Name:__________________________
Date:__________
Section:____
Lab # ____ Vector Resolution
Any vector directed at an angle to the horizontal (or the vertical) can be thought of as having two parts (or
components). That is, any vector directed in two dimensions can be thought of as having two components.
For example, if a chain pulls upward at an angle on the collar of a dog, then there is a tension force directed
in two dimensions. This tension force has two components: an upward component and a rightward
component. As another example, consider an airplane that is displaced northwest from John F. Kennedy
Airport to a destination in Canada. The displacement vector of the plane is in two dimensions (northwest).
Thus, this displacement vector has two components: a northward component and a westward component.
The parallelogram method of vector resolution involves using an accurately drawn, scaled vector diagram
to determine the components of the vector. Briefly put, the method involves drawing the vector to scale in
the indicated direction, sketching a parallelogram around the vector such that the vector is the diagonal of
the parallelogram, and determining the magnitude of the components (the sides of the parallelogram) using
the scale. If one desires to determine the components as directed along the traditional x- and y-coordinate
axes, then the parallelogram is a rectangle with sides that stretch vertically and horizontally.
The trigonometric method of vector resolution
involves using trigonometric functions to determine
the components of the vector. Use of trigonometric
functions to determine the direction of a vector.
Trigonometric functions will be used to determine
the components of a single vector. Trigonometric functions relate the ratio of the lengths of the sides of a
right triangle to the measure of an acute angle within the right triangle. As such, trigonometric functions
can be used to determine the length of the sides of a right triangle if an angle measure and the length of one
side are known.
The direction of a resultant vector can often be determined by use of trigonometric functions. Most
students recall the meaning of the useful mnemonic SOH CAH TOA from their course in trigonometry.
SOH CAH TOA is a mnemonic that helps one remember the meaning of the three common trigonometric
functions - sine, cosine, and tangent functions. These three functions relate an acute angle in a right triangle
to the ratio of the lengths of two of the sides of the right triangle. The sine function relates the measure of
an acute angle to the ratio of the length of the side opposite the angle to the length of the hypotenuse.
The cosine function relates the measure of an acute angle to the ratio of the length of the side adjacent the
angle to the length of the hypotenuse. The tangent function relates the measure of an angle to the ratio of
the length of the side opposite the angle to the length of the side adjacent to the angle. The three equations
below summarize these three functions in equation form.
Name:__________________________
Date:__________
Section:____
In your lab notebook draw the following vectors. Indicate the scale used. Resolve the vectors
you drew into their components. Show all work. Use the trig function on at least two of your
vectors.
1. A car going 28m/s at an angle of 108º. Scale used ______________
2. A boy walking home from school 15 m at an angle of 245º. Scale
used________________
3. A cart is being pulled up an incline of 15º with a force of 55N. Scale used
_____________
4. A plane is flying from New York to Taxes with an acceleration of 50m/s2 at an angle of
210º. Scale used _____________
Background
What do you know about vectors? Give examples of vector quantities
you know so far with their units.
Problem
Hypothesis
How do we resolve vectors into their components?
Materials
Procedures
Conclusion
Why do you think resolving vectors can be useful?