An observer in frame S standing at the origin observes two flashes of colored li
ID: 1330620 • Letter: A
Question
An observer in frame S standing at the origin observes two flashes of colored light separated spatially by x = 3490 m. A blue flash occurs first, followed by a red flash 5 µs later. An observer in S' moving along the x axis at speed v relative to S also observes the flashes 5 µs apart and with a separation of 3490 m, but the red flash is observed first. Find the magnitude of v.
A cosmic ray proton streaks through the lab with velocity 0.82c at an angle of 52° with the +x direction (in the xy plane of the lab). Compute the magnitude and direction of the proton's velocity when viewed from frame S' moving with = 0.74.
Explanation / Answer
xb' - xr' = y[(xb-xr) - v(tb-tr)] ......(1)
tb' - tr' = y [(tb - tr) - v(xb - xr)/c^2] ........(2)
xb - xr = 3490 m , tb - tr = 5 micro s
xb' - xr' = 3490 m tb' -tr' = - 5 micro s
divide 1 by 2
3490 / -5 x10^-6 = [3490 - v(5x10^-6)] / [ 5 x 10^-6 - v(2400/c^2)]
-3490 + v(3490)^2/5x10^-6 c^2 = 3490 - 5 x 10^-6 v
v[(3490)^2/5x10^-6c^2 + 5 x 10^-6] = 6980
v = 2.18 x 10^8 m/s