PHY111 Vector sum questions

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In summary, the conversation discusses finding the magnitude and direction of a resultant vector given two given vectors with their respective magnitudes and directions. The individual also mentions a previous question they had solved and finding help on it.
  • #1
chocolaterie
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Homework Statement




vector a = 100 units at 50.0 degrees vector b = 200 units at 270 degrees. find r, sketch a,b, r.


The Attempt at a Solution



The part I don't understand is the 270 degrees. Doesn't this cause vector b to lay on the -y axis? I've tried this question and another one like it:

vector a = 10 units at 40 degrees and vector b = 25 units at 180 degrees.

Answers given for

#1: 139 units at 62.4 degrees or 139 units at 297.5 degrees
#2: 18.5 units at 20.4 degrees above -x axis, or 18.5 at 159.7 degrees

This is the first physics class I have ever taken in my life. Help is greatly appreciated!
 
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  • #2
nevermind, I found a similar question and was able to solve this!

If anyone finds my question:

Bx = 0
By= -200

That should help with the equation.
 
  • #3


I would like to clarify that in vector addition, the direction of a vector is represented by the angle it makes with the positive x-axis, measured counterclockwise. Therefore, a vector at 270 degrees would actually be pointing downwards on the -y axis. In the first problem, vector b would have a magnitude of 200 units and a direction of 270 degrees, which would result in a vector pointing downwards with a magnitude of 200 units. This would be the same as a vector with a magnitude of 200 units and a direction of 90 degrees.

In the second problem, vector b would have a magnitude of 25 units and a direction of 180 degrees, which would result in a vector pointing to the left with a magnitude of 25 units. This would be the same as a vector with a magnitude of 25 units and a direction of 0 degrees.

To find the resultant vector (r), we can use the Pythagorean theorem to find the magnitude and trigonometry to find the direction. In the first problem, r would have a magnitude of √(100^2 + 200^2) = √(10000 + 40000) = √50000 = 223.6 units. To find the direction, we can use the inverse tangent function: tan^-1(100/200) = 26.6 degrees. However, since vector b is in the downward direction, we need to add 180 degrees to the angle, giving us a final direction of 206.6 degrees.

In the second problem, r would have a magnitude of √(10^2 + 25^2) = √(100 + 625) = √725 = 26.9 units. To find the direction, we can use the inverse tangent function: tan^-1(10/25) = 22.6 degrees. However, since vector b is in the left direction, we need to add 90 degrees to the angle, giving us a final direction of 112.6 degrees.

I hope this clarifies any confusion and helps you with your homework. Remember to always pay attention to the direction of the vectors in vector addition problems.
 

1. What is a vector sum?

A vector sum is the result of adding two or more vectors together. It is also known as the resultant vector.

2. How do you calculate the magnitude of a vector sum?

To calculate the magnitude of a vector sum, you can use the Pythagorean theorem, which states that the magnitude of a vector is equal to the square root of the sum of the squares of its components. In other words, you square each component of the vector, add them together, and then take the square root of the result.

3. Can the direction of a vector sum be negative?

Yes, the direction of a vector sum can be negative. This is because vectors have both magnitude and direction, and the direction can be positive or negative depending on the coordinate system used.

4. What is the difference between a scalar and a vector quantity?

A scalar quantity is a physical quantity that only has magnitude, while a vector quantity has both magnitude and direction. For example, speed is a scalar quantity, while velocity is a vector quantity as it includes both speed and direction.

5. How do you determine the components of a vector sum?

To determine the components of a vector sum, you can use trigonometric functions such as sine, cosine, and tangent. The x-component of the vector can be found by multiplying the magnitude of the vector by the cosine of the angle it makes with the x-axis, while the y-component can be found by multiplying the magnitude by the sine of the angle.

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