A\'cheetah\'of\'mass\'2M\'is\'in\'pursuit\'of\'a\'deer\'of\'mass\'M.\'Initially,

Question

A'cheetah'of'mass'2M'is'in'pursuit'of'a'deer'of'mass'M.'Initially,'the'cheetah' has'half'the'kinetic'energy'of'the'deer,'but'when'the'cheetah'speeds'up'by'5m/s,'its' kinetic'energy'is'the'same'as'the'deer.'What'were'the'initial'speeds'of'the'cheetah' and'the'deer?

A'bullet'of'mass'500'grams'moving'with'velocity'v'='100m/s'collides'with' and'gets'embedded'inside'a'heavy'iron'block'of'mass'10'Kg.'Find'the'kinetic'energy' of'the'system'(block'+'bullet)'before'and'after'the'collision.'Is'kinetic'energy' conserved?'If'not,'where'does'the'difference'in'energy'go?

Explanation / Answer

2)

Kinetic energy before bullet collides and and gets embedded inside a heavy iron block

KEbefore=(1/2)mbulletVbullet2+(1/2)mblockVblock2 =(1/2)*(500*10-3)*1002+(1/2)*10*02

KEbefore=2500 J

By Conservation of momentum

mbulletVbullet+mblockVblock=(mbullet+mblock)V

0.5*100+10*0=(10+0.5)*V

V=4.76 m/s

Kinetic energy after  bullet collides and and gets embedded inside a heavy iron block

KEafter=(1/2)(mbullet+mblock)*V2=(1/2)*(10+0.5)*4.762

KEafter=119.04 J

Kinetic energy is not Conserved

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