# Find if the boat will see the flare, what angle will they?

• Charlene
In summary, the problem presents a scenario where a person stranded on a deserted island has a flare gun and needs to signal a ship 300 meters off shore. The question asks if the flare will be seen if shot at an initial velocity of 161 km/hr and an angle of 33.3 degrees. Using the range formula, it is determined that the flare will reach a distance of 187 meters, but the ship will not see it due to daylight. It is then asked if there is an angle that will allow the ship to see the flare. By setting the desired horizontal distance to 200 meters, the formula is rearranged to find the corresponding angle, which is determined to be around 45 degrees. This means that if
Charlene

## Homework Statement

You have been stranded on a deserted island. Fortunately, you managed to bring a flare gun. You can see a ship 300. m off shore. Unfortunately, because of the daylight the ship cannot see your flare unless it is within 100. m of the ship.
A.) If you fire the flare gun from the shore line with an initial velocity of 161 km/hr at an angle of 33.3 degrees , will they see your flare? (You must show your work in explaining why/why not.)
B.) With this same initial speed, is there an angle you could fire that would allow them to see your flare? If so, what is that angle?

## Homework Equations

R= (vi^2sin2(theta))/g

## The Attempt at a Solution

plugging in the known information i get R=((44.72m/s)^2(sin(66.6))/9.8m/s^2 =187.

would this be correct? or is calculating the range just the x distance?

and i know 45 degrees is where the max is so for part b) i would plug in 45 degrees into the formula to get around 200. and therefore they'd see the flare.

When i initially did this problem i used the formula v^2=u^2+2as
u=44.72 m/s (sin(33.3)=24.6
a=-9.8 m/s^2
plugging in i got

0=(25.6^2)+2(-9.8)s
s=30.76
and this got me a distance of 30.76 (which is COMPLETELY different than the other formula. what is the correct way?

okay, so relooking at this i see that using range is how FAR it goes (horizontally) and the second way i showed is actually showing the max height it hits. so since I'm just looking for the flare to get at least 200.m off shore I'm assuming range is therefore the correct approach.

Would this be correct to think?

Last edited:
u*sin(33.3) will give the vertical velocity and distance not the horizontal range

Parixit said:
u*sin(33.3) will give the vertical velocity and distance not the horizontal range
okay, that's what i thought, therefore i would want to use the range formula R=((44.72m/s)^2(sin(66.6))/9.8m/s^2 =187. because this will give the horizontal distance which is all this question is really wanting i think, because it doesn't tell me about how high the flare needs to be, just how close to the boat it needs to be.

Charlene said:
okay, that's what i thought, therefore i would want to use the range formula R=((44.72m/s)^2(sin(66.6))/9.8m/s^2 =187. because this will give the horizontal distance which is all this question is really wanting i think, because it doesn't tell me about how high the flare needs to be, just how close to the boat it needs to be.
Yes exactly. And for the second part you can find the angle taking S as 200 in the same range formula and finding the angle. You may get a range of angles with 45 deg as the mid point of that range

Charlene

## 1. How can I determine if the boat will see the flare?

The boat will be able to see the flare if it is within the line of sight of the flare's trajectory. This means that there should not be any obstacles, such as land or large waves, between the boat and the flare.

## 2. What factors affect the visibility of the flare to the boat?

The visibility of the flare to the boat will depend on the intensity and duration of the flare, the distance between the boat and the flare, and any obstructions in the line of sight.

## 3. How can I calculate the angle at which the boat will see the flare?

To calculate the angle at which the boat will see the flare, you will need to know the distance between the boat and the flare, as well as the height of the flare from the water's surface. You can then use trigonometric functions, such as tangent or sine, to determine the angle.

## 4. Is there a specific angle that the boat needs to be at in order to see the flare?

No, there is no specific angle that the boat needs to be at in order to see the flare. As long as the boat is within the line of sight of the flare's trajectory, it will be able to see the flare.

## 5. Can the angle at which the boat will see the flare change?

Yes, the angle at which the boat will see the flare can change depending on the distance between the boat and the flare, as well as any changes in elevation of the flare. It is important to continuously monitor these factors in order to accurately determine the angle at which the boat will see the flare.

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