# Collisions in Two Dimensions

After a completely inelastic collision, two objects of the same mass and same initial speed are found to move away together at 1/4 their initial speed. Find the angle between the initial velocities of the objects.

I figured.. 2m(v/4)
but then i just get lost... can someone help! thanks!

## Answers and Replies

nrqed
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mb85 said:
After a completely inelastic collision, two objects of the same mass and same initial speed are found to move away together at 1/4 their initial speed. Find the angle between the initial velocities of the objects.

I figured.. 2m(v/4)
but then i just get lost... can someone help! thanks!

Pick a direction for the first object, let's say East. Let's say the second object is coming from an angle $\theta$ North of East. Then Decompose their momenta into x and y components, apply conservation of momentum along x and y directions. You will find the final x and y velocities along x and y in terms of the initial speed v and the angle $\theta$. Impose that ${\sqrt { v_{x final}^2 + v_{y final}^2}} = v/4$ and that will give you a single equation for $\theta$.

Patrick

OK, so the collision is in 2 dimensions, so you know you're going to be using vectors. So let me start you off with what you know.

$$m(\underline{v}_1 + \underline{v}_2 ) = 2m \underline{v}_{final}$$

Do you know how to make vectors loose their directional components?

(Hint: Multiply both sides by a vector you know)

Hope this Helps, Sam

OK, pick the vector carefully.

I have just done this question in 5 lines (instead of 10) by picking another vector. If you don't choose your vector well, you'll have to use some trig. identities (which I don't like if I can avoid it).

Draw a diagram and note what the angles have in relation to each other due to symmetry. If you want, I'll put up a diagram of what I'm trying to say... just ask if you want it.

Regards,
Sam

hey thanks. this is what i did so far. but im still have trouble.

M1V1i + M2V2i = M1V1f + M2V2f

initial for 1
X = mv cos Theta
y = mv sin theta

final for 1
X = mv
y=0

Initial for 2
X = mv cos theta
Y = mv sin theta

final for 2
X =mv
y = 0

mv cos theta + mv sin theta = MVi
Mv (cos theta + sin theta) = MVi

???? then i get lost.

The components of their initial velocities perpendicular to the direction of their final velocity adds to zero. And the components along this direction must thus be same and add upto v/4.

Sorry. The second sentence is - the component of their initial velocities along the direction of final velocity must thus be same and add upto v/4

im still confused.

can someone show me the steps?

Let a be the angle made with their initial velocities along the direction of final veloctitis.
Now,
v*cosa + v*cosa = v/4.
Thus cosa = 1/8