3. need help in physics....?

Question

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

Answer 1

Conservation of p

Initial p = 2 m v cos (theta/2)
=
final p = 2mv/3

cos (theta/2) = 1/3

theta = 2 arc cosine (1/3)

Answer 2

I'll try to get you started without giving away the answer (which would be cheating, of course).

Hints:

1. Draw a diagram. Choose a reference frame in which the the final velocity of the glob is directly to the right, along the x-axis. Draw an arrow showing the final momentum of the glob. Draw two other arrows showing the initial momentums of the original two objects (hint: one will be moving down & to the right; the other will be moving up & to the right). Your diagram of 3 arrows should look like a sideways "Y".

2. Use the law of conservation of momentum. The sum of the momentum vectors of the initial two objects, must equal the momentum vector of the final glob.

3. To help you add the momentum vectors, break them into their X and Y components. Use Sin(a) and Cos(a) to do that. (You don't yet know the value of "a" -- that's exactly what the problem is asking you to solve -- but use the variable anyway.)

4. The problem tells you that: (1) the two masses are equal; (2) the two initial speeds are equal; and (3) the final speed is 1/3 of the initial speed. Use those facts to reduce the number of variables to a minimum.

5. The sum of the X components of the initial vectors, must equal the X component of the final vector. And the sum of the Y components of the initial vectors, must equal the Y component of the final vector.