Two particles of masses m, and my collide on a frictionless surface, see Figure 1. Particle m, has an nitial speed of w, in the x-direction and particle my is initially stationary. After the collision particle m, has a speed v, with a trajectory that makes an angle 9, with the x-axis, and particle my has a speed ,with a trajectory that makes an angle d, with the x-ads. a) Determine the following kinematic qualities of the system in terms of v, V2.9, and 82. Each entry is worth 3 points, make sure to show your work by drawing the appropriate triangles. a. Vix = b. Vly= C. VIX= d. Vay= bj Write the equations for conservation of momentum in the x and y directions, each equation is worth 3 points. a. x-direction: b. y direction: c) Using the y-direction equation you derived above, a] Solve for the final speed of particle 1, F1, in terms of my, mz, #1, 82 and #2. (b) Using the equation from (a] determine the relationship between my, my, sin (8,), and sim(82) that must be true if the final speeds of both particles are equal (le. v, = v.). b. d) Using the equation for , derived in part (c), determine the equation for the final speed of particle 2, v2, in terms of my , my, 81. 82 and uj. a. V1= e) Use the equation for vy derived in part dj to determine the equation for the final speed of particle 1, vj, in terms of my. my.9,. 82 and wj- a. V1= f) Using the following values: I. m = 10- il. 81 = 45' iil. 87 = 30' wv. my = 5kg Determine the value of my that will make the collision elastic: my= BEFORE COLLISION AFTER COLLISION igant