# Boat light distance when it strikes bottom.

• rcmango
In summary, the problem involves finding the distance d where light strikes the bottom of a body of water with a spotlight located 2.5 m above the water's surface and 9.5 m horizontally displaced. The depth of the water is 4.0 m. Using Snell's law and trigonometry, the distance was found to be approximately 13.7 meters.
rcmango

## Homework Statement

A spotlight on a boat is y = 2.5 m above the water, and the light strikes the water at a point that is x = 9.5 m horizontally displaced from the spotlight (see the drawing). The depth of the water is 4.0 m. Determine the distance d, which locates the point where the light strikes the bottom.
m

http://img529.imageshack.us/img529/6...6100altza6.gif

## The Attempt at a Solution

I believe this is just a simple geometry problem? Or will it run into trouble.

Maybe some help to get it going and the idea of what to do.

Last edited by a moderator:
The physics is Snell's law. Yes, the rest is just geometry.

From my understanding I think you will need to take into consideration the bending (refraction) of light as it passes through the water.
The equation is:
N1*sin(A1) = N2*sin(A2)
The N's are indexes of refraction. I pulled these numbers off a website so I don't know how reliable they are but it says the index of refraction for air is 1.00029 and water is 1.33. But the problem should probably have those numbers somewhere maybe in the chapter if it's from a book.
So you should just plug in the index for air for N1 and water for N2 and then you will need trigonometry to solve for the angle above water (A1), and then you should be able to find the distance.

Ya i got it thanks, used the trig to get the angles above water, then used the snell's law of refraction to get the angle below water between the unknown distance points. Then used more trig to find the unknown distance, then just added the unknown distance to the rest of the known distance, and got an answer.

thanks alot.

## 1. What is boat light distance when it strikes bottom?

The boat light distance when it strikes bottom refers to the distance between the surface of the water and the bottom of the body of water that the boat is traveling on.

## 2. Why is boat light distance when it strikes bottom important?

This distance is important because it determines the depth of the water and helps the captain navigate and avoid hitting any obstacles or running aground.

## 3. How is boat light distance when it strikes bottom measured?

The distance is typically measured using a sonar device, which sends out sound waves that bounce off the bottom and return to the boat, giving an accurate measurement of the distance.

## 4. Does boat light distance when it strikes bottom vary in different bodies of water?

Yes, the distance can vary depending on the type of body of water (ocean, lake, river), the tides, and the clarity of the water.

## 5. Can boat light distance when it strikes bottom be affected by weather conditions?

Weather conditions such as strong winds or heavy rain can cause the water to become choppy and affect the accuracy of the measurement. It is important for the captain to adjust their speed and take caution in these conditions.

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