A spaceship of proper length Lp = 300 m moves past a transmitting station at a s

Question

A spaceship of proper length Lp = 300 m moves past a transmitting station at a speed of 0.65c. (The transmitting station broadcasts signals at the speed of light) A clock is attached to the nose of the spaceship and a second clock is attached to the transmitting station. The instant that the nose of the spaceship passes the transmitter, clocks at the transmitter and in the nose of the spaceship are set to zero. The instant that the tail of the ship passes the transmitter a signal is sent and subsequently detected by the receiver in the nose of the ship.
a) When, according to the clock attached to the nose of the ship, is the signal sent?
b) When, according to the clocks attached to the nose of the spaceship, is the signal received?
c)When, according to the clock attached to the transmitter, is the signal received by the spaceship?
d)According to an observer that works at the transmitting station, is the nose of the spaceship when the signal is received?
time answers in museconds and d) answer in meters

Explanation / Answer

(a)   According to the clock attached to the nose of the ship, is the signal sent       time tA   =   L0 / v    = 300 m / ( 0.65*3*108 m/s)   = 1.53 s (b)   according to the clock attached to the transmitter, is the signal received by the spaceship          t   =   time taken to travell length of the ship +    tA                   = (    L0 / c ) + 1.53 s   =    1.00 s +   1.53 s      =   2.53 s          t   =   time taken to travell length of the ship +    tA                   = (    L0 / c ) + 1.53 s   =    1.00 s +   1.53 s      =   2.53 s (c) According to inverse transformation    tB ' = ( t - vx /c2 )    ...............(1) Here    =   1/ sqrt ( 1 -v2 /c2 )   Here v = - 0.65 c ,   t =   2.53 s ,   x = L0   = 300 m =   1.31 plug all values in equation (1) we get      tB '    = 4.165 s      tB '    = 4.165 s (d)    x'   =   ( x - vt ) Here     t =   2.53 s , = 1.31 ,   v =  - 0.65*3*108 m/s     x'   = 1039.2885    =   1.039 km         

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