(PLEASE HELP THIS IS AN EMERGENCY!!!!) (MUCH APPRECIATED)

1. Prove these statements: (a) As long as you can neglect the effects of the air, if you throw anything vertically upward, it will have the same speed when it returns to the release point as when it was released. (b) The time of flight will be twice the time it takes to get to its highest point.

3. A movie stuntwoman drops from a helicopter that is 30.0 m above the ground and moving with a constant velocity whose components are 10.0 m/s upward and 15.0 m/s horizontal and toward the south. You can ignore air resistance. (a) Where on the ground (relative to the position of the helicopter when she drops) should the stuntwoman have placed the foam mats that break her fall? (b ) Draw x-t, y-t, vx-t and vy-t graphs of her motion.

4. A large box containing your new computer sits on the bed of your pickup truck. You are stopped at a red light. The light turns green and you stomp on the gas and the truck accelerates. To your horror, the box starts to slide toward the back of the truck. Draw clearly labeled free-body diagrams for the truck and for the box. Indicate pairs of forces, if any, that are third-law action-reaction pairs. (The bed of the truck is not frictionless).

5. Two crates, one with mass 4.00 kg and the other with mass 8.00 kg, sit on the frictionless surface of a frozen pond, connected by a light rope. A woman wearing golf shoes (so she can get traction on the ice) pulls horizontally on the 8.00 kg crate to the right with a force F that gives the crate an acceleration of 2.5 m/s2 . (a) What is the acceleration of the 4.00 kg crate? (b) Draw a free-body diagram for the 4 kg crate. Use that diagram and Newton's second law to find the tension T in the rope that connects the two crates. (c) Draw a free-body diagram for the 8 kg crate. What is the direction of the net force on the 8 kg crate? Which is larger in magnitude, force T or force F? (d) Use part (c) and Newton's second law to calculate the magnitude of force F.

7. Block B, with mass 5.00 kg, rests on block A, with mass 8.00 kg, which in turn is on a horizontal tabletop. There is no friction between block A and tabletop, but the coefficient of static friction between block A and block B is 0.750. A light string attached to block A passes over a frictionless, massless pulley, and block C is suspended from the other end of the string. What is the largest mass that block C can have so that blocks A and B still slide together when the system is released from rest?

8. A falling brick has mass 1.5 kg and is moving straight downward with a speed of 5.0 m/s. A 1.5 kg physics book is sliding across the floor with a speed of 5.0 m/s. A 1.5 kg melon is traveling with a horizontal velocity component 3.0 m/s to the right and a vertical component 4.0 m/s upward. Do these objects all have the same velocity? Do these objects all have the same kinetic energy? For each question, give the reasoning behind your answer.

9. A 20.0 kg crate sits at rest at the bottom of a 15.0 m long ramp that is inclined at 34.0 above the horizontal. A constant horizontal force of 290 N is applied to the crate to push it up the ramp. While the crate is moving, the ramp exerts a constant frictional force on it that has a magnitude 65.0 N. (a) What is the total work done on the crate during its motion from the bottom to the top of the ramp? (b) How much time does it take the crate to travel to the top of the ramp?

10. A small block with mass 0.0400 kg slides in a vertical circle of radius R=0.5 m on the inside of a circular track. During one of the revolutions of the block, when the block is at the bottom of its path, point A, the magnitude of the normal force exerted on the block by the track has a magnitude 3.95 N. In this same revolution, when the block reaches the top of its path, point B, the magnitude of the normal force exerted on the block has a magnitude of 0.680 N. How much work was done on the block by friction during the motion of the block from point A to point B?

11. Two marbles are pressed together with a light ideal spring between them, but they are not attached to the spring in a any way. They are then released on a frictionless horizontal table and soon move free of the spring. As the marbles are moving away from each other, discuss the following statements. (a) The momentum of the marbles are conserved. (b) The mechanical energy of the marbles is conserved. (c) The kinetic energy of the marbles is conserved.

12. A small wooden block with mass 0.800 kg is suspended from the lower end of a light cord that is 1.6 m long. The block is initially at rest. A bullet with mass 12.0 g is fired at the block with a horizontal velocity v0. The bullet strikes the block and becomes embedded in it. After the collision the combined object swings on the end of the cord. When the block has risen a vertical height of 0.8 m, the tension in the cord is 4.8 N. What was the initial speed v0 of the bullet?

15. A 5.0 kg ball is dropped from a height of 12.0 m above one end of a uniform bar that pivots at its center. The bar has mass 8.0 k and is 4.0 m in length. At the other end of the bar sits another 5.0 kg ball, unattached to the bar. The dropped ball sticks to the bar after the collision. How high will the other ball go after the collision?