Finding Vectors .. Physics 1?

To add or subtract vectors, you need to separate the vectors into their components (x and y measurements):

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Vector A magnitude = 15 m

Angle = 88 degree

X = 15 cos(88) = 0.52

Y = 15 sin(88) = 15.00

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Vector B magnitude = 4 m

Angle = 180 degree (along negative x axis)

X = 4 cos(180) = -4

Y = 4 sin(180) = 0

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For (A+B) coordinates, you'll add the X's together and the Y's together

X coordinate: 0.52 + (-4) = -3.48

Y coordinate: 15 + 0 = 15

Now Pythagorean theory for the length, square root of [(-3.48)^2 + 15^2] = 15.40

To find the angle, you do: arctan (Y/X)

arctan(15/-3.48) = -76.94 add 180 to this to get 103.06 degree

You add 180 degrees because if you drew out Vector A and B, you can see that right between those two vectors is where (A+B) should be and that angle is between 88 degree and 180 degree

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For (A-B) coordinates, you'll subtract the X's and Y's from each other.

X coordinate: 0.52 - (-4) = 4.52

Y coordinate: 15 - 0 = 15

Now Pythagorean theory: square root of [(4.52)^2 + 15^2] = 15.67

Find the angle:

arctan(15/4.52) = 73.23

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arctan is tan^-1 on your calculator.

X-axis -a million.7 - 6.3 = -8.2 Y-axis 6.5 - -a million.4 = 7.9 Now that we've the stunning vector in element kind ---> (-8.2,7.9) purely be conscious the Pythagorean theorem and discover that is magnitude So Sqrt(7.9^2+-8.2^2) for the magnitude and then resolve tan?=7.9/-8.2 for the attitude desire you already know now ;)