Inelastic Collision and Finding Initial Velocity

[pitaaa]

Homework Statement

Two rolling gold balls of the same mass collide. The velocity of one ball is initially 2.70 m/s [E]. After the collision, the velocities of the balls are 2.49 m/s [62.8 degrees N of W] and 2.37 m/s [69.2 degrees S of E]. What are the magnitude and direction of the unknown initial velocity?

Homework Equations

mv₁ + mv₂ = mv₁' + mv₂'

The Attempt at a Solution

First off, I drew the resulting velocities, and found their components.

The x and y components of the 2.49 m/s velocity are -2.49cos62.8 and 2.49sin62.8 respectively. The x and y components of the 2.37 velocity are 2.37 cos 69.2, and -2.37sin69.2 respectively. Knowing this, I figure I have to incorporate the components somewhere into the equation - I just don't know where! Given the above equation, since the masses are equal, I can eliminate the masses from the equation entirely - likewise, I can eliminate the 1/2, by multiplying the entire equation by two - thus, I have a simplified equation ... I just don't know where to go from here. Can anybody give me a hint as to what to do with the components? Any insight is greatly appreciated!

The answer is supposed to be 3.00 m/s, for the initial velocity of the unknown.

 

[LowlyPion]

Your inelastic collision will result in the conservation of momentum. Total before is total after as you have given.

Draw a careful vector diagram. Note that you can use vector addition by adding the x and y components separately and still insure that Total momentum before is the same as Total momentum after in each axis.

A careful diagram will help you keep the signs of the values straight.

 

[pitaaa]

Okay, I redrew the vector diagram.
But what do I do once I have my components? :/
I don't know what to do with them.

 

[LowlyPion]

Okay, I redrew the vector diagram.
But what do I do once I have my components? :/
I don't know what to do with them.

Doesn't the sum of the x components of the velocity vectors (you've discarded mass as both are the same, but momentum vectors if you were still carrying the mass) before properly add to the sum of the after collision velocity (or momentum) components? The same for the y components?

 

[pitaaa]

Hmm I'll try it :/ Unless my diagram is totally wrong :P

 

[joolspools]

i kinda have a proble like that but in mine i have a 5,000 kg railroad car moving at 2 m/s collides and connects to another identical car intially at rest.what is the finial velocity of the two connected train cars?