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9.4 (part 2):
Applications with
Solve problems using vectors and right
triangle trigonometry.
Vectors can be used to represent any
quantity, such as force, that has magnitude
and direction.
Velocity, weight and gravity are some
quantities that physicists represent with
Prep for Vector Application
You need to be able to draw a vector and
represent a force as a vector.
A force with magnitude F and angle A can be
written as <FcosA, FsinA>.
Represent each force as a
1. A force of 130 N is applied at θ=30˚
2. A force of 25 N is applied at =135˚.
3. A force of 12N at 30˚ from the horizontal.
Example 1
Make a sketch to show the forces acting on a
ship traveling at 23 knots at an angle of 17°
with the current.
Example 2
Find the magnitude and direction of the
resultant vector for the diagram.
170 N
300 N
Example 3
A 100-newton force and a 50-newton force act
on the same object. The angle between the
forces measures 90°. Find the magnitude of
the resultant force and the angle between the
resultant force and the 50-pound force.
Example 4
Denzel pulls a wagon along level ground with a
force of 18 newtons on the handle. If the
handle makes an angle of 40° with the
horizontal, find the horizontal and vertical
components of the force.
Example 5
A 33-newton force at 90° and a 44-newton
force at 60° are exerted on an object. What is
the magnitude and direction of a third force
that produces equilibrium on the object.
Example 6
Two ferry landings are directly across a river
from each other. A ferry that can travel at a
speed of 12 mph in still water is attempting
to cross directly from one landing to the
other. The current of the river is 4 mph.
a. Make a sketch of the situation.
b. If a heading of 0° represents the line
between the two landings, at what angle
should the ferry's captain head?
Vector Application Problems Worksheet