \mathrm {~ms} ^ { - 1 }\). After \(A\) and \(B\) collide, \(A\) moves with speed \(2 \mathrm {~ms} ^ { - 1 }\). Find the greater of the two possible total losses of kinetic energy due to the collision. \includegraphics[max width=\textwidth, alt={}, center]{3a6ecf05-127f-4ddf-959e-233f6bae9171-06_2722_43_107_2004} \includegraphics[max width=\textwidth, alt={}, center]{3a6ecf05-127f-4ddf-959e-233f6bae9171-07_197_1142_254_460} A particle of mass 12 kg is going to be pulled across a rough horizontal plane by a light inextensible string.The string is at an angle of \(30 ^ { \circ }\) above the plane and has tension \(T \mathrm {~N}\)(see diagram).The coefficient of friction between the particle and the plane is 0.5 .
  1. Given that the particle is on the point of moving,find the value of \(T\) .
  2. Given instead that the particle is accelerating at \(0.2 \mathrm {~ms} ^ { - 2 }\) ,find the value of \(T\) .
CAIE M1 2024 November Q6
10 marks Standard +0.3
6 A particle moves in a straight line. It starts from rest, at time \(t = 0\), and accelerates at \(0.6 t \mathrm {~ms} ^ { - 2 }\) for 4 s , reaching a speed of \(V \mathrm {~m} \mathrm {~s} ^ { - 1 }\). The particle then travels at \(V \mathrm {~m} \mathrm {~s} ^ { - 1 }\) for 11 s , and finally slows down, with constant deceleration, stopping after a further 5 s .
  1. Show that \(V = 4.8\).
  2. Sketch a velocity-time graph for the motion. \includegraphics[max width=\textwidth, alt={}, center]{3a6ecf05-127f-4ddf-959e-233f6bae9171-08_2722_40_107_2010}
  3. Find an expression, in terms of \(t\), for the velocity of the particle for \(15 \leqslant t \leqslant 20\).
  4. Find the total distance travelled by the particle. \includegraphics[max width=\textwidth, alt={}, center]{3a6ecf05-127f-4ddf-959e-233f6bae9171-10_592_608_251_731} Two particles, \(A\) and \(B\), of masses 3 kg and 5 kg respectively, are connected by a light inextensible string that passes over a fixed smooth pulley. The particles are held with the string taut and its straight parts vertical. Particle \(A\) is 1 m above a horizontal plane, and particle \(B\) is 2 m above the plane (see diagram). The particles are released from rest. In the subsequent motion, \(A\) does not reach the pulley, and after \(B\) reaches the plane it remains in contact with the plane.
  5. Find the tension in the string and the time taken for \(B\) to reach the plane. \includegraphics[max width=\textwidth, alt={}, center]{3a6ecf05-127f-4ddf-959e-233f6bae9171-10_2718_42_107_2007}
  6. Find the time for which \(A\) is at least 3.25 m above the plane.
    If you use the following page to complete the answer to any question, the question number must be clearly shown.
CAIE M1 2020 Specimen Q1
4 marks Easy -1.3
1 A rticle \(P\) is p j ected rticallyw ard with \(\mathbf { p }\) ed \(\mathrm { ms } ^ { - 1 }\) frm a \(\dot { \mathrm { p } } \mathrm { n } \mathbf { d }\) b gd
  1. Fid b g eatest b in a th gd each dy \(P\).
  2. Fid \(\mathbf { b }\) to al time frm \(\mathrm { p } \dot { \mathrm { p } }\) ectim il \(P\) retu \(\mathbf { B }\) to \(\mathbf { b } \mathbf { g d }\)
CAIE M1 2020 Specimen Q2
5 marks Moderate -0.8
2 ACB tan resistan e of mag itd ( ) N acts \(\boldsymbol { \infty }\) car \(\boldsymbol { 0 }\) mass \(\boldsymbol { 0 }\) g
  1. Th car is mi gr lor straig le lro de taco tan sp e \(\varnothing \quad 3 \mathrm {~ms} ^ { - 1 }\). Fid \(n \mathrm {~W} , \mathrm { t } \mathbf { b }\) rate at wh cht b eg \(\mathbf { B }\) the car is work g
  2. Th car tra ls at a co tan sp ed n a h ll in lie d at an ag e \(\boldsymbol { 6 } \theta ^ { \circ }\) to to b izo al, wh re \(\sin \theta ^ { \circ } = \frac { 1 } { 20 }\), w ittl b eg e wo kg t\\( \)\mathbb { N }$. Fid b sp e \(\boldsymbol { \varnothing }\) th car.
CAIE M1 2020 Specimen Q3
6 marks Standard +0.3
3 Th ee small smo h se res \(A , B\) ad \(C 6\) eq l radi ad 6 masses \(4 \mathrm {~g} \quad 2 \mathrm {~g}\) ad 3 g resp ctie ly, lie in th todr in a strait lie o a smo hb izt al p ae. In tially, \(B\) ad \(C\) are at rest ad \(A\) is mi g ard \(B\) with sp ed \(6 \mathrm {~ms} ^ { - 1 }\). After th cb liso with \(B\), se re \(A\) co in s to mo in the same d rectim withs p ed \(\mathrm { ms } ^ { - 1 }\).
  1. Fid b sp e \(\boldsymbol { \Phi } \quad B\) after th s cb liso Se re \(B\) cb lid s with \(C\).I it \(h\) s cb lisd \(\mathbf { b }\) se two se res co lesce tof \(\mathbf { o }\) m am \(\mathbf { b }\) ect \(D\).
  2. Fid b sp e \(D\) after th s cb lisin \includegraphics[max width=\textwidth, alt={}, center]{0a1cec7f-f9d1-4628-b979-443514c73eb9-05_65_1652_1146_242}
CAIE M1 2020 Specimen Q4
6 marks Standard +0.3
4 A \(\boldsymbol { p }\) rticle of mass \(\emptyset \mathrm { g }\) is \(\mathbf { n }\) a rg p an in lin d at an an \(\mathrm { e } \boldsymbol { 6 } \mathbf { B } ^ { \circ }\) to th \(\mathbf { b }\) izn tal. A fo ce \(\boldsymbol { 6 }\) mag te \(\quad\) z N, actig at an ag e 6 O \(^ { \circ }\) ab a lin 6 g eatest sle 6 th p aB , is s ed to p e n th \(\mathbf { P }\) rticle frm slid g n th p as. Th co fficient
CAIE M1 2020 Specimen Q5
9 marks Standard +0.3
5 A car 6 mass \(\mathbb { I } \quad\) g is p lig a trailer 6 mass \(\theta \quad\) g ah ll in lin d at an ag e \(6 \sin ^ { - 1 } ( \mathbb { I } )\) ) to th b izo al. Th car and to trailer are co cted b a lig rig d -b r wh ch is \(\boldsymbol { \rho }\) rallel to th ro d Th d iv g fo ce \(\varnothing\) th car's eg A is \(\theta \mathrm { N }\) ad th resistan es to th car ad trailer are \(\theta \mathrm { N }\) ad (1) N resp ctie ly.
  1. Fid b acceleratio th sy tem ad b tensio it b tw -b r.
  2. Wh it b car ad railer are tra llig tasp e \(\boldsymbol { \Theta } \quad \mathbf { b } \mathrm { ms } ^ { - 1 } , \mathrm { t } \mathbf { b }\) divg \(\mathbf { o }\) ce b cm es zero Fid th time, in sect , \(\mathbf { b }\) fo e the sy tem cm es to rest ad th fo ce in th ro \(\mathbf { r d }\) ig th s time.
CAIE M1 2020 Specimen Q6
11 marks Moderate -0.3
6 A \(\boldsymbol { p }\) rticle \(P \mathrm {~m}\) s ira straitg lie . Tb ± lo ity \(v \mathrm {~ms} ^ { - 1 }\) at time \(t \mathrm {~s}\) is g ஓ ity $$\begin{array} { l l } v = 5 t ( t - 2 & \text { fo } 0 \leqslant t \leqslant 4 \\ v = k & \text { fo } 4 \leqslant t \leqslant 4 \\ v = 82 \quad t & \text { fo } 4 \leqslant t \leqslant \Omega \end{array}$$ wh re \(k\) is a co tan.
  1. Fid \(k\).
  2. Sk tcht b lo ity ime g aff \(\mathbf { 0 } \quad 0 \leqslant t \leqslant 0\)
  3. Fid bet \(\mathbf { 6 }\) le \(\mathrm { s } \mathbf { 6 } t\) fo wh cht b acceleratio \(P\) is \(\mathbf { p }\) itie .
  4. Fid \(\mathbf { b }\) to ald stan e trac lledy \(P\) irt \(\mathbf { b }\) in era \(10 \leqslant t \leqslant 0\)
CAIE M1 2020 Specimen Q7
9 marks Standard +0.3
7 \includegraphics[max width=\textwidth, alt={}, center]{0a1cec7f-f9d1-4628-b979-443514c73eb9-12_248_674_260_699} Two \(\boldsymbol { \rho }\) rticles \(A\) ad \(B , 6\) masses 08 k ad 0 g resp ctie ly, are co cted \(\varphi\) a lig inex en ib e strig Particle \(A\) is p aced \(\mathbf { n }\) ab izb al sn face. Th strig \(\boldsymbol { p }\) sses rasmall smo hp ley \(P\) fiæ d at th ed 6 th su face, and \(B \mathbf { h }\) g freely. Th \(\mathbf { b }\) izo alsectin 6 th strig \(A P\), is \(\mathbf { 6 }\) leg \(\mathrm { h } \otimes \mathrm { m }\) (see id ag am). Th \(\boldsymbol { p }\) rticles are released rm rest witb lo ectim of th strig atı.
  1. Gie it \(\mathbf { h }\) th sn face is smo lf id \(\mathbf { b }\) time tak if \(\mathbf { D }\) A tor eacht \(\mathbf { b }\) p ley. [
  2. It is \(\dot { \mathbf { g } }\) ven in tead that th sn face is rg ad th t th sp ed \(6 A\) immed ately \(\mathbf { b }\) fo e it reach s th p leỳ \(\mathrm { s } v \mathrm {~ms} ^ { - 1 }\). Th wo ld ag in t frictim \(\mathrm { s } A \mathrm {~m}\) s frm rest to b p leyi s 2 J . Use an ee rgn eth \(\quad\) f id \(v\). [4] If B e th follw ig lin dpg to cm p ete th an wer(s) to ay q stin (s), th q stin \(\mathrm { m } \quad \mathbf { b } \quad \mathrm { r } ( \mathrm { s } )\) ms tb clearlys n n
CAIE M1 2002 June Q1
3 marks Moderate -0.8
1 \includegraphics[max width=\textwidth, alt={}, center]{430f1f9a-7a3a-47a0-b742-daf74e68adfd-2_300_748_274_708} One end of a light inextensible string is attached to a ring which is threaded on a fixed horizontal bar. The string is used to pull the ring along the bar at a constant speed of \(0.4 \mathrm {~ms} ^ { - 1 }\). The string makes a constant angle of \(30 ^ { \circ }\) with the bar and the tension in the string is 5 N (see diagram). Find the work done by the tension in 10 s .
CAIE M1 2002 June Q2
5 marks Moderate -0.8
2 A basket of mass 5 kg slides down a slope inclined at \(12 ^ { \circ }\) to the horizontal. The coefficient of friction between the basket and the slope is 0.2 .
  1. Find the frictional force acting on the basket.
  2. Determine whether the speed of the basket is increasing or decreasing.
CAIE M1 2002 June Q3
5 marks Moderate -0.3
3 \includegraphics[max width=\textwidth, alt={}, center]{430f1f9a-7a3a-47a0-b742-daf74e68adfd-2_368_584_1302_794} Two forces, each of magnitude 10 N , act at a point \(O\) in the directions of \(O A\) and \(O B\), as shown in the diagram. The angle between the forces is \(\theta\). The resultant of these two forces has magnitude 12 N .
  1. Find \(\theta\).
  2. Find the component of the resultant force in the direction of \(O A\).