SPH3U Homework: Vectors and Components
1.
Reason. Three vectors are drawn on the grid shown to
the right. Rank the six components of these three
vectors in order of increasing size. For example: |Ay| >
|Bx|
Name:
5.
Represent and Calculate. A plane is travelling with a
velocity of 340 km/h [N40o W]. Sketch a component
triangle and calculate the components of this vector.
(Don’t draw a scale diagram!)
6.
Reason. Vector equations have components too! You
were doing this last year without realizing it when you
wrote separate expressions for Fnetx and Fnet y. Imagine



we are adding two force vectors: Fnet = F f + Ft where


F f = 17 N [N 30o E] and Ft = 9 N [N 50o E]. (The force
+y
A
B
C
+x
2.
Reason. A vector makes a 30o angle with the x-axis.
Which of its two components has the larger size?
Explain.
vectors are not drawn to scale!)
+y
3.
Reason. Two vectors are shown on the grid to the right.
Rank the four components of these two vectors in
increasing order according to size.

Ft
+y

Ff
A
+x
+x
(a) Draw a component triangle attached to each of the
three vectors in the diagram above. Calculate the
components of the vectors you know.
B
4.

Fnet
Represent and Calculate. A vector has the
components: dx = - 46 m and dy = 30 m. Sketch a
component triangle for the resultant vector (not a scale
diagram!). Calculate the complete vector

d .
(b) The x-component of the net force can be found
from taking the x-component of the entire
equation! Fnet x = Ff x + Ft x. Fill in this equation
and solve for Fnet x.
+y (N)
(c) Do the same for the y-component.
+x
(E)

(d) Use the component triangle for Fnet to find Fnet
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