Vectors Worksheet



Vectors Worksheet

[Vector Addition and Resolution Relationship]

What is Vector Addition?

Vector addition is the process of finding the resultant vector when given the components of the vector.

In one-dimensional vector addition, you will be working on either the x (horizontal) or y (vertical) axis. The vector addition is simply the addition (or subtraction if the vectors are in opposite directions) of the two vectors. If they are in opposite directions, the resultant direction will be in the same direction as the vector with the greatest magnitude.

In two-dimensional vector addition, you have both an x (horizontal) and a y (vertical) component. You add the vectors by using the Pythagorean theorem since the two vectors are at right angles to each other. This value is the magnitude of the result vector. The direction of the result vector is the angle between the hypotenuse of the triangle and the horizontal. To find this value, you use the tan -1 function on the calculator.

What is Vector Resolution?

Vector resolution is the reverse to vector addition. In vector resolution, you know the magnitude and direction (angle) of the resultant vector and you are solving for the horizontal and vertical components.

To find the x (horizontal) component, you use the cosine function and the formula:

A=[pic]; where R is the magnitude of the resultant

To find the y (vertical) component, you use the sine function and the formula:

B=[pic]; where R is the magnitude of the resultant

Vector Resolution practice:

4. The given vector represents a hot air balloon that has a 0.25 m/s velocity at an angle of 60° above the horizontal.

0.25 m/s

60°

A. Draw the horizontal and vertical components of the vector on the diagram above.

B. Use the Pythagorean theorem to check these values. (Show work)

5. A motorcycle stunt person leaves the jump a ramp traveling at 35 m/s at 22° above the horizontal.

A. Draw a vector representing the velocity of the motorcycle.

B. Draw the horizontal and vertical components of the vector.

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