find the magnitude and direction of the resulting force?

Question

three forces, (-i + 4j)N, (2i - j)N and 3iN, i and j being vectors due east and due north resptively, act on a particle. find the magnitude and direction of the resulting force

you said that tan^-1 (3/4)=36.9....
but when i typed it to my calculator, i get 0.644...am i typeing it incorrectly into my calculator?

Answer 1

The resultant [4i + 3j]N has a direction of arc tan 3/4 (abt 36.9 degrees) and a magnitude of 5N.

[You add the corresponding x-components and y-components to get the resultant (given above). Then y-comp / x-comp gives you tangent function of direction.]

RYUJIN: Your calculator is giving you radian units (not degree units; do a conversion from the fact that pi radians = 180 degrees (which is the same as saying 1 radian = 180/pi degrees = 57.2957795 degrees) You'll note that your answer times this conversion factor gives you a degree answer (which isn't in any way superior to your answer, but it is equivalent).

No, you're not typing it in incorrectly; the units you're getting areN'T degrees; they're radians (which is fine, as long as you know that your answer equates to alternative right answers).

Lastly, as MRJEFFY indicates, the angle is measured counterclockwise from the positive x-axis.

Answer 2

Just add the vectors together.
Add the i components to the i components, add the j components to the j components.

-i + 2i + 3i = 4i
4j - j = 3j

So the resultant vector would be:
<4i, 3j> Newtons

To get the magnitude of th vector add the square of each component, then take the square root.

Magnitude = sqrt (4^2 + 3^2) = sqrt (25) = 5
Magnitude = 5 Newtons

Or one could realize that these two components of the vector are the sides of a "3-4-5" right triangle. Realizing this about their lengths would save you the step of having to square and then take the square root. With practice you will start seeing this more easily.

To find direction,
take the arctangent of the y component over the x component to get the angle the vector is acting above the horizontal.
angle = arctan (3/4) = tan^-1 (3/4)
angle = 36.9 degrees above the horizontal.

So the resulting force would be:
5 Newtons at 36.9 degrees above the horizontal.


EDIT:

No, you are typing it into your calculator correctly; it is just that your angle is coming out in radian measure instead of degrees. Radians are just another way to measure angles. 2*pi radians = 360 degrees.
There should be a setting you can change on your calculator to set it on degree mode…or you can convert radians to degrees by,
Degrees = Radians * 180 / pi
or the other way,
Radians = Degrees * pi / 180