A car weighing `2xx10^(3)kg` and moving at `20 m//s` along a main road collides with a lorry of mass `8xx10^(3)kg ` which emerges at `5 m//s` from a cross road at right angles to the main road. If the two vehicles lock, what will be their velocity after the collision ?

Options

A. `4//sqrt(2)m//s, 45^(@)` with cross road
B. `4//sqrt(2)m//s, 60^(@)` with cross road
C. `4//sqrt(2)m//s, 60^(@)` with main road
D. `4//sqrt(2)m//s, 45^(@)` with main road

Answer

D

Explanation

As is clear from figure, total momentum before impact
`=vec(p_(C))+vec(p_(L))=|vec(p_(L))+vec(p_(L))|`
`=sqrt(p_(C)^(2)+p_(L)^(2))=sqrt((2xx10^(3)xx20)^(2)+(8xx10^(3)xx5)^(2))`
`=40xx10^(3)sqrt(2)kg m//s`
Direction of momentum with main road
`tan theta=(p_(L))/(p_(C))=(8xx10^(3)xx5)/(40xx10^(3))=1:. theta=45^(@)`
Accroding to the law of conservatio of linear momentum,
`10^(3)xx40sqrt(2)=(2xx10^(3)+8xx10^(3))xxV`
`V=4sqrt(2)//s`