# Relativity of Velocities

1. Dec 8, 2009

### jderm

[STRIKE][/STRIKE]1. The problem statement, all variables and given/known data
Two spaceships approach each other, each moving with the same speed as measured by an observer on the Earth. If their relative speed is 0.89c, what is the speed of each spaceship as measured on Earth?

2. Relevant equations
u=$$\frac{u'+v}{1+u'v/c^2}$$

3. My work
so ship A moves to the right at speed u, (according to an observer on earth)
and ship B moves to the left at speed v, (according to an observer on earth)
within Ship A's inertial frame, ship B is moving at u', known to be .89c
i need to solve for u, the speed on Ship A.
u=-v

substituting -v for u,
u= $$\frac{u'-u}{1-u'u/c2}$$

i then get
0=-$$\frac{u'u2}{c2}$$+u

I am sure i am thinking of this problem the wrong way, maybe that v does not equal the negative of u?

Last edited: Dec 8, 2009
2. Dec 8, 2009

### jderm

i accidently posted this before adding my work, ill get it on in a moment

3. Dec 8, 2009

### jderm

Found my error.
since the ships are approaching each other, the equation was
u=$$\frac{v-u'}{1-\frac{u'v}{c^{2}}}$$

then substituting -v = u

$$\frac{u'u^{2}}{c^{2}}$$+u'+2u=0

which yields the correct answer of 1.8326x108 m/s