What is the speed of the missile, relative to ship B?

[vachan]

Two spaceships, named A and B, are flying toward each other with relative speed .80c .
The captain of ship B knows that ship A uses 2-m-long missiles. She measures the length of the first missile, once it has finished accelerating, and finds it to be only 0.872m long. What is the speed of the missile, relative to ship B?
I tried to find it by L=Lo(1/sqrt 1- v2/c2)...

BUt i don't seem to find the right answer... any help i will be happy! thanks

 

[Doc Al]

I tried to find it by L=Lo(1/sqrt 1- v2/c2)...

Make sure you're using the correct equation for length contraction:

$$L = L_0/\gamma$$

Where:

$$\gamma = \frac{1}{\sqrt{1 - v^2/c^2}}$$

 

[Moetasim]

The speed of the missile, relative to ship B, can be calculated using the formula v = (L/Lo)c, where L is the measured length of the missile and Lo is the original length of the missile. Plugging in the values given, we get v = (0.872m/2m)(0.80c) = 0.348c. This means that the missile is traveling at 0.348 times the speed of light, relative to ship B.