Applications With
Vectors
Section 8-5
WHAT YOU WILL LEARN:
1.
How to solve word problems using vectors and
right triangle trigonometry.
Fun and Games with Vector Word Problems
•
Two rodeo clowns are attempting to lead a bull back to the
paddocks. Suppose one clown is exerting a force of 270
newtons due north and the other is pulling with a force of
360 due east. What is the resultant force on the bull?
•
Find the angle the resultant force makes with the eastwest axis (x-axis).
You Try
Suppose two wrestlers are pulling horizontally and at a right angle
to each other on the arms of a wrestling opponent. Lenny exerts
a force of 180 pounds due north while his partner exerts a force
of 125 pounds due east.
A. Draw a picture
B. Determine the resultant force exerted on the opponent.
C. Determine the angle the resultant force makes with the eastwest axis.
Two Forces Working “Against” Each Other
• Suppose someone is pushing a cart full of packages weighing 100
pounds up a ramp 8 feet long at an incline of 25o. Find the work
done by gravity as the cart moves the length of the ramp.
Assume that friction is not a factor.
You Try
• Suppose someone is pushing a cart full of packages weighting 125
pounds up a ramp 10 feet long at an incline of 20o. Find the work
done by gravity as the cart moves the length of the ramp.
Assume that friction is not a factor.
Balancing Forces
• Someone is hanging a sign for her restaurant. The sign is
supported by two lightweight support bars as shown in the
diagram. If the bars make a 30o angle with each other, and the
sign weighs 200 pounds, what are the magnitudes of the forces
exerted by the sign on each support bar?
F2
30o
F1
You Try
• A sign is held by two support bars as shown in the figure. If the
bars make a 60o angle with each other and the sign weighs 100
pounds, what are the magnitudes of the forces exerted by the
sign on each support bar?
F2
60o
F1
Balanced Forces – Non-Right Triangles
• A lighting system for a theater is supported equally by two
cables suspended from the ceiling of the theater. The cables
form a 140o angle with each other. If the lighting system weighs
950 pounds, what is the force exerted by each of the cables on
the lighting system?
You Try
• A large television screen inside a restaurant is supported equally
by on each of its sides by two cables suspended from the ceiling
of the restaurant. The cables form a 100o angle with each other.
If the screen weighs 800 pounds, what is the force exerted by
each of the cables on the screen?
Homework
• Page 517, 12, 13, 14, 16, 18, 20, 24, 28
• Homework tips: 18, 20 and 24, draw on an x/y
coordinate plane. The “positives” and “negatives” make
a difference.
• Example together: #23