Two particles \(P\) and \(Q\) are moving in opposite directions along the same horizontal straight line. Particle \(P\) is moving due east and particle \(Q\) is moving due west. Particle \(P\) has mass \(2 m\) and particle \(Q\) has mass \(3 m\). The particles collide directly. Immediately before the collision, the speed of \(P\) is \(4 u\) and the speed of \(Q\) is \(u\). The magnitude of the impulse in the collision is \(\frac { 33 } { 5 } m u\).
- Find the speed and direction of motion of \(P\) immediately after the collision.
- Find the speed and direction of motion of \(Q\) immediately after the collision.
VILIV SIMI NI III IM I ON OC
VILV SIHI NI JAHMMION OC
VALV SIHI NI JIIUM ION OC
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\caption{Figure 1}
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A boy is pulling a sledge of mass 8 kg in a straight line at a constant speed across rough horizontal ground by means of a rope. The rope is inclined at \(30 ^ { \circ }\) to the ground, as shown in Figure 1. The coefficient of friction between the sledge and the ground is \(\frac { 1 } { 5 }\). By modelling the sledge as a particle and the rope as a light inextensible string, find the tension in the rope.