Two discs, P of mass 4 kg and Q of mass 5 kg , are sliding along the same line on a smooth horizontal plane when they collide. The velocity of P before the collision and the velocity of Q after the collision are shown in Fig. 4. P loses \(\frac { 5 } { 9 }\) of its kinetic energy in the collision.
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Show that after the collision P has a velocity of \(4 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) in the opposite direction to its original motion.
While colliding, the discs are in contact for \(\frac { 1 } { 5 } \mathrm {~s}\).
Find the impulse on P in the collision and the average force acting on the discs.
Find the velocity of Q before the collision and the coefficient of restitution between the two discs.
A particle is projected from a point 2.5 m above a smooth horizontal plane. Its initial velocity is \(5.95 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) at an angle \(\theta\) below the horizontal, where \(\sin \theta = \frac { 15 } { 17 }\). The coefficient of restitution between the particle and the plane is \(\frac { 4 } { 5 }\).
Show that, after bouncing off the plane, the greatest height reached by the particle is 2.5 m .
Calculate the horizontal distance between the two points at which the particle is 2.5 m above the plane.