Jane and Bob see each other when 100 m apart. They are moving toward each other, Jane at speed 3.6m/s and Bob at speed 2.2m/s with respect to the ground. Find the time elapsed for Bob and Jane to meet up.

The measured mean lifetime of an elementary particle when it is at rest in the lab is measured to be 2.6x10-8 s. If the particle is observed while traveling at a speed v=0.9 c with respect to the lab. What will be the value of the measured mean lifetime while the particle is moving?

A car traveling at 35.0 m/s takes 26.0 minutes to travel a certain distance according to the driver’s clock in the car. How long does the trip take according to an observer at rest on Earth? Hint: The following approximation is helpful:

A spaceship approaching an asteroid at a speed of 0.77c launches a rocket forward with a speed of 0.27c relative to the spaceship. At what factor of the speed of light c is the rocket approaching the asteroid as measured by an astronaut on the asteroid?

2. An observer P stands on a train station platform as a high-speed train passes by at u/c = 0.8. The observer P, who measures the platform to be 60 m long, notices that the front and back ends of the train line up exactly with the ends of the platform at the same time. How long does it take the train to pass P as he stands on the platform, as measured by his watch?

Observers in reference frame S see an explosion located at x1=620 m. A second explosion occurs 6.0 micro-s later at x2=1500 m.In reference frame S', which is moving along the +x-axis at speed V, the explosions occur at the same point in space. What is the separation in time delta t' between the two explosions as measured in frame S'? Express your answer in microseconds (micro-s). delta t' = ? micro-s

The distance to a particular star, as measured in the earth's frame of reference, is 7.11 light- years (1 light-year is the distance that light travels in 1 y). A spaceship leaves the earth and takes 3.35 y to arrive at the star, as measured by passengers on the ship. (a) How long does the trip take, according to observers on earth? (b) What distance for the trip do passengers on the spacecraft measure?

Consider a 5.75 m long sports car going past you at great speed. How fast would it have to be going past you in order for it to appear only 5.25 m long? Give you answer as a ratio of the velocity to the speed of light c.  v/c=