# A level south west regional mock gce 2022 mathematics with mechanics 3

### A level south west regional mock gce 2022 mathematics with mechanics 3

A level south west regional mock gce 2022 mathematics with mechanics 3

A Particle of mass 8 kg moves such that its displacement
(((cba)))Calculate Determine Prove thatthe the thework force magnitude done acting on of on this Itothis !particle ninndii particle^from when n and thetHnrtfe instance — 6 sraeigydf *swhen of magnitude t =))
, the angle between the acceleration and velocity of the particle when t =-
(2 marks)
1.
5.
(d) Find, to two decimal places
placed on a smooth horinzontal floor.
2. (i) Two spheres Sx and S2 of masses 3m kg and m kg respectively . Given that
Sphere Sa is projected with speed 2u m/s and impinges directly on S2 which is at rest
S2 receives an impulse of magnitude 2mu kgm/s.
Calculate,
(a) the speed of Sx and S2 after impact,
(b) the coefficient of restitution between and S2.
are
(4 marks)
(2 marks)
(ii) Two forces Fx and F2 act at points with position vectors ax anda2 respectively, where
Fi = (3i + 2 j)N ,
F2 = (-4i + 5j)N ,
Find
(c) the position vector of the point of intersection of the lines of action of the two forces
(d) the magnitude of the resultant of the two forces
(e) the magnitude of the resulatant moment of the two forces –
a!= (2i + 5j) m
a2 = (3i- 2 j) m.

3. (i) Two particles Pi and P2 at time t — 0 have position vectors (i- j + 2k) m and (i+5j +4k) m respectively.
Pa moves with a speed of 6 m/s in the direction of the vector i + 2j — 2k and P2 moves with a speed of 7 m/s
in the direction of vector 2i + 3j- 6k.
(a) Determine the equation of path of each particle and show that the particles do not collide. (7 marks)
(ii) A uniform ladder of length 2a, a > 0 , rests in equilibrium with its lower end on a rough horizontal ground
and its upper end against a smooth vertical wall. The plane containing this ladder is perpendicular to the wall
and makes an angle a with the ground where tan a = V3. Determine the coefficient of friction between the
ladder and the ground. . (6 marks)
4. (i) A particle moves along a straight line with speed m/s where x m is the distance covered by the particle
from a fixed point O on the line.
Calculate,
(a) the time taken to cover a distance of 4 m from O,
(b) the acceleration when the particle has covered a distance of 4 m from O.
(4 marks)
(3 marks)
(ii) Two points E and F are such that F is 3a metres vertically below E. A particle G of mass m kg is connected
to E by a spring of natural length a metres. Each of the two springs has modulus of elasticity 2mg.
Determine the height above F that the particle G rests in equilibrium. (6 marks)
5. (I) A ball is projected from the top of a wall which is 3m high, with an initial speed of 20 m/s, this ball just clears
a pole 13 m high on its path which is a horizontal distance of 20 m from the foot of the wall.
(a) Determine the tangent of the two possible angles of projection.