River Width Estimation Problem

[Meliora]

1. Jean camps beside a wide river and wonders how wide it is. She spots a large rock on the bank directly across from her. She then walks upstream until she judges that the angle between her and the rock, which she can still see clearly, is now at an angle of 30 downstream (as shown in the figure). Jean measures her stride to be about one yard long. The distance back to her camp is 120 strides.

About how far across, in yards, is the river?

About how far across, in meters, is the river?

(there is also a diagram drawn up for this but I am unsure on how to include that in this post)



2. I am honestly unsure of any sort of equation in this case. I am taking intro to physics and my book still hasn't come in the mail yet. My instructor is very hard to understand, but possibly something utilizing the Pythagorean theorem?



3. I am not really sure where to even begin once I have established that one side is 120 yards in length. I feel like a complete idiot here, but this homework is due tonight at 10pm, and this is the last problem I need to complete the assignment.

Any help and pointers in the right directions would be greatly appreciated.

 

[supratim1]

Hi Meliora! Welcome to Physics Forums!try to attempt using trigonometry. go on and try to do something and show us your work. if you are stuck, we are here to help.

 

[Meliora]

Thanks supratim1, I appreciate it.


Upon further investigation I realized how simple the solution to this problem is, hah. I guess I owe it to a brain fart.


Thanks for the reply.

 

[supratim1]

its fine, welcome...

 

[rwisz]

I can suggest a solution to the River Width Estimation Problem using basic geometry and trigonometry principles. First, let's break down the problem into smaller parts and gather all the information given.

1. Jean measures her stride to be one yard long, and the distance back to her camp is 120 strides. This means the distance from the camp to the rock is 120 yards.
2. Jean walks upstream until the angle between her and the rock is 30 degrees. This forms a right triangle with the river's width as the hypotenuse, the distance from the camp to the rock as one side, and the distance Jean walked upstream as the other side.
3. We can use the Pythagorean theorem to find the length of the hypotenuse (river's width). The formula is c^2 = a^2 + b^2, where c is the hypotenuse and a and b are the other two sides. In this case, c is the unknown width, a is the distance from the camp to the rock (120 yards), and b is the distance Jean walked upstream.
4. To find the distance Jean walked upstream, we can use trigonometry. The formula is sinθ = opposite/hypotenuse, where θ is the angle (30 degrees) and the opposite side is the distance Jean walked upstream. Rearranging the formula, we get opposite = sinθ x hypotenuse. In this case, opposite = sin30 x 120 = 60 yards.
5. Now, we have all the information we need to solve for the width of the river. Using the Pythagorean theorem, we get c^2 = 120^2 + 60^2 = 14400 + 3600 = 18000. Taking the square root of both sides, we get c = √18000 = 134.16 yards.
6. To convert to meters, we can use the conversion factor 1 yard = 0.9144 meters. Therefore, the width of the river is approximately 134.16 x 0.9144 = 122.68 meters.

In conclusion, the river's width is approximately 134.16 yards or 122.68 meters. I hope this explanation helps you understand the problem and find the solution. If you have any further questions, feel free to ask your instructor or a tutor for help. It's important to understand the