4. Derive an equation that relates Christine's initial velocity (v1,0) and the speed vy of the human-skateboard system after the collision in terms of m, m2, and fundamental constants, as appropriate. 5. Calculate Christine's initial velocity (11,0) immediately prior to colliding with the skateboard. 6. Construct a force as function of time graph that accurately depicts Christine's change in momentum (Ap) from immediately prior to immediately after the collision. Appropriately scale and label all axes, including units. (Hint: The collision occurs over 0.06 seconds) 7. Suppose you did not have access to the video clip, but only the data for all masses, initial velocities, and final velocity(ies). a. In coherent paragraph-length response that may also contain drawings and/or equations, explain, using the conservation of momentum and the conservation of energy, how you would determine the specific type of interaction occurring based only on the data. b. Perform all calculations as indicated in your claim in part 7(a). c. Do the quantities obtained in part 7(b) serve to support or reject your claim in part 6(a)? Justify your response. Data: Watch this video clip. Record all relevant information (data) in the space below. Analysis: 1. State the basic physics principles, laws, or equations that you could use to determine the relationship between the initial velocity of m and the speed at which the human- skateboard system travels after they collide and stick together. 2. Derive an equation for determining the velocity of the human-skateboard system immediately after the collision (v) in terms of tfinal, tinitial, and x. 3. Calculate the human-skateboard system's velocity immediately after the collision.