Key 11 - properHoc

1. Move the movable point at (7, 9) to the spaceship’s position, and read off the time in the primed system. I got about -7.8 time units in the primed system.
2. Find the same time using some appropriate calculations.
  We have that $\displaystyle t=\gamma {{t}_{0}}$
  So, since t0 is the proper time (in this case, the time as seen from the spaceship) we get $\displaystyle {{t}_{0}}=t/\gamma =-9\cdot \sqrt{{1-{{{0.5}}^{2}}}}=-7.79$

Find the time when the light from the rightmost flash reaches the spaceship:
1. According to the people on the Asteroid,
  We can follow a line tilted at 45 degrees to the left until we reach the Spaceship’s time axis. That would be at t=2 time units.
2. According to the people in the Spaceship.
  We can move the movable point to the point (1,2) and read about 1.73 time units, or use the time dilation formula, so we get
  $\displaystyle {{t}_{0}}=t/\gamma =2\cdot \sqrt{{1-{{{0.5}}^{2}}}}=1.73$
At what distance will the right flash be according to the people in the spaceship?
1. Find this by using the movable point.
  I get about 3.47, space units away.
2. Find this by using suitable calculations.
  Using the Lorentz’s transform for space, we get
  $\displaystyle {x}'=\gamma (x-vt)=\sqrt{{1-{{{0.5}}^{2}}}}\cdot (3-0.5c\cdot 0)=3.46$
Here we can use the movable point to get about 2.60. Remember that you have to put the movable point at the right end of the asteroid as seen from the Spaceship.

We can also simply use the length contraction formula,
$\displaystyle L=\frac{{{{L}_{0}}}}{\gamma }=3\cdot \sqrt{{1-{{{0.5}}^{2}}}}=2.60$

Last modified: Jul 19, 2025 @ 22:57