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?
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.