Question

Two identical vehicles are moving with same velocity $v$ towards an intersection as shown in the figure. If the collision is completely inelastic, then:

• A. The velocity of separation is zero
• B. The velocity of approach is $2vsin\frac{\theta }{2}$
• C. The common velocity after collision is $vcos\frac{\theta }{2}$
• D. All of the above

Answer 1

Answer: (D)

All of the above

Resolving the initial velocities into components along $x$ and $y$ axis, we observe that the the x-components are same as shown in the figure.
The $y-$components are opposite each other.

Hence, velocities of approach is $2v\sin \frac{\theta }{2}$.

Since, collision is inelastic, both the bodies will stick together after collision.
$\Rightarrow$ Velocity of separation is zero.

$\Rightarrow 2mu\cos \frac{\theta }{2}=Totalmass\times v_{cm}=2m{v}_{cm}$;

$\Rightarrow v_{cm}=u\cos \frac{\theta }{2}$