Spaceship a is 10 meters long and approaching you from the south at a speed of.7c while spaceship b, which is also 10 meters long, is approaching you from the north at a speed of.7c. a. what is the relative speed of a as measured by b? b. what is the length of a as measured by you? c. what is the length of a as measured by b? d. an event on a lasts 1 second as measured by a. how long does the event last as measured by you? e. an event on a lasts 1 second as measured by a. how long does the event last as measured by b?

a) 0.94 C

b) 7.14 m

c) 3.11 m

d) 1.40 s

e) 2.93 s

Explanation:

First we need to set up a coordinate system. This will have the positive X axis pointing north. So spaceship A has positive speed, and spaceship B has negative speed.

The Lorentz transformation for speed is:

u: speed of spaceship A as observed by you

v: speed of spaceship B as observed by you

In the case of the speed of spaceship A as observed by spaceship B:

The transform for lengths is:

For the case of spaceship A as observed by you:

For the case of spaceship A as observed by spaceship B:

The time dilation equation is:

For the case of the event as observed by you:

For the case of the event as observed by spaceship B: