A particle \(P\) of mass 1.5 kg is moving along a straight horizontal line with speed \(3 \mathrm {~m} \mathrm {~s} ^ { - 1 }\). Another particle \(Q\) of mass 2.5 kg is moving, in the opposite direction, along the same straight line with speed \(4 \mathrm {~m} \mathrm {~s} ^ { - 1 }\). The particles collide. Immediately after the collision the direction of motion of \(P\) is reversed and its speed is \(2.5 \mathrm {~m} \mathrm {~s} ^ { - 1 }\).
- Calculate the speed of \(Q\) immediately after the impact.
- State whether or not the direction of motion of \(Q\) is changed by the collision.
- Calculate the magnitude of the impulse exerted by \(Q\) on \(P\), giving the units of your answer.
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A plank \(A B\) has mass 40 kg and length 3 m . A load of mass 20 kg is attached to the plank at \(B\). The loaded plank is held in equilibrium, with \(A B\) horizontal, by two vertical ropes attached at \(A\) and \(C\), as shown in Figure 1. The plank is modelled as a uniform rod and the load as a particle. Given that the tension in the rope at \(C\) is three times the tension in the rope at \(A\), calculate