A railway truck \(A\) of mass \(m\) and a second railway truck \(B\) of mass \(4 m\) are moving in opposite directions on a smooth straight horizontal track when they collide directly. Immediately before the collision the speed of truck \(A\) is \(3 u\) and the speed of truck \(B\) is \(2 u\). In the collision the trucks join together. Modelling the trucks as particles, find
- the speed of \(A\) immediately after the collision,
- the direction of motion of \(A\) immediately after the collision,
- the magnitude of the impulse exerted by \(A\) on \(B\) in the collision.
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\caption{Figure 1}
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A block of mass 50 kg lies on a rough plane which is inclined to the horizontal at an angle \(\alpha\), where \(\tan \alpha = \frac { 7 } { 24 }\). The block is held at rest by a vertical rope, as shown in Figure 1, and is on the point of sliding down the plane. The block is modelled as a particle and the rope is modelled as a light inextensible string. Given that the friction force acting on the block has magnitude 65.8 N, find