Transcript to view the Ch 8

You used trigonometry to solve triangles. (Lesson 5-4)
• Represent and operate with vectors geometrically.
• Solve vector problems and resolve vectors into their
rectangular components.
• vector
• equivalent vectors
• initial point
• opposite vectors
• terminal point
• resultant
• standard position
• triangle method
• direction
• parallelogram method
• magnitude
• zero vector
• quadrant bearing
• components
• true bearing
• rectangular
components
• parallel vectors
Identify Vector Quantities
Vector – a quantity that has both magnitude (length)
and direction.
A. State whether a hockey puck shot northwest at
60 miles per hour is a vector quantity or a scalar
quantity.
B. State whether a tennis ball served at 110 miles
per hour is a vector quantity or a scalar quantity.
C. State whether a sprinter running 100 meters
north is a vector quantity or a scalar quantity.
Represent a Vector Geometrically
A. Draw an arrow diagram for v = 10 newtons of
force at 30° to the horizontal.
B. Draw an arrow diagram for z = 25 meters per
second at a bearing of S70°W.
Represent a Vector Geometrically
C. Draw an arrow diagram for z = 150 meters per
second at a bearing of W45°N.
D. Draw an arrow diagram for t = 10 miles per hour
at a bearing of 025°.
Operations with Vectors
Draw a vector diagram of a + b
Operations with Vectors
Draw a vector diagram of a – 3b.
Draw a vector diagram of n + 2m.
A.
C.
B.
D.
ROWING Jamie rows her boat due east at a speed
of 20 feet per second across a river directly toward
the opposite bank. At the same time, the current of
the river is carrying her due south at a rate of
4 feet per second. Find Jamie’s speed and direction
relative to the shore.
Use Vectors to Solve Navigation
Problems
AVIATION An airplane is flying with an airspeed of
475 miles per hour on a heading of 070°. If an 80mile-per-hour wind is blowing from a true heading
of 120°, determine the velocity and direction of the
plane relative to the ground.
Resolve a Force into
Rectangular Components
A. GARDENING While digging in his garden, Will
pushes a shovel into the ground with a force of
630 newtons at an angle of 70° with the ground.
Draw a diagram that shows the resolution of the
force that Will exerts into its rectangular
components.
Resolve a Force into
Rectangular Components
B. GARDENING While digging in his garden, Will
pushes a shovel into the ground with a force of
630 newtons at an angle of 70° with the ground.
Find the magnitudes of the horizontal and vertical
components of the force.
The horizontal and vertical components of the force
form a right triangle. Use the sine or cosine ratios to
find the magnitude of each force.
SOCCER A player kicks a soccer ball so that it
leaves the ground with a velocity of 39 feet per
second at an angle of 37° with the ground. Find the
magnitude of the horizontal and vertical
components of the velocity.
A. horizontal component ≈ 28.75 ft/s;
vertical component ≈ 23.28 ft/s
B. horizontal component ≈ 37 ft/s;
vertical component ≈ 39 ft/s
C. horizontal component ≈ 31.15 ft/s;
vertical component ≈ 23.47 ft/s
D. horizontal component ≈ 23.47 ft/s;
vertical component ≈ 31.15 ft/s