Physics, 02.04.2020 02:51 mommer2019

According to observer O, a blue flash occurs at xb = 10.4 m when tb= 0.124 μs, and a red flash occurs at xr= 23.6 m when tr= 0.138 μs. According to observer O’, who is in motion relative to O at velocity u, the two flashes appear to be simultaneous. Find the velocity u.

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Answer from: alwaysneedhelp84

u = 95.46 * 10⁶ m/s

Explanation:

For the first observer O,

Time of the blue flash, $t_{b} = 0.124 \mu s$

Time of the red flash, $t_{r} = 0.138 \mu s$

Distance covered before the blue flash, $x_{b} = 10.4 m$

Distance covered before the red flash, $x_{r} = 23.6 m$

Difference in time observed by the first observer O, Δt = $t_{r} - t_{b}$

Δt = 0.138 - 0.124 = 0.014 μs

Difference in the distance observed by the observer O, Δx = $x_{r} - x_{t}$

Δx = 23.6 m - 10.4 m

Δx = 13.2 m

Since for the observer O', the two flashes are simultaneous, there will be no time difference between the two flashes. i.e. Δt' = 0

Using the lorent'z transformation equation:

$\triangle t' = \frac{\triangle t - \frac{u \triangle x}{c^{2} } }{\sqrt{1 - \frac{u^{2} }{c^{2} } } }$ ...................(1)

But Δt' = 0,

equation (1) becomes

$0 = \triangle t - \frac{u \triangle x}{c^{2} } \\$

$0 = (0.014 * 10^{-6} ) - \frac{u * 13.2}{(3*10^{8}) ^{2} }$

$(0.014 * 10^{-6} ) = \frac{u * 13.2}{(3*10^{8}) ^{2} } \\u = 95454545.46 m/s$

u = 95.46 * 10⁶ m/s

Answer from: Quest

i'm thinking more like energy

Answer from: Quest

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According to observer O, a blue flash occurs at xb = 10.4 m when tb= 0.124 μs, and a red flash occur...