Ships in the Night

Classical Mechanics Level 2

You are keeping watch on the deck of a ship at night. You are trying to keep a steady distance from your sister ship, which is sailing alongside you, but it is difficult as you can't see them properly in the night.

Luckily you have an accurate light meter, and both ships have identical lamps on their bows. The bow of your ship is 50 m \SI{50}{\m} away and the intensity of light from its lamp where you stand is 80 W m − 2 \SI{80}{\W \m^{-2}} . The intensity of light from the lamp on the other ship is 5 W m − 2 \SI {5}{\W \m^{-2}} .

Assuming the light from both lamps spreads equally in all directions, how far (in m \text{m} ) away is the lamp on the other ship?


The answer is 200.

View wiki
Andrew Normand by Andrew Normand , 31, United Kingdom

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

1 solution

Chew-Seong Cheong
Jan 29, 2017

Assuming the light intensities of the two lamps follow the inverse square law, then we have:

I ∝ 1 r 2 ⟹ I 1 I 2 = r 2 2 r 1 2 ( r 2 50 ) 2 = 80 5 r 2 = 200 . \begin{aligned} I & \propto \frac 1{r^2} \\ \implies \frac {I_1}{I_2} &= \frac {r_2^2}{r_1^2} \\ \left(\frac {r_2}{50}\right)^2 &= \frac {80}{5} \\ r_2 &=\boxed {200}.\end{aligned}

5 Helpful 2 Interesting 1 Brilliant 2 Confused

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...