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Ma9\rNg ll1. A car of mass1000kg moveswith constant peedz m s-' up a straigh
an angled to the horizontal.wheresind= $. Theengineof the car s wof 12kW.Theresistanceo motion rom non-gravitationalorceshasmaFind thevalueof tr/.
' 5@+
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2. A particleP of mass??s moving n a straight ine on a smoothhorizospeed zr.TheparticleP collidesdirectlywith aparticleQ of mass3m wthe surface. hecoefficient f restitution etween andQ is e. The dirofP is reversed y the collision.IShowhat e>:.
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3. A ball of mass0.5 kg is movingwith velocity12i m s-l when t is struckbimpulse eceived y the ball is ( 4i +7j) N s.By modelling he ball asapar(a) the speed f the ball immediately fter he mpact,
(b) the angle,n degrees, etween he velocityof the ball immediately ftand he vector ,
(c) the kineticenergy ained y the ball asa resultof the mpact.
L\+1'.
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r' +a B
-d\9t,/E
9r qD
Figure1Figure 1 showsa uniform laminaABCDE such hat ABDE is a rect,4.8 Ca andAE :2a. ThepointF is themidpoint f BDandFC:a'(a) Find, n termsof a, the distance f thecentre f massof the amina
s4.
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5 .
2A' j o - _ _ _ _Figure2
A particle P of mass0.5 kg is projected rom a point I up a line of greatefixed plane.The plane is inclined at 30oto the horizontal andAB : 2 m was shown in Figure 2. The particle P passes hrough B with speed5 m ssmooth rom I to B.
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6. A particleP moves n hex-axis.TheaccelerationfP at ime secondssthepositive -direction. hevelocityof P at timeI secondss v m s-1'WhFind(a) v in termsof r,
(b) thevaluesof I whenP is instantaneouslyt rest,
(c) thedistance etweenhe wo pointsatwhichP is instantaneouslyt
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1D
1aIFigure3
AuniformrodlB,ofmass3rnandlength4a,isheldinahorizontlagainstaroughvert icalwall .oneendofal ight inextensiblest
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i 6q+3zC = lSa. =) 3>c=4o. =..) )Cb) 4t 10- tt I!4t =ErS, + -c) ({f=o a Sr.,tron 6^9:-S =
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8, A particle is projected rom a point O with speedu at an angleof elevationahorizontal and moves freely under gravity When the particle has moved adistancer, ts heightaboveO isY.(a) Show hat
v = xtana - .8t ,' Zu ' cos 'a
A girl throwsa ball from a point ,4 at the top."i t ttlf The point I is 8 ',oi"ontut U"u.t . Theball s projected ith speed m s I at anangleof elevaBy modellingheball asaparticlemoving reelyundergraviry(b)f indthehorizontaldistanceofthebal l fromlwhenthebal l islmab
A boy is standing n thebeachat thepointB verticaliy^elow ' He startsstraijht inewith speed m s-t, leavingB 0'4 seconds fter heball is throwHe catchesheball when t is I m abovehebeach'
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s2-V(r)
8.7226 .-.
-'. 1Ao- bo-r {ahos t.9026(,-. to catch w=J.i *J,.*o- V-=?L; g-'.JEg6!\t e 6:?!bnq-- 9-6.