Time Dilation and Length Contraction – Practice
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?
1) 153 seconds
2) 44.8 m
3) 2.85 × 108 m/s
4) a) 1.83 ly b) 2.03 ly c) 4.67 years