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**Linnus** In a game of marbles, a purple marble makes an off-center collision with a red marble of the same mass. Before the collision, the purple marble travels in the positive *x* direction and the red marble is at rest. After the collision, the purple marble's velocity of 0.0900 m/s makes a 35.0 degree angle above the positive *x* axis and the red marble's velocity makes an angle of negative 20.0 degrees with the axis. Find the initial speed of the purple marble.

I think this is a completely elastic collision which means the kinetic energy is conserved. The momentum is also conserved. I'm a bit lost on how to do the problem because it doesn't tell me what is the red marble's final velocity (maybe I don't need it...).

Thank you!