1) Momentum conservation in 1D: two asteroids collide head-on and stick together. Before the collision, asteroid A (mass = 1,000kg) was moving at a speed of 100m/s, and asteroid B (mass = 2,000kg) was moving at a speed of 80m/s in the opposite direction. Use momentum conservation to find the velocity of the asteroids after the collision. Make a complete momentum chart to help you solve the problem. Note, that you do not need to complete the entire chart to find the final velocity. (That is, you don't need to find the change in momentum of each asteroid separately. Still, finding the individual changes is a good opportunity to check your understanding of momentum conservation.) 2) Momentum conservation in 2D: two asteroids identical to the ones described in 1) collide at right angles and stick together. Let us choose asteroid A to be initially moving to the right (defined as ta direction), and B to be initially moving upward (defined as ty direction). Use momentum conservation to find the velocity of the asteroids after the collision. To express velocity, your answer should have magnitude and direction given as an angle in the x-y plane. Make a complete momentum chart to help you solve the problem.
3) Is the total kinetic energy of the two asteroids in the previous two problems conserved when they collide? Why or why not? Write down an energy conservation equation for the two asteroids, including all the energies that change before and after the collision. Assuming that the asteroids started at the same temperature and that their average specific heat is that of ice (2.05kJ/kg°C), by how much does the temperature of the combined asteroids rise as a result of each of the two collisions described above?