Question

Bjorn is standing at $x=600m$. Firecracker $1$explodes at the origin and firecracker$2$explodes at $x=900m$. The flashes from both explosions reach Bjorn’s eye at $t=3.0\mu s$. At what time did each firecracker explode?

Short answer

We have given that, Bjorn is standing at $x=600m$.

Firecracker$1$explodes at the origin and firecracker explodes at $x=900m$.

The flashes from both explosions reach Bjorn’s eye at $t=3.0\mu s$.

t2=1.0μsLight left firecracker $2$explode at$t_2=2\mu s$.

Step-by-step solution

Given Information

We have given that, Bjorn is standing at $x=600m$.

Firecracker$1$explodes at the origin and firecracker explodes at $x=900m$.

The flashes from both explosions reach Bjorn’s eye at $t=3.0\mu s$.

Simply

Bjorn is $600m$away from the source. It takes $2.0\mu s$for light to reach Bjorn.

$$\begin{gathered} t=\frac{600}{\text{speedoflight}} \\ t=\frac{600}{3\times {10}^8} \\ t=2\times {10}^{-6}\mathrm{s} \\ \mathrm{t}=2\mathrm{\mu s} \end{gathered}$$

This flash arrived at Bjorn at $t=2.0\mu s$leaving firecracker at $t_1=1.0\mu s$.

$$\begin{gathered} t_2=\frac{300}{3\times {10}^8} \\ {t}_2={10}^{-6} \\ {t}_2=1\mu \mathrm{s} \end{gathered}$$

It takes $1.0\mu s$for the flash from Firecracker $2$to reach Bjorn.

Light left firecracker $2$at $t_2=1.0\mu s$.