Question

After a completely inelastic collision, two objects of the same mass and same initial speed are found to move away together at 1/3 their initial speed. Find the angle between the initial velocities of the objects.

Answer 1

Answer:

The angle is $141.058^{\circ}$

Solution:

As per the question:

Mass of the objects are same, say m Kg each

Let their initial speed be 'u'

Both the objects move apart from each other at $\frca{1}{3}u$ m/s

Now, the angle between the objects' initial velocities is given by using the law of conservation of momentum:

Now, applying the principle of momentum conservation along the horizontal axis:

$mucos\theta + mucos\theta = 2m\frac{u}{3}$

$cos\theta = \frac{1}{3}$

$theta = cos^{- 1}(\frac{1}{3}) = 70.528^{\circ}$

Now, momentum conservation along vertical axis:

$musin\theta - musin\theta = 0$

Now, angle between the initial velocities of the objects:

$2\theta = 2\times 70.528^{\circ} = 141.058^{\circ}$