Quiz – Special Relativity

What is the Lorentz factor for an object travelling at 99.6% of the speed of light?

What is the Lorentz factor for an object travelling at 181000000 m/s? Assume that the speed of light in a vacuum is 3.00 x 10^8 m/s.

A train with a resting length of 275 m is travelling at 45.0% of the speed of light relative to a stationary observer. How long will the train appear to the stationary observer? Answer in metres, using numbers only (i.e. '1.9' for an answer of 1.9 m).

A train with a resting length of 125 m is travelling at 1.11 x 10^8 m/s relative to a stationary observer. How long will the train appear to the stationary observer? Assume that the speed of light in a vacuum is 3.00 x 10^8 m/s. Answer in metres, using numbers only (i.e. '1.9' for an answer of 1.9 m).

A train with a resting length of 125 m is travelling very fast relative to a stationary observer. The train appears 35.0 m long to the stationary observer. How fast is the train moving relative to the observer (in c)? Answer using numbers only (i.e. '0.75' for an answer of 0.75c).