Download 8-1: Geometric Vectors

9.4 (part 2):
Applications with
Vectors
Objectives

Solve problems using vectors and right
triangle trigonometry.
Applications

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
vectors.
Prep for Vector Application
Problems:


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
vector:

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
55°
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.
Solution
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.
Solution
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.
Solution
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?
Solution
Homework
Vector Application Problems Worksheet