4. I'm elastic! Fantastic!. (10 points)
Suppose a particle with mass \( m_{1}=2.00[\mathrm{~kg}] \) approaches a stationary particle with an unknown mass \( m_{2} \) at the origin. The initial speed of particle 1 is \( v_{i 1}=2.34[\mathrm{~m} / \mathrm{s}] \) and is oriented at \( \theta=30^{\circ} \) below the horizontal axis as shown. Upon collision, both particles move with an unknown speed. particle 1 is oriented at \( \beta=25.0^{\circ} \) above the horizontal axis while particle 2 is oriented \( \phi=60^{\circ} \) below the horizontal axis. Assume that the collision is elastic. Refer to the figure, the dashed lines refer to particles before the collision and the solid lines are after the collision.
A. (4 points) What are the equations for the conservation of linear momentum and kinetic energy?
B. (2 points) Using the above equations, what is the final speed of particle 1?
C. (2 points) What is the mass of the second particle?
D. ( 2 points) What is the final speed of particle 2 ?