Question

Events 1 and 2 are exploding firecrackers that each emit light pulses. In the reference frame of the detector, event 1 leaves a char mark at a distance 3.40 m from the detector, and event 2 leaves a similar mark at a distance 2.10 m from the detector. If the two events are simultaneous in the reference frame of the detector and occur at instant t=0, at what instant of time will each light pulse be detected?

Answer 1

Answer:

$1.13333\times 10^{-8}\ s$ and $0.7\times 10^{-8}\ s$

Explanation:

Light which travels from the crackers reaches the detector at $c=3\times 10^{8}\ m/s$

$\Delta x_1$ = Distance at which event 1 leaves a char mark = 3.4 m

$\Delta x_2$ = Distance at which event 2 leaves a char mark = 2.1 m

The speed of light in a medium is a universal constant

$c=\dfrac{\Delta x_1}{\Delta t_1}\\\Rightarrow \Delta t_1=\dfrac{\Delta x_1}{c}\\\Rightarrow \Delta t_1=\dfrac{3.4}{3\times 10^8}\\\Rightarrow \Delta t_1=1.13333\times 10^{-8}\ s$

$c=\dfrac{\Delta x_2}{\Delta t_2}\\\Rightarrow \Delta t_2=\dfrac{\Delta x_2}{c}\\\Rightarrow \Delta t_2=\dfrac{2.1}{3\times 10^8}\\\Rightarrow \Delta t_2=0.7\times 10^{-8}\ s$

The pulse will be detected at $1.13333\times 10^{-8}\ s$ and $0.7\times 10^{-8}\ s$