What are the velocity components after an inelastic collision in 2D?

[corvus606]

Homework Statement

Two balls od the same masses collide, the first one is moving with the velocity $$v_1$$, the second is stationary. The angle between them is given by the statement: "the direction of the velocity of the first ball forms an angle $$\alpha=30^\circ$$ with the plane of osculation of the balls after the collision"
I have to find magnitude and direction of the velocity after the collision.

Homework Equations

$$\vec{p_1}=\vec{p_2}$$

The Attempt at a Solution

$$m\vec{v_1}=(m+m)\vec{v_2}$$
$$\vec{v_2}=0,5\vec{v_1}$$
$$v_{2x}=0,5v_{1x}=0,5v_1cos\alpha$$
$$v_{2y}=0,5v_{1y}=0,5v_1sin\alpha$$

4. The problem
Sounded good to me but the answer is:
velocity perpendicular to the plane: $$0,5v_1sin\alpha$$
velocity parallel to the plane: $$vcos\alpha$$
And I don't have any idea where did I make the mistake :/

 

[Andrew Mason]

Homework Statement

Two balls od the same masses collide, the first one is moving with the velocity $$v_1$$, the second is stationary. The angle between them is given by the statement: "the direction of the velocity of the first ball forms an angle $$\alpha=30^\circ$$ with the plane of osculation of the balls after the collision"
I have to find magnitude and direction of the velocity after the collision.

Homework Equations

$$\vec{p_1}=\vec{p_2}$$

The Attempt at a Solution

$$m\vec{v_1}=(m+m)\vec{v_2}$$
$$\vec{v_2}=0,5\vec{v_1}$$
$$v_{2x}=0,5v_{1x}=0,5v_1cos\alpha$$
$$v_{2y}=0,5v_{1y}=0,5v_1sin\alpha$$

4. The problem
Sounded good to me but the answer is:
velocity perpendicular to the plane: $$0,5v_1sin\alpha$$
velocity parallel to the plane: $$vcos\alpha$$
And I don't have any idea where did I make the mistake :/

Two things are conserved: energy and momentum.

Write out the equations that result from the conservation of energy and momentum. You are given the angle of one ball relative to the direction of the incident ball (30 degrees from that direction. At least that is what I am assuming from the peculiar wording you have given).

AM

 

[corvus606]

The energy is not conserved in the inelastic collision ;)

 

[Andrew Mason]

The energy is not conserved in the inelastic collision ;)

Then you will have to explain the question better. What exactly happens after the collision?

AM

 

[corvus606]

It isn't clearly stated but most probably the balls are moving "together" (they stick to each other) with a new velocity.