# Homework Help: Please check my Lorentz Transforms

1. Oct 14, 2008

### mattst88

1. The problem statement, all variables and given/known data

At x = x' = 0 and t = t' = 0, a clock ticks on a fast spaceship (gamma = 100). The captain of the ship heads it tick again 1.0 s later. Where and when do we (the stationary observers) measure the second tick to occur?

2. Relevant equations

$$t = \frac{t'}{\gamma}$$
$$x' = \gamma(x - vt)$$
$$\gamma = \frac{1}{\sqrt{1 - \frac{v^2}{c^2}}}$$

3. The attempt at a solution

First, I solve for velocity.
$$v = c\sqrt{1 - \frac{1}{100}^2} = 0.9995c$$

Next, solve for t when t' = 1.
$$t = \frac{t'}{\gamma} = \frac{1}{100} sec$$

Finally, solve for x'.
$$x' = \gamma(x - vt) = 100(0 - (0.9995c)(\frac{1}{100})) = 0.9995c$$

Have I answered this correctly? Thanks.

2. Oct 15, 2008

### BerryBoy

The spaceship is defined as the moving object, so proper time is measured on the Earth. Time appears to be going slower for the spaceship. So we could write that:

$$t_{earth} = \gamma t_{spaceship}$$

Sam