Vectors Worksheet
[Addition and Resolution]
What is a Vector?
Vectors are graphic representations of physical occurrences. We use vectors to
visualize what physically happens to an object under certain conditions. Vectors
designate the magnitude and direction of things like forces, accelerations, velocities,
and displacements. They help us to describe motion through a common symbology.
Magnitude
-
the amount of the force, acceleration, velocity, or displacement.
Direction
-
a specific direction in which the force is applied, or the
acceleration, velocity, or displacement occur.
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 used in two-dimensional vector analysis and 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:
Rx  R cos ; where R is the magnitude of the resultant
To find the y (vertical) component, you use the sine function and the formula:
Ry  R sin  ; where R is the magnitude of the resultant
Vector Addition
1.
You pull a rope to the left with 300 N and a friend pulls the rope to the right with
425 N. (Don’t forget about relative size of vectors)
A.
Draw a vector diagram for the two forces acting on the rope.
B.
Use (one dimensional) vector addition to find the result vector.
(Show work)
C.
What is the magnitude and direction of the result vector?
_____________________
D.
2.
___________________
Draw a vector which represents the result vector.
You sail a boat due east at 25 knots. The wind is blowing the boat due north
at 10 knots.
A.
Draw a vector diagram of the velocities of the boat.
B.
Use (two dimensional) vector addition to find the result vector.
(Show work)
D.
What is the magnitude and direction of the result vector?
_______________________
E.
______________________
Draw a vector which represents the final velocity of the boat.
3.
The wing of an airplane experiences the forces as depicted in the
vector diagram to the right. Using both one and two dimensional
vector addition, find the result force acting on the wing. Give the
magnitude and direction of the vector and draw the vector.
(Show work)
2000N
500 N
3500 N
Magnitude
__________________
Direction
__________________
Vector Resolution
4.
The given vector represents a hot air balloon that experiences a 0.25 m/s2
acceleration at an angle of 60° above the horizontal.
0.25 m/s2
60°
A.
Draw the horizontal and vertical components of the vector on the diagram
above.
B.
Use vector resolution to find the magnitude of each component.
(Show work)
__________________
__________________
C.
Use the Pythagorean theorem to check these values. (Show work)
5.
A motorcycle stunt person leaves the jump 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.
C.
Use vector resolution to find the magnitude of each component.
(Show work)
__________________
__________________
6.
The diagram below depicts all the forces acting on an object. Use both vector
resolution and vector addition to find the final resultant force acting on the box.
(Show work)
10 N
45°
A.
Resolve the 10N vector into its horizontal and vertical components.
(Show work)
B.
Add/Subtract the horizontal components. (Show work)
C.
Use the resulting horizontal and vertical components to do twodimensional vector addition. Find the magnitude and direction of the
resultant vector. (Show work)
15N
__________________
7. A pack of three Artic wolves are fighting over the carcass of a
dead polar bear. A top view of the magnitude and direction of the
three forces is shown in the diagram to the right.
a. Determine the resultant or net force acting upon the
carcass.
b. Determine the acceleration of the 750-kg polar bear
carcass.