# Theory of Relativity

1. Two airplanes are flying side by side at the same altitude. Plane A is slowly overtaking plane B at 4 km/h. A stewardess in plane A is walking toward the rear of the plane at a speed of 2 km/h, and a passenger is walking toward the front at 2 km/h. What are their speeds relative to a passenger watching them from place B?

2. A spaceship approaching a planet at a speed of 0.23c fires a probe toward a planet. Observers on the planet see the probe approaching at a speed of 0.67c. What is the speed of the probe as measured from the spaceship?

3. An astronaut journeying to the nearby star Lacaille 9352 at a speed of 0.850c relative to earth requires 20.0 years measured on earth to complete his trip. How many years does he age during his journey?

4. The mean life of muons is 2.2 micro.s. What is the mean life of a beam of muons moving at a speed of 0.9995c relative to you?

5. A spaceship moves with a speed v = 0.90c relative to a space platform that has a landing strip 5000m long. What is the apparent length of the landing strip as measured in the frame of the spaceship?

6. A meterstick is accelerated to a velocity such that it is contracted to only 50 cm relative to an interested observer. How fast must the meterstick be moving in the observer's frame reference?

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#### Solution Preview

1. The relative velocity of plane A wrt plane B = 4km/hr

The relative velocity of the stewardess wrt plane B will be = rel velocity of plane A - vel of stewerd = 4-2 = 2km/hr

Similarly, the relative velocity of the passenger wrt plane B will be = rel velocity of plane A + vel of passenger = 4+2 = 6km/hr

When two bodies A and B are moving along a straight line with constant velocities Va and Vb in the ...

#### Solution Summary

Solution includes calculations and explanation. 330 words.