### cameroon gce A level June 2023 pure maths with mechanics 3

cameroon gce A level June 2023 pure maths with mechanics 3

1 .

Find, when t = 1,

(a) the momentum of P, (5 marks)

(3 marks)

(5 marks)

(b) the kinetic energy of P,

(c) the cosine of the angle between the velocity and the acceleration.

2. Two particles of mass 6 kg and M kg are connected by a light inelastic string passing over a fixed smooth

pulley and then released from rest. The acceleration of the system is 5 m s .

Find,

(a) the value of M,

(b) the tension in the string,

(c) the force exerted by the string on the pulley,

(d) the velocity after 2 seconds,

(e) the distance each mass travels in 2 seconds.

(Take g as 10 m s 2.)

3. Two smooth spheres A and B of mass 3m and 2m respectively lie in a straight line, on a smooth

horizontal floor, with sphere B between A and a smooth vertical wall. A is projected with speed 2u

to collide directly with B , and B in turn strikes the wall. The coefficient of restitution of either impact

is-. Find

4

(a) the speeds of A and B after the first collision,

(b) the kinetic energy loss in the first impact.

After B rebounds from the wall, show that the speed of sphere A after the second collision

with B is — m s-1.

(5 marks)

) * • I * (2 marks)

16 (6 marks)

4. A lorry of mass 1400 kg moving along a straight horizontal road at a steady speed of 20 m s-1 with its engine

working at the rate of 96 kW experiences constant a non-gravitational resistance R.

(a) Find R.

The lorry descends a plane inclined at sin-1 to the horizontal with a steady speed of 12 m s-1. ‘

Given that the non-gravitational resistance remains unchanged, .

(b) calculate the rate at which the engine is now working,

(c) find the retardation of the lorry if the rate of working of the engine is decreased by 20 kW.

(Take g as 10 m s 2.)

5. ( i) A particle is projected from a point A on a horizontal with speed 50 m s-1 at an angle of elevation a so

that it passes through the point (120,10).

(a) Show that there are two possible angles of projection.

If the angle of projection is 30°, find,

(b) the maximum height,

(c) the range of the particle on the horizontal plane through the point of projection,

(d) the time of flight.

(ii) The velocity of a particle A relative to particle B is (2i + 7 j ) m s”1 and the velocity of particle C relative to

A is (5i — 4 j ) m s-1. Find the velocity of C relative to B. (2 marks)