cameroon gce advanced level June 2022 pure maths with mechanics 3
cameroon gce advanced level June 2022 pure maths with mechanics 3
The position vectorV of a particle of mass 3 kg af time Fseconds is’givcn by
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r = [(3sin 2t)i + (4 cos 2t)j)] m.
* i;
* it it U VUi’ i
Find when t –
o
(a) the magnitude of the momentum of the particle,
(b) the force acting on the particle,
(c) the power developed by the particle.
. U 7 ;i. s u oAv / n /
: >t . y
(6 marks)
(4 marks)
(3 marks)
#-
iivi
/vinntF.’vi.’ rlliw o*tsn | J:!;i’ ivi- -‘Ur . i
– 2. ( i ) another A body Pbody of mass ‘ Qy of10mass kg, lying 20 kgon , by a smooth a light inextensjble plaqe.jij^ljiipd ,siring at 30 ‘ which ° to the passes horizontal over ,a isfixed ,connected smooth to
pulley at the top of the plane. The system is released from rest when Q is hanging vertically. Given
that • the coefficient • of friction between P and the plane is -9, find
(a) the acceleration of P, (5 marks)
(2 marks)
(2 marks)
(b) the tension in the string, • ^ : f* i
<* ; f * fl * 4 * * 1 .
(c) the magnitude of the force exerted by the string on the pulley.
5,. r .
• s r 2 – ‘ i- l. 1 t
(ii) A particle moves in a circle of radius 2 m with an acceleration of m s
Find its angular displacement in 3 s.
-2
. – A •• (4 marks)
(Take g as 10 m s 2)
i.
( r 1 ‘ it • ;;; Pin ‘! r. . r
3. Sphere A of mass 2 kg moving with speed 4 ms 1 along a horizontal smooth surface collides directly
with sphere B of mass 8 kg initially at rest. ;Given that the coefficient of restitution between A and B
IS I calculate
2’
(a ) the velocities of A and B after impact and comment on the result,
J S • « . . • * •. ii
(7 marks)
(2 marks)
(4 marks)
(b) the the magnitude of the impulse experience by A due to the impact,
(c) the total loss of kinetic energy due to the impact.
jt -: * •
4. (i) An dasticstring’/lP;of naturaHengtlrTm; hasu particle of mass 2‘kg attached to the end B and the end A is
attached to a fixed point. When the system is in equilibrium with B hanging vertically below A , the length of
the loaded string is 1.2 m.. Calculate the work that must be done in stretching the loaded string from a
length of 1.5 m to a length of 1.75 m. (6 marks)
(ii). A car of mass 1000 kg moves along a straight horizontal road. The engine works at a constant
rate of 50 kW against a constant resistance of magnitude 5000 N to the motion of the car.
(a) Find the maximum speed of the car.
( b) If the speed v of the car is not maximum, show that the acceleration a of the car is given by
50 — 5v
(3 marks)
:
a = (4 marks)
v
5. A particle P is projected from a point O on a horizontal plane at time t = 0 with velocity
(5i + 5x/3 j) m s-3, where i and j are are unit vectors along Ox and Oy respectively.
Find,
(a) the cartesian equation of the trajectory of P,
(b) the maximum height which P attains above the horizontal plane through O ,
(c) the distance of P from the point 0 when t = 2 s.
(4 marks)
(5 marks)
(4 marks)
A *y/k > ;v.\ (Take g as 10 m s~ 2)
