Question

A car weighing $2\times {10}^{3}kg$ and moving at $20m/s$ along a main road collides with a lorry of mass $8\times {10}^{3}kg$ which emerges at $5m/s$ from a cross road at right angle to the main road. If the two vehicles lock, what will be their velocity after the collision?

• A. $4/\sqrt{2}m/s,{45}^{\circ }$ with cross road
• B. $4/\sqrt{2}m/s,{45}^{\circ }$ with main road
• C. $4/\sqrt{2}m/s,{60}^{\circ }$ with cross road
• D. $4/\sqrt{2}m/s,{60}^{\circ }$ with main road

Answer 1

The correct option is B $4/\sqrt{2}m/s,{45}^{\circ }$ with main road

The given situation can be shown as
Total momentum before impact
$=p_C+p_L=|p_C+p_L|$
$=\sqrt{p_C^2+P_L^2}$
$=\sqrt{(2\times {10}^3\times 20{)}^2+(8\times {10}^3\times 5{)}^2}$
$=40\times {10}^3\sqrt{2}kgm/s$
Direction of momentum with main road
$\tan \theta =\frac{p_L}{p_C}=\frac{8\times {10}^3\times 5}{40\times {10}^3}=1$
$\Rightarrow \theta ={45}^{\circ }$
By the law of conservation of linear momentum,
${10}^3\times 40\sqrt{2}=(2\times {10}^3+8\times {10}^3)v$
$\Rightarrow v=4\sqrt{2}m/s$.