Student Solutions

1.  A law enforcement officer in an intergalactic "police car" turns of a red flashing light and sees it generate a flash every 1.5s. A person on the earth measures that the time between flashes is 2.5s. How fast is the "police car" moving relative to the earth?

2.   Suppose that you are traveling on board a spacecraft that is moving with respect to the earth at a speed of 0.975c. You are breathing at a rate of 8.0 breaths per minute. As monitored on earth, what is your breathing rate?

3.  An astronaut travels at a speed of 7800 m/s relative to the earth, a speed that is very small compared to c. According to a clock on the earth, the trip lasts 15 days. Determine the difference (in seconds) between the time recorded by the earth clock and the astronaut's clock.

4.  As observed on earth, a certain type of bacteria is known to double in number every 24.0 hours. Two cultures of these bacteria are prepared, each consisting initially one bacterium. One culture is left of earth and the other placed on a rocket that travels at a speed of 0.866c relative to the earth. At a time when the earthbound culture has grown to 256 bacteria, how many bacteria are in the culture on the rocket, according to an earth-based observer?

 

5.  A meter stick moves past you at great speed. If you measure the length of the moving meter stick to be 0.760 m. -- for example, relative to a meter stick that is at rest relative to you -- what is the speed that the meter stick is moving relative to you?

6.    In the year 2010 a spacecraft flies over the moon Station III at a speed of 0.800c. A scientist on the moon measures the length of the spacecraft to be 160m. The spacecraft later lands on the moon, and the same scientist measures the length of the now stationary spacecraft. What value does he get?

 

7.   An unstable particle is created in the upper atmosphere from a cosmic ray and travels straight down towards the surface of the earth with a speed of 0.99860c relative to the earth. A scientist on the surface of earth measures that the particle was created at an altitude of 60.0 Km.


a) As measured by the scientist, how much time does it take for the particle to travel to the surface of the earth?

b) Use the length contraction formula to calculate the distance from when the particle is created to the surface of the earth, in the particle's frame?

c) In the particle’s frame, how long does it take for it to travel from its origin to the surface of the earth? Calculate this time both by the time dilation formula and also from the distance calculated in part b) Do the two results agree?

 

8.   A muon created 20.0 Km. above the earth's surface (as measured in earth's frame) is moving with a speed relative to the earth of 0.9954c. The lifetime of the muon, as measured in its own frame, is 2.2 x 10^-6 seconds. In the frame of the muon, the earth is moving towards the muon with a speed of 0.9954c.


a) In the muon's frame, what is ist height above the earth?

b) In the muon's frame, how much closer does the earth get during its lifetime? What fraction of this is the muon's height as measured from the muon's frame?

c) In the earth's frame, what is the lifetime of the muon? In the earth's frame, how far does the muon travel during its lifetime? What fraction of this is the muon's height as measured from the earth's frame?