A particle of mass 2 kg moving with a velocity `v_(1)=(2hat(i)-3hat(j))m//s` experience a perfectly inelastic collision with another particle of mass 2 kg having velocity `vec(v)_(2)=(3hat(j)+6hat(k))m//s`. Find the velocity and speed of the particle formed.

Explanation

Mass `m_(1)=2kg " Mass" m_(2) = 2kg`
Velocity `v_(1)=(2hat(i)-3hat(j))m//s` Velocity `v_(2)=(3hat(j)+6hat(k))m//s`
When two particle experiences a perfectly inelastic collision. So,
`V=(m_(1)v_(1)+m_(2)v_(2))/(m_(1)+m_(2))=(2(2hat(i)-3hat(j))+3(3hat(j)+6 hat(k)))/(2+2)`
`= (4hat(i)-6hat(j)+9hat(j)+18hat(k))/(4)=(4hat(i)+3hat(j)+18hat(k))/(4)`
Speed of combined two particles,
`= hat(i)+(3)/(4)hat(j)+(9)/(2)hat(k)`
`v=sqrt(1^(2)+((3)/(4))^(2)+((9)/(2))^(2))`
`v=sqrt(1+(9)/(16)+(81)/(4))`
Velocity, `v=sqrt(21.81)m//s`