Answer:
The angle is [tex]141.058^{\circ}[/tex]
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 [tex]\frca{1}{3}u[/tex] 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:
[tex]mucos\theta + mucos\theta = 2m\frac{u}{3}[/tex]
[tex]cos\theta = \frac{1}{3}[/tex]
[tex]theta = cos^{- 1}(\frac{1}{3}) = 70.528^{\circ}[/tex]
Now, momentum conservation along vertical axis:
[tex]musin\theta - musin\theta = 0[/tex]
Now, angle between the initial velocities of the objects:
[tex]2\theta = 2\times 70.528^{\circ} = 141.058^{\circ}[/tex]
