A particle, \(P\), of mass 5 kg moves with speed \(3 \mathrm {~ms} ^ { - 1 }\) along a smooth horizontal track. It strikes a particle \(Q\) of mass 2 kg which is at rest on the track. Immediately after the collision, \(P\) and \(Q\) move in the same direction with speeds \(v\) and \(2 v \mathrm {~ms} ^ { - 1 }\) respectively.
Calculate the value of \(v\).
Calculate the magnitude of the impulse received by \(Q\) on impact.
A particle \(P\) moves with a constant velocity \(( 3 \mathbf { i } + 2 \mathbf { j } ) \mathrm { ms } ^ { - 1 }\) with respect to a fixed origin \(O\). It passes through the point \(A\) whose position vector is \(( 2 \mathbf { i } + 11 \mathbf { j } )\) m at \(t = 0\).
Find the angle in degrees that the velocity vector of \(P\) makes with the vector \(\mathbf { i }\).
Calculate the distance of \(P\) from \(O\) when \(t = 2\).
A car of mass 1250 kg is moving at constant speed up a hill, inclined at an angle \(\alpha\) to the horizontal, where \(\sin \alpha = \frac { 1 } { 10 }\). The driving force produced by the engine is 1800 N .
Calculate the resistance to motion which the car experiences.
At the top of the hill, the road becomes horizontal.