The following applies to questions 1-6:[br]A truck of mass 2m and moving at speed v along the x-direction, crashes into a the rear of a car of mass m while the car is at rest at a stoplight. [br]1. If neither vehicle has its brakes applied, and if e=0, what will be the velocity (not speed) of the vehicles immediately after collision in E?[br]2. What is the velocity of the center of mass (in earth frame E) before, during and after the collision in problem number 1?[br]3. What is the momentum of the system in C before and after the collision?[br]4. If the same collision takes place with e=0.2, what are the initial velocities of the two vehicles in C?[br]5. What are the final velocities of the two vehicles in C?[br]6. What are the final velocities of the two vehicles in E?[br]7. A ping pong paddle being swung at speed v (assume mass is much larger than the ball) strikes a stationary ball. If e=1, how fast will the ball be moving in E immediately after impact? In C?[br]8. A tennis ball is thrown against a brick wall that is in the y-z plane. The ball is moving in the x-direction at speed 5 m/s. If e=0.60, what is ball's velocity after impact in E?[br]9. The same tennis ball (b) in the last problem has an initial velocity of [math]\vec{v}_{b,E_i}=(10\hat{i}+3\hat{j})m/s[/math]. What is its final velocity if it undergoes a collision with the same e=0.60 as in the last problem. Keep in mind that only the component of velocity perpendicular to the wall is affected during the collision.[br]10. In parallel to the baseball and bat example problem in the section titled "collisions", find the ball's and the wooden bat's final velocies in E with only one change: Make the ball's initial velocity in E such that it's moving leftward and dropping, or [math]\vec{v}_{b,E}_{i} = (-40\hat{i}-10\hat{j})m/s[/math].

1. 2v/3[math]\hat{i}[/math][br]2. 2v/3[math]\hat{i}[/math][br]3. [math]\vec{0}[/math], [math]\vec{0}[/math][br]4. v/3 [math]\hat{i}[/math], -2v/3 [math]\hat{i}[/math][br]5. -0.07v[math]\hat{i}[/math], 0.13v[math]\hat{i}[/math][br]6. 0.60v[math]\hat{i}[/math], 0.80v[math]\hat{i}[/math][br]7. 2v, v[br]8. -3m/s [math]\hat{i}[/math][br]9. -6m/s [math]\hat{i}[/math] + 3m/s [math]\hat{j}[/math][br]10. [br][math]\vec{v}_{b,E_f}=42.92\frac{m}{s}\hat{i}+12.22\frac{m}{s}\hat{j} \\[br]\vec{v}_{w,E_f}=11.34\frac{m}{s}\hat{i}+1.34\frac{m}{s}\hat{j} [/math]