# Adding vectors algebraically for football runner

• valon
In summary: I am still stumped. I don't even know where to begin on this. All I know is 35m and 15m, and 25 degrees and that it isn't a right triangle. Sorry I am so bad at this, I am sure you are annoyed by now.In summary, a football player runs 35m down the field and then turns right at a 25 degree angle and runs 15m before getting tackled. To find the total displacement, the vectors must be converted into rectangular coordinates, added component-wise, and then converted back to polar form. The first vector's components would be (0, 35) and the second vector's components would be (15, 50). It is important to
valon

## Homework Statement

A football player runs directly down the field for 35m before turning to the right at an angle of 25 degrees from his original direction and running an additional 15m before getting tackled. What is the magnitude and direction of the runner's total displacement?

## Homework Equations

None that I know of.

## The Attempt at a Solution

[PLAIN]http://img269.imageshack.us/img269/7127/whatigotv.png

This is how far I get, its not a right triangle so I am pretty lost :/

Last edited by a moderator:
valon said:

## Homework Statement

A football player runs directly down the field for 35m before turning to the right at an angle of 25 degrees from his original direction and running an additional 15m before getting tackled. What is the magnitude and direction of the runner's total displacement?

## Homework Equations

None that I know of.

## The Attempt at a Solution

[PLAIN]http://img269.imageshack.us/img269/7127/whatigotv.png

This is how far I get, its not a right triangle so I am pretty lost :/

Welcome to the PF!

Convert the vectors into rectangular coordinates, add the x components, add the y components, and convert back to polar form. You will generally always add vectors in rectangular coordinates, so get good at converting back and forth.

Show us what your calculation looks like now.

(And BTW, try to post smaller images in the future so they don't blow up the size of the page. Thanks.)

Last edited by a moderator:
berkeman said:
Welcome to the PF!

Convert the vectors into rectangular coordinates, add the x components, add the y components, and convert back to polar form. You will generally always add vectors in rectangular coordinates, so get good at converting back and forth.

Show us what your calculation looks like now.

(And BTW, try to post smaller images in the future so they don't blow up the size of the page. Thanks.)

Yeah sorry about the giant picture :x

Unfortunately I am unsure of exactly how to convert these I really only have experience doing this with a ruler or right triangle in which you just apply SOH-CAH-TOA :/

valon said:
http://en.wikipedia.org/wiki/Polar_...rting_between_polar_and_Cartesian_coordinates

i looked at that part and doesn't that only work for right triangles?

Yes. For each vector in polar form (the hypotenuse), there are x and y components that form a right triangle. That's why you use those familiar formulas to convert from polar to rectangular and back again.

Convert each of your two vectors into their rectangular components, and add the vectors component-wise. Then convert back to polar form.

So for the first vector that is straight down, what are its x and y components (you don't even need a calculator for this first vector conversion...)?

berkeman said:
Yes. For each vector in polar form (the hypotenuse), there are x and y components that form a right triangle. That's why you use those familiar formulas to convert from polar to rectangular and back again.

Convert each of your two vectors into their rectangular components, and add the vectors component-wise. Then convert back to polar form.

So for the first vector that is straight down, what are its x and y components (you don't even need a calculator for this first vector conversion...)?

well the first vector would be (0,35) right? and the second would be (15, 50) I guess. Or I am still not getting this, sorry if I am a little slow I am just totally missing this :/

valon said:
well the first vector would be (0,35) right? and the second would be (15, 50) I guess. Or I am still not getting this, sorry if I am a little slow I am just totally missing this :/

Correct-ish on the first one. Keep in mind that the + x direction is to the right, and the + y direction is up. so the first vector's components would be _____ ?

And two things on the 2nd vector. Draw the x and y components of that vector -- they have nothing to do with the first vector -- just draw the right triangle that has the 2nd vector as the hypotenuse, and show the x and y sides of that triangle. The second thing is that I just noticed that you mislabeled which angle is 25 degrees. Look at your figure, and put the 25 degrees on the correct angle, and then find any other angles that you need in order to use the polar-rectangular conversion formulas.

I have to bain for a while, but will try to check in later. Others will hopefully also chime in if you have further questions.

Also, here's a vector addition tutorial that may help (which I found by googling vector addition tutorial):

.

berkeman said:
Correct-ish on the first one. Keep in mind that the + x direction is to the right, and the + y direction is up. so the first vector's components would be _____ ?

And two things on the 2nd vector. Draw the x and y components of that vector -- they have nothing to do with the first vector -- just draw the right triangle that has the 2nd vector as the hypotenuse, and show the x and y sides of that triangle. The second thing is that I just noticed that you mislabeled which angle is 25 degrees. Look at your figure, and put the 25 degrees on the correct angle, and then find any other angles that you need in order to use the polar-rectangular conversion formulas.

I have to bain for a while, but will try to check in later. Others will hopefully also chime in if you have further questions.

Also, here's a vector addition tutorial that may help (which I found by googling vector addition tutorial):

.

[PLAIN]http://img704.imageshack.us/img704/1728/35794242.png

how was my degrees on the wrong angle?
Unless i can do the 3, 4, 5 triangle rule with that gray triangle but I doubt that is what I'm supposed to do.
I am completely and hopelessly lost I thank you for trying to help and not just doing it all for me but I honestly have no idea what is happening and that tutorial is just talking about right triangles and i don't have a right and whatever I am too frustrated for this now.

Last edited by a moderator:
The object is originally headed on a vector of 270°. It changes course by -25° from 270°. Thus, the angle should be labeled from the 270° axis to the vector of the newest direction.

You should be able to visually see that the angle you labeled in the OP is not 25°, as it is clearly obtuse.

## 1. What is the purpose of adding vectors algebraically for a football runner?

The purpose of adding vectors algebraically for a football runner is to determine the resulting velocity and direction of the runner's movement. This can help coaches and players understand and improve the runner's performance on the field.

## 2. How do you represent vectors algebraically for a football runner?

Vectors for a football runner can be represented using magnitude and direction, usually in the form of a diagram or coordinate system. The magnitude represents the runner's speed and the direction represents the direction they are moving in on the field.

## 3. What are the steps for adding vectors algebraically for a football runner?

The steps for adding vectors algebraically for a football runner are:
1. Draw a diagram or coordinate system to represent the vectors.
2. Determine the magnitude and direction of each vector.
3. Use trigonometric functions to find the horizontal and vertical components of each vector.
4. Add the horizontal components together and the vertical components together.
5. Use the Pythagorean theorem to find the resulting magnitude.
6. Use inverse trigonometric functions to find the resulting direction.
7. Represent the resulting vector in the diagram or coordinate system.

## 4. How does adding vectors algebraically affect a football runner's overall movement?

Adding vectors algebraically affects a football runner's overall movement by determining the resulting velocity and direction. This can help coaches and players understand how different factors, such as speed and direction, contribute to the runner's overall movement on the field.

## 5. Can adding vectors algebraically help improve a football runner's performance?

Yes, adding vectors algebraically can help improve a football runner's performance by providing a better understanding of their movements on the field. Coaches and players can use this information to make adjustments and improve the runner's speed, direction, and overall performance.

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