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'

$\frac{m}{m'}=\frac{1}{4}$

$m'=4m$

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

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

In x- direction

By law of conservation of momentum

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

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

$13m=5mV_x$

$V_x=\frac{13}{5}$

In y- direction

By law of conservation of momentum

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

$4m(13)=5mV_y$

$V_y=\frac{52m}{5m}=\frac{52}{5}$

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

Direction:$\theta=tan^{-1}(\frac{V_y}{V_x})$

$\theta=tan^{-1}(\frac{\frac{52}{5}}{\frac{13}{5}})=75.96^{\circ}$