Vector Components and Adding Non-Perpendicular Vectors
Name:____________________
Vector Components
Any vector can be “resolved” into two component vectors.
Diagram
How do we calculate Ax and Ay?
Ax is the horizontal component – or x component -- of the vector.
Ay is the vertical component – or the y component – of the vector.
Example A plane heads east, while the wind moves a plane north. As a result, the plane moves with velocity of 34 m/s
@ 48°relative to the ground.
Calculate the plane's heading and wind velocity.
What does this mean??
It means we need to find the ________________________________________________________________________
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Draw the diagram and solve the problem, below.
Example A plane moves with a velocity of 63.5 m/s at 32 degrees South of East. Calculate the plane's horizontal and
vertical velocity components.
You Do problems
 A person walks 450 m @ 120 degrees. Find the x and y component vectors.
 A car accelerates 6 m/s2 at 40 degrees. Find the x and y component vectors.
You can reverse the problem and find a vector from its components.
Let:
Fx = 4 N
Fy = 3 N .
Find magnitude and direction of the vector
This problem may be written differently, but its exactly the same
type of problem we did during our first lesson on vectors!
Just add the components to find the overall vector
Diagram and solve the problem below.
Adding vectors at any angle
1) We start like we always do … moving vectors head to tail.
2) Next, we draw a resultant (as always).
3) Next step is also same as before … we use the other sides of
a right triangle to calculate the magnitude and direction of
the resultant (C).
4) The difference? We just have to do a little more reasoning
to ‘see’ the right triangle and find its sides.
5) We can always – ALWAYS – find a right triangle that is made
from combining the vector components of the vectors we
are adding.
6) The resultant’s x component is equal to the sum of the x
components of the vectors we are adding. Cx = Ax + Bx
7) The resultant’s y component is equal to the sum of the y
components of the vectors we are adding. Cy = Ay + By
And we can figure all these out with trig.
Example: Two people are lugging a heavy suitcase. One pulls with a 68N force at 24o; the other pulls with a 32 N force
at 65O. What is the total force exerted by the two people on the suitcase?
Solving procedure
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3)
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Diagram and solve the problem below
You do
1)
V1 = 35 m/s @ 28 degrees, V2 = 40 m/s @ 60 degrees
Find V = V1 + V2
2) X1 = 4.8 km @ 140 degrees, X2 = 5.3 km @ 30 degrees
Find X = X1 + X2
Hint: if the x or y components go in different directions, subtract the smaller from the bigger. You diagram will
show you!