Physics

Vandebilt Catholic High School

W. Dupre

Assignment: Relative Velocity Problems and Time Dilation

Note: Problems in red are of a higher degree of difficulty. Accept the challenge to your mental ability that these problems present. DO NOT GIVE UP! Remember you are a highly intelligent individual capable of these mathematical manipulations.

Regular Class:

1. A car travels north with a speed of 60 km/h on a straight highway. A truck travels in the opposite direction with a speed of 50 km/h. (a) What is the velocity of the car relative to the truck? (b) What is the velocity of the truck relative to the car?
2. A motorist traveling west on Interstate Route 80 at 80 km/h is being chased by a police car traveling at 95 km/h. (a) What is the velocity of the motorist relative to the police car? (b) What is the velocity of the police car relative to the motorist?
3. A river has a steady speed of 0.5 m/s. A student swims upstream a distance of 1 km and returns to the starting point. If the student can swim at a speed of 1.2 m/s in still water how long does the trip take? Compare this with the time the trip would take if the water were still.
4. A shopper in a department store can walk up a stationary (stalled) escalator in 30 s. If the normally functioning escalator can carry the standing shopper to the next floor in 20 s, how long would it take the shopper to walk up the moving escalator? Assume the same walking effort for the shopper whether the escalator is stalled or moving.
5. A person going for morning jog on the deck of a cruise ship is running toward the bow of the ship at 2.0 m/s while the ship is moving ahead at 8.5 m/s. What is the velocity of the jogger relative to the water? Later, the jog is moving toward the stern of the ship. What is the jogger’s velocity relative to the water now?
6. Two planes approach each other head-on. Each has a speed of 800 km/h and they spot each other when they are initially 10.0 km apart. How much time do the pilots have to take evasive action?
7. A passenger is on a ship that is moving forward at 10 m/s. What are his velocities, as measured by an observer at rest on the shore, if the passenger walks (a) with a velocity of 2 m/s toward the front of the ship? (b) with a velocity of —2 m/s toward the rear?
8. From the reference frame of a stationary observer, a car traveling at a constant speed of 92 km/h, is passed by a truck moving at105 km/h. (a) From the point of view of the car what is the truck’s speed? (b) From the point of view of the truck, what is the car’s speed?
9. As you travel at a constant 95 km/h, a car that you know to be 3.5 m long, passes you in 1.8 s. How fast is it going relative to Earth?
10. The pilot of an airplane notes that the compass indicates a heading due west. The airplanes speed relative to the air is 150 km/h. If there is a wind of 30 km/h toward the west, find the velocity of the airplane relative to the ground.

Level 1:

11. A motorist traveling west on Interstate Route 80 at 80 km/h is being chased by a police car traveling at 95 km/h. (a) What is the velocity of the motorist relative to the police car? (b) What is the velocity of the police car relative to the motorist?
12. A river has a steady speed of 0.5 m/s. A student swims upstream a distance of 1 km and returns to the starting point. If the student can swim at a speed of 1.2 m/s in still water how long does the trip take? Compare this with the time the trip would take if the water were still.
13. Two planes approach each other head-on. Each has a speed of 800 km/h and they spot each other when they are initially 10.0 km apart. How much time do the pilots have to take evasive action?
14. As you travel at a constant 95 km/h, a car that you know to be 3.5 m long, passes you in 1.8 s. How fast is it going relative to Earth?
15. Two canoeists in identical canoes exert the same effort paddling in a river. One paddles directly up stream (and moves upstream), whereas the other paddles directly downstream. An observer on the riverbank reckons their speeds to be 1.2 m/s and 2.9 m/s. How fast is the river flowing?
16. A boat requires 2.00 min to cross a river that is 150 m wide. The boat's speed relative to the water is 3.00 m/s , at some angle theta, and the river current has a speed of 2.00 m/s. At what possible upstream or downstream points does the boat reach the opposite shore?
17. The pilot of an airplane notes that the compass indicates a heading due west. The airplanes speed relative to the air is 150 km/h. If there is a wind of 30 km/h toward the north, find the velocity of the airplane relative to the ground.
18. A car travels due east with a speed of 50 km/h. Rain falling vertically with respect to the earth. The traces of the rain on the side windows of the car make an angle of 60 with the vertical. Find the velocity of the rain with respect to (a) the car and (b) the earth.
19. A boat, whose speed in still water is 2.2 m/s. must cross a 260 m-wide river and arrive at a point 110 m upstream from where it starts. To do so, the pilot must head the boat at a 45^O upstream angle. What is the speed of the river’s current?
20. What is the speed of a beam of pions if their average lifetime is measured to be 3.80 x l0^-8 s? At rest, their lifetime is 2.60 X l0^-8 s?
21. The period of a pendulum is measured to be 3.0 s in the inertial frame of the pendulum. What is the period of the pendulum when measured by an observer moving at a speed of 0.95 c with respect to the pendulum?
22. Consider two twins 25 years old. One twin steps on a space ship (after studying physics in college) and travels through space at 0.95c for 4 years according to her. How old is each twin when she returns?
23. If you were to board a craft and travel at 0.8c, how long would 1 hour be?
24. If you were to board a craft and travel at c, how long would 1 hour be?