Kinematics in Two Dimensions; Vectors and Dynamics: Newton’s Laws of Motion
Please solve the following problems. You must show all work for full/partial credit.
1. A ship has a top speed of 3.0 m/s in calm water. The current of the ocean tends to push the boat at 2.0 m/s on a bearing of due South. What will be the net velocity of the ship if the captain points his ship on a bearing of 55° North of West and applies full power?
2. An airplane is 5,000 m above an observer and 2.1 km to the west of them and 1.5 km to the north of you. Determine the angle to the plane in the x – y axis and the total distance to the plane from you. Choose the x-axis east, y axis north, and z axis up.
3. A bullet is fired from at a shooting range. The bullet hits the ground after 0.32 seconds. How far did it travel horizontally and vertically in this time if it was fired at a velocity of 1100 m/s?
4. A not so brilliant physics students wants to jump from their 3rd floor apartment window to the swimming pool below. The problem is the base of the apartment is 8.00 meters from the pool’s edge. If the window is 20.0 meters high, how fast does the student have to be running horizontally to make sure they make it to the pool’s edge?
5. If a 1500 kg car stopped from an in 5.6 seconds with an applied force of 5000 N, how fast was it initially traveling?
6. If the acceleration due to gravity on the Moon is 1/6 that what is on the Earth, what would a 100 kg man weight on the Moon? If a person tried to simulate this gravity in an elevator, how fast would it have to accelerate and in which direction?
7. A 7.93 kg box is pulled along a horizontal surface by a force F_P of 84.0 N applied at a 47.0o angle. If the coefficient of kinetic friction is 0.35, what is the acceleration of the box?
8. If a car is traveling at 50 m/s and then stops over 300 meters (while sliding), what is the coefficient of kinetic friction between the tires of the car and the road?