Question

Two vehicles approach a right angle intersection and then suddenly collide. After the collision, they become entangled. If their mass ratios were 1:4 and their respective speeds as they approached the intersection were both 13 m/s, find the magnitude and direction of the final velocity of the wreck.

Answer 1

Answer with Explanation:

Let mass of one vehicle =m

Mass of other vehicle=m'

`(m)/(m')=(1)/(4)`

`m'=4m`

Velocity of one vehicle=
`v=13 im/s`

Velocity of other vehicle=
`v'=13jm/s`

In x- direction

By law of conservation of momentum

`mv+0=(m+m')V_x`

`13m=(m+4m)V_x`

`13m=5mV_x`

`V_x=(13)/(5)`

In y- direction

By law of conservation of momentum

`0+m'v'=(m+m')V_y`

`4m(13)=5mV_y`

`V_y=(52m)/(5m)=(52)/(5)`

Magnitude of velocity of the wreck,V=
`√(V^2_x+V^2_y)=\sqrt{((13)/(5))^2+((52)/(5))^2}=10.72 m/s`

Direction:
`\theta=tan^(-1)((V_y)/(V_x))`

`\theta=tan^(-1)(((52)/(5))/((13)/(5)))=75.96^(\circ)`