Download Topic #8: X and Y COMPONENTS of VECTORS

Topic #8: X and Y COMPONENTS of VECTORS
In example M on the last handout, you found the resultant force vector
for this: “A force of 100n North and 100n East acting on the same object:
find their resultant, FR.”
The answer was:
FR = 141newtons NorthEast
But what do you call the other two vectors, namely the 100n North and
100n East vectors that combined to make the resultant?
These are called the COMPONENTS of FR, and in your diagram are the legs
of the triangle formed, while FR is the hypotenuse. 100n East is Fx, the
horizontal or X component, and 100n North is Fy, the vertical or Y component.
Remember their vector sum is not 200n; FR was found by the Pythagorean
Theorem and the angle’s tangent.
In example N: “A rower’s velocity
of 3 km/hr West: find their resultant,
The answer was:
VR = 5 km/hr @< 37º
resultant velocity has two components,
VY = 4 km/hr South?
of 4 km/hr South and a river’s current
VR.”
West of South
Do you see that this
namely, VX = 3 km/hr West and
Often the value of a vector, its magnitude and direction, is known or
given in a problem, but the question is to find the X and Y components of the
vector. This is the opposite process from finding a resultant vector.
The Mathematical Solution Method: Make a vector triangle, and use the
sine and cosine functions to find the Y and X components of a known vector.
A carefully plotted diagram, done to scale, also allows you to measure the
two components when using the graphical solution method.
For each example below, draw a vector diagram and find the vector’s X and Y
components. Use the mathematical method. (We will also practice the
graphical method in class for (C) and (E) below, and compare the answers
obtained by the two different methods.)
A) An applied force of 100n North
B) A car’s velocity of 30 km/hr East
C) A walk of 20m Northeast
D) A Displacement of 5km Southwest
E) A force of 50n @ <60ºS of E
F) A plane’s velocity = 10m/s @ <30ºE of N