1. Two cars are traveling at constant speed along a road in the same direction. Car A moves at 60 km/h and car B moves at 40 km/h, each measured relative to an observer on the ground. What is the speed of car A relative to car B? 2. A supersonic plane moves away from you, and in the +x direction, at a speed of 1000 m/s relative to you. A second plane, traveling in the same direction and ahead of the first plane, moves away from you, and away from the first plane, at a speed of 500 m/s relative to the first plane. How fast is the second plane moving relative to you? 3. Astronauts in a spaceship traveling at v = 0.6c relative to Earth sign off from space control, saying that they are going to nap for 1.00 h and then call back. How long does their nap last as measured on Earth? 4. A stick that has a proper length of 1 m moves in a direction parallel to its length with speed v relative to you. The length of the stick as measured by you is 0.914 m. What is the speed v? T 5. Muons are generated in the upper atomsphere because of high-energy cosmic ray bombardments. They have large speeds (v/c = 0.9978). The mean lifetime mea- sured for a muon at rest is 7 = 2.2μs. How far would a muon travel (on average) towards the earth during this lifetime? Explain how does one still observe plenty of muons at sea-level, after they have travelled around 10 000 m after being produced in the atmosphere. 6. A space ship moves past earth at speed v. It shoots a laser beam away from the earth while doing so. Calculate the speed of the laser beam as measured by a stationary observer using Galilean physics. What answer do you get using relativistic physics. 7. Repeat the calculation in question 2, assuming that the first airplane moves with speed v = 0.8c relative to you and the second air plane moves with the same speed 0.8c relative to the first plane. 8. An electron (rest energy 0.511 MeV) moves with speed v = 0.800c. Find (a) its total energy, (b) its kinetic energy, and (e) the magnitude of its momentum. 9. An airplane moves at 3000 km/hr. What is the percentage change in its mass Mc² 4100 because of its motion?

1. Two cars are traveling at constant speed along a road in the same direction. Car A moves at 60 km/h and car B moves at 40 km/h, each measured relative to an observer on the ground. What is the speed of car A relative to car B? 2. A supersonic plane moves away from you, and in the +x direction, at a speed of 1000 m/s relative to you. A second plane, traveling in the same direction and ahead of the first plane, moves away from you, and away from the first plane, at a speed of 500 m/s relative to the first plane. How fast is the second plane moving relative to you? 3. Astronauts in a spaceship traveling at v = 0.6c relative to Earth sign off from space control, saying that they are going to nap for 1.00 h and then call back. How long does their nap last as measured on Earth? 4. A stick that has a proper length of 1 m moves in a direction parallel to its length with speed v relative to you. The length of the stick as measured by you is 0.914 m. What is the speed v? T 5. Muons are generated in the upper atomsphere because of high-energy cosmic ray bombardments. They have large speeds (v/c = 0.9978). The mean lifetime mea- sured for a muon at rest is 7 = 2.2μs. How far would a muon travel (on average) towards the earth during this lifetime? Explain how does one still observe plenty of muons at sea-level, after they have travelled around 10 000 m after being produced in the atmosphere. 6. A space ship moves past earth at speed v. It shoots a laser beam away from the earth while doing so. Calculate the speed of the laser beam as measured by a stationary observer using Galilean physics. What answer do you get using relativistic physics. 7. Repeat the calculation in question 2, assuming that the first airplane moves with speed v = 0.8c relative to you and the second air plane moves with the same speed 0.8c relative to the first plane. 8. An electron (rest energy 0.511 MeV) moves with speed v = 0.800c. Find (a) its total energy, (b) its kinetic energy, and (e) the magnitude of its momentum. 9. An airplane moves at 3000 km/hr. What is the percentage change in its mass Mc² 4100 because of its motion?