A sphere of mass `m` is moving with a velocity `4hat"i"+3hat"j"-5hat"k"` when it hits a smooth wall and rebounds with velocity `2hat"i"+2hat"j"+3hat"k"`. Find the impulse it receives. Find also the coefficient of restitution between the sphere and the wall.

Answer

`m(-2hati-hatj+8hatk),(6)/(17)`

Explanation

`vecI=(vecv_(f)-vecv_(i))=m(-2hati-hatj+8k)`
`"coefficient of restitution"=(("velocity of separation along line of impact")/("velocity of approch along line of impact"))`
line of impact is along the direction of impulse.
`e=-(((vecv_(f).vecI)/(I)))/(((vecv_(i).vecI)/(I)))=(vecv_(f).vecI)/(vecv_(f).vecI)=((2hati+2hatj+3hatk).[m(-2hati-hatj+8hatk)])/((4hati+3hatj-5hatk).[m(-2hati-hatj+8hatk)]`
`=-((-4-2+24)m)/((-8-3-40)m)=(18)/(51)=(6)/(17)`