What are the Magnitude and Angle of Vectors in Terms of their Components?

[Susanem7389]

Rewrite the following vectors in terms of their magnitude and angle (counterclockwise from the +x direction)
a) A velocity vector with an x component of -75 m/s and a y component of 35 m/s
- I found the magnitude by using A= square root of ( Ax squared plus Ay squared ), however I did not get the correct answer for the angle. I used the formula angle = tan -1 ( Ay/ Ax)

b) A force vector with a magnitude of 50 lb that is in the third quadrant with an x component whose magnitude is 40 lb.
- I could not find the correct magnitude and angle with the same formula used in part A.

 

[Kruum]

Could you show your angel for part a) as well as magnitude and angel for part b)?

 

[robphy]

Note that your calculator cannot distinguish arctan(1/1) from arctan(-1/-1).
Rule of thumb... if the x-component is negative, add 180 degrees to what your calculator tells you when using arctan. (Some calculators may have something like an atan2 function.)

 

[Susanem7389]

For part A, adding 180 degrees to what the calculator gave me, I got the correct answer, however it did not work for part b.

 

[robphy]

For part A, adding 180 degrees to what the calculator gave me, I got the correct answer, however it did not work for part b.

You'll have to show your work...

 

[mplayer]

I would strongly suggest drawing out each of these vectors on an x-y coordinate plane so you can see exactly what the angles the formulas are giving you. The vector angle is always going to be measured with respect to the +x direction, in a counter-clockwise fashion; in other words, a vector in this +x direction would have an angle of 0 degrees.

Try to not just remember formulas, look at the right triangles the vector magnitude, x-component, and y-component are forming. The magnitude is going to be the hypotenuse of the right triangle that is formed.

for b) They give the the magnitude of the vector already, you just need to find the angle. Remember that the angle will be measure from the +x direction rotating counter-clockwise until it meets the vector in question.