Name: _______________________________ Date: ___________ Class: ___________
Vector Notes
Resultant vector: _____________________________________________________
_____________________________________________________________________
Rules for Resultant Vectors:
1. Vectors in the ___________ direction can be __________ and keep the same direction.
2. Vectors in _______________ directions are __________________ and whichever
vector is largest will represent the direction of the resultant.
3. The combined resultant will be based on the combination of arrows (Head to Tail)
When solving problems using vectors:
1) ALWAYS draw a ____________!
2) ALWAYS draw the __________ vector first!
3) Watch the ___________ and _________ of the vectors.
4) ALL answers should have a magnitude (amount) and a direction.
Example Problems:
1. If a car drives 10m east and then drives another 4m east, what is the resultant
displacement of the car?
2. If a soccer ball gets kicked with a velocity of 10m/s north and then the ball gets kicked
with a velocity of 25m/s south, what is the resultant of the velocity of the soccer ball?
3. If a box is pushed with a force of 10N east, then pushed with a force of 2N west, and
then pushed with a force of 8N east, what is the resultant force being used to push the
box?
4. What is the resultant displacement of a runner who runs 4m north, 10m south, 2m north,
and then and 6m south?
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CP Physics
Name: _______________________________ Date: ___________ Class: ___________
Solving Resultant Vectors mathematically: Pythagorean Theorem
Instead of using the words adjacent, opposite, and hypotenuse to describe the sides we will use
the letters given in the Pythagorean Theorem.

_________ represents the longest vector, and is adjacent the angle (θ) we measure for
the resultant direction.

________ represents the shortest vector and is opposite to the angle (θ) of the resultant
direction.

_________ is the resultant vector which will be the longest side of the triangle
To find the length of side c, use the Pythagorean
Theorem:
c
____________________
b
To find the angle θ, use the inverse tangent function:

a
_______________________________________
Vector Directions:
How do we describe vectors that are not exactly North, South, East, and West?
______________________________________________________________________
Primary direction – ______________________________________________________
Secondary direction – ___________________________________________________
A vector is always illustrated in a specific way:
___________°
of
of
Examples: _______________________________________________________
Draw the vectors below:
17° North of East
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34° West of South
40° South of West
CP Physics
Name: _______________________________ Date: ___________ Class: ___________
What vector is illustrated below?
_____o ____ of ____
_____o ____ of ____
_____o ____ of ____
Example Problems:
1. If a bird is flying with a speed of 10m/s west and a wind blows the bird 6m/s, what is the
resultant velocity of the bird?
__________, _____o ____ of ____
2. If a jogger runs 14m North and then takes a right and runs 5m East, what is the
displacement of the runner?
__________, _____o ____ of ____
3. IA field goal kicker kicks a ball north with a force of 1.3 N. If a wind blowing west pushes
the ball with a force of .6N, what is the resultant force on the football?
__________, _____o ____ of ____
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CP Physics
Name: _______________________________ Date: ___________ Class: ___________
Practice – Solve the following problems mathematically, including magnitude and direction.
All problems should have vectors drawn with them.
1. A bird flies due south for the winter at a velocity of 13.5 m/s. The bird experiences a wind
which blows due east a 5.4 m/s. What is the bird’s resultant velocity?
__________, _____o ____ of ____
2. A plane is flying to Minnesota with a velocity of 450 km/h, N. The plane encounters a
crosswind with a velocity of 25 km/h, W. What is the resultant velocity of the plane?
__________, _____o ____ of ____
3. A cue ball is hit simultaneously by two forces. One is 34 N, south and the other is 15 N,
east. What is the resultant force applied to the cue ball?
__________, _____o ____ of ____
4. A football player is hit from behind with a force of 25 N, north while being hit from the side
with a force of 47 N, west. What is the resultant force on the player?
__________, _____o ____ of ____
5. A hiker walks 56 m, N and 89 m, E. What is his resultant displacement?
__________, _____o ____ of ____
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CP Physics