Question

Two cars of same mass are moving with same speed v on two different roads inclined at an angle $\theta$ with each other, as shown in the figure. At the junction of these roads the two cars collide inelastically and move simultaneously with the same speed. The speed of these cars would be

• A. $v\cos\frac{\theta}{2}$
• B. $\frac{v}{2}\cos\theta$
• C. $\frac{v}{2}\cos\frac{\theta}{2}$
• D. $2v\cos\theta$

Answer 1

Answer: (A)

$v\cos\frac{\theta}{2}$

Answer 2

Initial horizontal momentum of the system

$= mv\cos\frac{\theta}{2} + mv\cos\frac{\theta}{2}.$

If after the collision cars move with common velocity V then final horizontal momentum of the system = 2mV.

By the law of conservation of momentum, 2mV $= mv\cos\frac{\theta}{2} + mv\cos\frac{\theta}{2} \Rightarrow V = v\cos\frac{\theta}{2}.$