A spaceship of proper length L_p = 450 m moves past a transmitting station at a

Question

A spaceship of proper length L_p = 450 m moves past a transmitting station at a speed of 0.73c. (The transmitting station broadcasts signals that travel at the speed of light.) A dock is attached to the nose of the spaceship and a second dock is attached to the transmitting station. The instant that the nose of the spaceship passes the transmitter, the clock attached to the transmitter and the dock attached to the nose of the spaceship are set equal to zero. The instant that the tail of the spaceship passes the transmitter a signal is sent by the transmitter that is subsequently detected by a receiver in the nose of the spaceship. When, according to the dock attached to the nose of the spaceship, is the signal sent? 2.06 mu s When, according to the docks attached to the nose of the spaceship, is the signal received? 4.96 mu s When, according to the dock attached to the transmitter, is the signal received by the spaceship? 3.39 mu s According to an observer that works at the transmitting station, how from the transmitter is the nose of the spaceship when the signal is received? 1744.69 m

Explanation / Answer

Let S be the reference frame of the ship and S be that of the earth (transmitter station). Let event A be the emission of the light pulse and event B the reception of the light pulse at the nose of the ship.

(a)

In both S and S the pulse travels at the speed c.

Thus, tA = 450/0.73c

tA = 2.06 s.

(c)

The time of travel of the pulse to the nose is 450/c s = 1.5 s

So, the pulse arrives at tB = 3.56 s

For (b) & (d)

To find the time and location of event B in frame S

here V, the velocity of reference frame S relative to S, is -0.73c.

(b)

V = -0.73c

= 1.46; tB = 1.46(3.56×10-6 + 0.73×450/c) = 6.79 s

(d)

xB = 1.46(450 + 0.73c*3.56×10-6) m = 1795.27 m

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