# University of Wisconsin Green Bay

What are the x- and y-components of the following vectors? The magnitude of vector A is 8.0 m/s and the magnitude of vector B is 17 m/s.

• In this problem, you are asked to find the components of a vector. You aren’t doing any physics in this problem; it is practice for a mathematical step that you will use in future physics problems which involve vector quantities.

• The most visual way to see vector components is to draw a right triangle with the vector as the hypotenuse and the sides of the triangle enclosing the given angle.

• The reason we pick a coordinate system with perpendicular axes is so that we can use definitions based on right triangles. For a right triangle:

Sinθ = (opposite side)/(hypotenuse)

These relations are often remembered as soh-cah-toa. In this case, you know the vector (the hypotenuse) and want to find the opposite and adjacent sides, so will use the sin and cos relations.

• Step 1

There is no further calculation required for Vector A. Scroll down to step 2 to find the components of Vector B.

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Step 2

There is no further calculation required for Vector B and no other information requested in this problem.

• This problem asked you only to practice the math of dividing vectors into components. A good double check is that no component is greater than the length of the vector, and that the shorter component is less than the longer one. It is also a good idea to go back to the picture to make sure that you correctly assigned signs to each component.

Note that when you replace a vector with its components you have the same physical effect as for the original vector. So, in this case, driving at a 40o angle north of east for say one hour at 17 m/s would have the same effect as driving east for one hour with a speed of 13 m/s and north for one hour with a speed of 11 m/s.