# Calculating Velocity Components of Running Horses Using SOHCAHTOA

• junesmrithi
In summary, a discussion was had regarding the calculation of the northward and westward components of a herd of running horses. The use of SOHCAHTOA and the correct orientation of the triangle were discussed, as well as the potential difference between magnetic and geographic north. It was suggested that the teacher may have meant for the students to correct for this difference, but it was also noted that the question specifically mentioned a compass heading of 340 degrees.
junesmrithi
Running Horses-----SOHCAHTOA

## Homework Statement

A herd of wild horses races across the flat, open plains of the Great Basin in central Nevada. If the horses are running at 12.2 m/s at a compass heading of 340 degrees, what is the northward component of their velocity?

And, what is the westward component of the horses' velocity?

SOHCAHTOA

## The Attempt at a Solution

i tried to draw the triangle/sketch. but it doesn't work out when i plus it into the SOHCAHTOA.
my diagram had 20 deg, and i had the hypotenuse at 12.2m/s.
was tht a wrong diagram?
can someone tell me know to draw the correct diagram?

What direction is 340 degrees?

well these are Compass heading in degrees: N=0, E=90, S=180, and W=270

- i think N can also be counted as 360

The directions you state are not typical. Usually, 0 degrees is due east, 90 degrees is due north etc.

junesmrithi said:
i tried to draw the triangle/sketch. but it doesn't work out when i plus it into the SOHCAHTOA.
my diagram had 20 deg, and i had the hypotenuse at 12.2m/s.
was tht a wrong diagram?
can someone tell me know to draw the correct diagram?

Did you have the angle 20 from the vertical? If so, that seems the correct diagram to me.

What do you mean when you say it doesn't work when you try and use SOHCAHTOA?

Assuming for a moment that you're working on a relatively simple vector problem, the approach you're taking is correct. Don't forget, 0 degrees is due North (magnetic north); orient your triangle accordingly. You're still finding the same two perpendicular components.

However, if you're using compass headings, and are referring to "northward" as meaning the geographic north, then the problem will become a bit more complicated, as geographic north and magnetic north differ by a bit, which depends on where you're at. For me, in Western NY, magnetic North is actually about 10 degrees west of true North. For central Nevada, magnetic north is actually about 16 degrees East of true North.

If you want to have some fun with your teacher, you can correct for this with your original 340 degree angle. I doubt that's what the teacher's actually looking for though. Here's a reference for the direction toward North. (I may be misinterpreting this graph.)
http://www.ssec.honeywell.com/magnetic/datasheets/an203.pdf

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robb_ said:
The directions you state are not typical. Usually, 0 degrees is due east, 90 degrees is due north etc.

I've never come across this convention, but in this question it is not the case:

junesmrithi said:
And, what is the westward component of the horses' velocity?

Using the convention that 90 degrees is north, this would ask for the easterly component.

@junesmrithi: You are correct in taking the north direction as 0 or 360 degrees.

My bad, i guess. Not the convention I am used to.
Using the convention that 90 degrees is north, this would ask for the easterly component.
I understand this, but you could say a negative westerly component (and negative northerly as well). That is what confused me after first reading the OP.

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I still think it'd be fun to see if the teacher gets flustered with, "then why'd you say 'horses in central Nevada' if you didn't want us to correct the heading? Why not simply say, 'what are the North and West components of a vector...' "

## 1. What is the meaning of SOHCAHTOA in relation to running horses?

SOHCAHTOA is an acronym representing the three main trigonometric functions: sine, cosine, and tangent. In relation to running horses, SOHCAHTOA can be used to calculate the angle of a horse's leg in motion and the distance it travels.

## 2. How does SOHCAHTOA help in understanding the movement of running horses?

SOHCAHTOA helps in understanding the movement of running horses by using the trigonometric functions to analyze the angle and distance of their legs in motion. This can provide valuable insights into their speed, gait, and overall movement patterns.

## 3. Can SOHCAHTOA be used to improve horse racing strategies?

Yes, SOHCAHTOA can be used to improve horse racing strategies by providing information about a horse's speed and gait. This can help trainers and jockeys make more informed decisions about race tactics and track conditions.

## 4. Are there any limitations to using SOHCAHTOA in horse racing?

While SOHCAHTOA can provide valuable insights into the movement of running horses, it is important to note that other factors such as breed, training, and track conditions also play a significant role in horse racing. Therefore, SOHCAHTOA should be used in conjunction with other methods for a more comprehensive analysis.

## 5. Can non-scientists use SOHCAHTOA to better understand horse racing?

Yes, non-scientists can use SOHCAHTOA to better understand horse racing by learning the basics of trigonometry and how it relates to the movement of running horses. However, a more in-depth understanding of horse racing and additional knowledge in other areas such as physics and biology may be necessary for a more comprehensive analysis.

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