Adding Components and Finding Magnitude/Angle: Q&A

[htk]

Given:

at 70 pounds
<60.02, -35>

at 40 pounds
<28.28, 28.28>

at 60 pounds
<-42.43, 42,43>

now add the components to find the resultant of the system and use it to find the magnitude and direction angle. ----------------------> can anyone please explain it to me how to add the components by using those numbers above? and how can I use those number to find the magnitude and direction angle? Thank you for answering my question!

 

[VeeEight]

If those are vectors and you are asking for the magnitude and direction of each, apply the dot product formula for finding angles.

 

[Architeuthis Dux]

To add the components, you will need to add the x and y values separately. For example, for the first set of numbers at 70 pounds, you will add 60.02 and -35. This will give you the resultant vector: <60.02, -35>. You will repeat this process for the other two sets of numbers, resulting in two more resultant vectors: <28.28, 28.28> and <-42.43, 42.43>.

To find the magnitude of each resultant vector, you will use the Pythagorean theorem, which states that the magnitude (or length) of a vector is equal to the square root of the sum of the squares of its components. In this case, for the first resultant vector, the magnitude would be √(60.02^2 + (-35)^2) = √3604.0004 = 60.01 pounds. You will repeat this process for the other two resultant vectors, resulting in magnitudes of 40 pounds and 60 pounds, respectively.

To find the direction angle, you will use trigonometric functions such as sine, cosine, and tangent. The direction angle is the angle between the resultant vector and the x-axis. To find this angle, you will use the formula: θ = tan^-1(y/x), where y is the y-component and x is the x-component of the resultant vector. For the first resultant vector, the direction angle would be tan^-1(-35/60.02) = -30.59 degrees. You will repeat this process for the other two resultant vectors, resulting in direction angles of 45 degrees and -45 degrees, respectively.

In summary, to add the components, you will add the x and y values separately. To find the magnitude, you will use the Pythagorean theorem. To find the direction angle, you will use trigonometric functions. I hope this helps to explain the process of adding components and finding magnitude/direction angle.