Question

2. (40 pts) You are a member of the Resistance, tasked with destroying the latest Death Star. After planting a bomb on the Death Star, you escape in your 0.6c spaceship (event E). When you are 1 light-minute from the Death Star, you hit the button to trigger the bomb (event F). The trigger message is sent via a RADIO SIGNAL

Answer 1

2 1F 1 . 2 x (Lm) (115 F3 Events from space ship

From space ship perspective event E has happened in the past ( x= -1 Lm and t = -1.67 m )

Our reference frame is moving with the spaceship , our space ship is always at the origin in our reference frame. Event F is at the origin. Event E is located at 1 Lm on the -ve x-axis and time elapsed

t = 1/0.6 = 1.67 m

b) the button signal is sent to death start at speed c , (radio signal , light speed) and the shock wave also travels at almost light speed.

When the button is pressed , the radio signal travels a distance of L = 1 Lm , to reach death star. the shock wave from the death star travel towards the space ship at a speed of c.

By the time the radio signal reaches death star and the shock wave reached the space ship time elapsed is $\Delta$t, during this time the space ship moves by a distance of $\Delta$x and the shock wave has to travel a distance of L+$\Delta$x , to reach the space ship

(L + L+$\Delta$x)/c = $\Delta$t

the space ship is moving at a speed of 0.6c, hence

$\Delta$x = 0.6c$\Delta$t

2L/c + 0.6$\Delta$t = $\Delta$t

$\Delta$t = (2L/c)/0.4 ; L = 1 Lm

   = 5 m

c)

The space ship is 1 Lm away at the time of pressing the button ( send radio signal) . 1 min has elapsed. It took another 1 min for the radio signal to reach the death star.

Total 2 min elapsed from escape to death star explosion - in the frame of space ship.

death star is at rest relative to the space ship

$\Delta$t = $\Delta$t_p /( 1-v²/c²)^1/2 = 2 /( 1- 0.6²)^1/2  

= 2.5 min - with reference to death star.