What Is the Angle Between Initial Velocities in a Perfectly Inelastic Collision?

[bearhug]

After a completely inelastic collision, two objects of the same mass and same initial speed move away together at half of their initial speed.
(a) Find the angle between the initial velocities of the objects

∑pxi = mvi
∑pxf = 2mvfcosӨ
mvi = 2mfvcosӨ

∑pyi= mvi
∑pyf = 2mvfsinӨ
mvi=2mvfsinӨ

2mvfsinӨ = 2mfvcosӨ
1= sinӨ/cosӨ
1=tanӨ

Ө=45°

I feel like there's something I'm not doing right in this problem. Can anyone point out any mistakes?

 

[OlderDan]

I'm seeing some unprintables on my screen, so I won't fight to interpret your equations. If you take the final direction to be the x axis, then you know the initial total y momentum must be zero, and the total initial x momentum is the final momentum. That, combined with the equal masses and speeds forces a fairly obvious symmetry to the problem. The half speed at the end suggests to me there are angles of 30 or 60 degrees involved. I doubt the angle between the initial velocities is 45, but I have not worked it out.

 

[kyle8921]

Your calculations seem to be correct. The angle between the initial velocities of the objects would indeed be 45° in this scenario. However, it is worth noting that in a perfectly inelastic collision, the objects would stick together and move as one unit, so there would not be two separate initial velocities to consider. Instead, the initial velocity would be the combined velocity of the two objects. In this case, the angle between the initial velocity and the final velocity would still be 45°.