Given impulse, find velocity or mass

2. Two particles \(A\) and \(B\) have mass 0.12 kg and 0.08 kg respectively. They are initially at rest on a smooth horizontal table. Particle \(A\) is then given an impulse in the direction \(A B\) so that it moves with speed \(3 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) directly towards \(B\).

1. Find the magnitude of this impulse, stating clearly the units in which your answer is given.
   (2) Immediately after the particles collide, the speed of \(A\) is \(1.2 \mathrm {~m} \mathrm {~s} ^ { - 1 }\), its direction of motion being unchanged.
2. Find the speed of \(B\) immediately after the collision.
3. Find the magnitude of the impulse exerted on \(A\) in the collision.

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 \(2m\) and particle \(Q\) has mass \(3m\). The particles collide directly. Immediately before the collision, the speed of \(P\) is \(4u\) and the speed of \(Q\) is \(u\). The magnitude of the impulse in the collision is \(\frac{33}{5}mu\).

1. Find the speed and direction of motion of \(P\) immediately after the collision. [4]
2. Find the speed and direction of motion of \(Q\) immediately after the collision. [4]

A particle \(P\) is moving with constant acceleration along a straight horizontal line \(ABC\), where \(AC = 24\) m. Initially \(P\) is at \(A\) and is moving with speed \(5\) m s\(^{-1}\) in the direction \(AB\). After \(1.5\) s, the direction of motion of \(P\) is unchanged and \(P\) is at \(B\) with speed \(9.5\) m s\(^{-1}\).

1. Show that the speed of \(P\) at \(C\) is \(13\) m s\(^{-1}\). [4]

The mass of \(P\) is \(2\) kg. When \(P\) reaches \(C\), an impulse of magnitude \(30\) Ns is applied to \(P\) in the direction \(CB\).

1. Find the velocity of \(P\) immediately after the impulse has been applied, stating clearly the direction of motion of \(P\) at this instant. [3]

Two particles \(A\) and \(B\) are moving on a smooth horizontal plane. The mass of \(A\) is \(2m\) 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 \(2u\) and the speed of \(B\) is \(3u\). The magnitude of the impulse received by each particle in the collision is \(\frac{7mu}{2}\). Find

1. the speed of \(A\) immediately after the collision, [3]
2. the speed of \(B\) immediately after the collision. [3]

A railway truck \(S\) of mass 2000 kg is travelling due east along a straight horizontal track with constant speed 12 m s\(^{-1}\). The truck \(S\) collides with a truck \(T\) which is travelling due west along the same track as \(S\) with constant speed 6 m s\(^{-1}\). The magnitude of the impulse of \(T\) on \(S\) is 28800 Ns.

1. Calculate the speed of \(S\) immediately after the collision. [3]
2. State the direction of motion of \(S\) immediately after the collision. [1]

Given that, immediately after the collision, the speed of \(T\) is 3.6 m s\(^{-1}\), and that \(T\) and \(S\) are moving in opposite directions,

1. calculate the mass of \(T\). [4]