A human car driver observes an alien spaceship flying by at v=0.8c. The alien pi

Question

A human car driver observes an alien spaceship flying by at v=0.8c. The alien pilot has measured the length of his ship to be 10m. describe the alien's intertical frame with primed coordinates (x', t') and the human's intertial frame with un-primed coordinates (x,t). The origins of the two coordinate systems overlap at t=t'=0. The alien is flying the positive x direction, and his tail-light is located at x'=0

a.) make a sketch of the situation

b.) the alien flashes his headlights and his tailights at t'=0 (simultaneously as measured by the alien). Find the expression for the times t1 and t2 when the human will measure that the tailights and headlights flash.

c.) Calculate t2-t1 for v=0.8c and v=0 Are the results consistent with your expectation?

Explanation / Answer

b)

= 1/(1-(v/c)2) = 1/(1 - 0.8*0.8) = 1.667

t1 = (t' + (v/c2 ) x')

t1 = 1.667 * (0 + 0.8/3e8 * 0) = 0

>>>> t1 = 0 s

t2 = (t' + (v/c2 ) x')

t2 = 1.667 * (0 + 0.8/3e8 * 10) = 4.445e-8 s

>>>> t2 = 4.4e-8 s

c)

for v=0.8C >>>> t2 - t1 = 4.4e-8 s

for v=0 >>>> t2 - t1 = 0

When v is zero, the car driver and spaceship are in a same frame, and therefore both of them measures same values. But when v is 0.8c, they are in defferent frames and therefore measures different values.

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