Advanced level 2023 northwest regional mock pure mathematics with mechanics 3

Advanced level 2023 northwest regional mock pure mathematics with mechanics 3

Advanced level 2023 northwest regional mock pure mathematics with mechanics 3

A sphere A of mass m, travelling with speed u on a smooth horizontal floor, collides directly with a
stationary sphere B of inuss3w, at a distance •—m from a perpendicular wall. The sphere B hits the
wall, rebounds and collides with the sphere again. Given that the coefficient of restitution between the
spheres is j.und between the wall and the sphere is
a) calculate the speeds ofthe spheres after their first impact
b)calculate thetime it takesB to hit the wall
c)determine whether or not, the sphereB can hit the wall a second time.

(5mks)
(2mks)
(6mks)
5. A particle P of mass4/«, lies on a roug^horizontal tabjle.IheToefficient of friction between the table
and the particle is//=~.P is connected by means of a light inextensible string, passing over a smooth
fixed pulley at the edge of the table,
from rest with the siring taut. In the ensuing to a particle motion Q,ofQmass hits the 2mground hangingwith freely speed . Thegsystem m/s und isdoes released not
rebound. After Q hits the ground,P moves for a while before coming to rest, withoutreaching the pulley.
I)Fmdin termsol g,theaccelerationofthe particle,andinterms ofmandg,the tensioninthe
string. * (7mk)
ii)Findthe timeQtakes tohit the ground (2mks)
IV m))Find Fmd,the IIIextra termstime of gfor , the which further I-moves distant before covered coming bytoPrest before coming to rest, after Q hits (2mks the)
ground. (2mks)