Time Dilation and Length Contraction – Practice

Questions:

1) A stationary observer measures a rocket travelling past Earth at 0.92c. In the rockets frame of reference, a clock measures a time interval of 60 seconds. Calculate how many seconds are recorded by the observer on Earth.

2) A stationary observer on Earth watched a spaceship fly past at 2.88 x 108 ms-1. An astronaut on the spaceship measures the length of the spaceship to be 160m. How long would the observer on Earth measure the length to be?

3) A stationary observer on Earth measures the length of a very fast truck to be 7.9m. The driver of the truck measures the length to be 25m. Calculate the speed of the truck as seen by the stationary observer:

4) The nearest star, apart from the Sun, is 4.2 light-years away.

a) How far is it to that star according to astronauts in a spacecraft travelling at 0.9c?

b) How long would it take to get there in this spacecraft?

c) How long would it take according to observers on Earth?