9709/41/M/J/25q5

When a particle P of mass m kg has speed u ms^-1, its momentum is 4N s and its kinetic energy is 16J.

(a) Find the value of m and the value of u. [3 marks]

P is now projected on a smooth horizontal surface with speed v ms^-1 towards a particle Q of mass 1.25kg which is stationary. After P and Q collide, the velocity of P is w ms^-1 and the velocity of Q is 2w ms^-1. The loss of kinetic energy in the collision is 25J.

(b) Find the value of v and the value of w. [4 marks]

9709/42/M/J/25q2

Two particles P and Q, of masses 0.2kg and 0.1kg respectively, are free to move in a straight line on a smooth horizontal plane. P is projected towards Q with speed 5ms^-1. At the same instant, Q is projected away from P with speed 2ms^-1. When P collides with Q, the particles coalesce.

Find the kinetic energy lost during the collision. [4 marks]

9709/43/M/J/25q1

Two particles P and Q, of masses 0.1kg and 0.3kg respectively, are at rest on a smooth horizontal plane. P is projected directly towards Q with speed 4u ms^-1. At the same instant, Q is projected directly towards P with speed u ms^-1. After P and Q collide, P moves with speed 2ms^-1 and Q moves with speed 4ms^-1.

(a) Find the two possible values of u. [3 marks]

(b) Find the largest possible loss of kinetic energy in the collision. [2 marks]

9709/42/F/M/25q5

Three particles P, Q and R, of masses 0.6kg, 0.4kg and 0.8kg respectively, are at rest in a straight line on a smooth horizontal plane. The distance from P to Q is 3m, and the distance from Q to R is also 3m (see diagram). P is projected directly towards Q with speed 3ms^-1. After P and Q collide, P continues to move in the same direction with speed 1.5ms^-1.

(a) Find the speed of Q after the collision. [2 marks]

In the subsequent collision between Q and R, these particles coalesce.

(b) Find the speed of the combined particle after this collision. [1 mark]

(c) Find the time that it takes from when P is initially projected until the instant at which P collides with the combined particle. [4 marks]

9709/41/O/N/24q5

A particle, A, is projected vertically upwards from a point O with a speed of 80ms^-1. One second later a second particle, B, With the same mass as A, is projected vertically upwards from O with a speed of 100ms^-1. At time T s after the first particle is projected, the two particles collide and coalesce to form a particle C.

(a) Show that T = 3.5 [4 marks]

(b) Find the height above O at which the particles collide. [1 mark]

(c) Find the time from A being projected until C returns to O. [5 marks]