A railway truck \(P\) of mass 2000 kg is moving along a straight horizontal track with speed \(10 \mathrm {~m} \mathrm {~s} ^ { - 1 }\). The truck \(P\) collides with a truck \(Q\) of mass 3000 kg , which is at rest on the same track. Immediately after the collision \(Q\) moves with speed \(5 \mathrm {~m} \mathrm {~s} ^ { - 1 }\). Calculate
- the speed of \(P\) immediately after the collision,
- the magnitude of the impulse exerted by \(P\) on \(Q\) during the collision.
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In Fig. 1, \(\angle A O C = 90 ^ { \circ }\) and \(\angle B O C = \theta ^ { \circ }\). A particle at \(O\) is in equilibrium under the action of three coplanar forces. The three forces have magnitude \(8 \mathrm {~N} , 12 \mathrm {~N}\) and \(X \mathrm {~N}\) and act along \(O A\), \(O B\) and \(O C\) respectively. Calculate