adding vectors algebraically
DESCRIPTION
dTRANSCRIPT
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3.1 Introduction to Vectors
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Section Objectives
Distinguish between a vector and a scalar. Add and subtract vectors by using the
graphical method.
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Scalar Quantities
Scalars can be completely described by magnitude (size)
Scalars can be added algebraically They are expressed as positive or negative
numbers and a unit examples include: mass, electric charge,
distance, speed, energy
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Vector Quantities
Vectors need both a magnitude and a direction to describe them (also a point of application)
They need to be added, subtracted and multiplied in a special way
Examples :- velocity, weight, acceleration, displacement, momentum, force
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Distinguish between a scalar and a vector.
The acceleration of a plane as it takes off. The duration of a flight. The displacement of the flight The amount of fuel required for the flight. The force acting on the plane in the form of
air resistance.
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3.2 Vector Operations
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Section Objectives
Calculate the magnitude and direction of a resultant vector.
Resolve vectors into components. Add vectors that are not perpendicular.
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Terminology
Two or more vectors can be combined together to form a resultant
A vector that does not lie along the x or y-axis may be resolved into its components
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Calculate the magnitude and direction of a resultant vector.
Draw 20 south of west.
Draw 20 west of south.
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Calculate the magnitude and direction of a resultant vector.
Use the Pythagorean Theorem to find the magnitude of the resultant.
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Calculate the magnitude and direction of a resultant vector.
Use SOHCAHTOA to find the direction of the resultant.
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Resolve vectors into components.
Every vector can be resolved into its x and y components using trigonometry.
If a vector is located on the x or y axis, then the other component of that vector is zero.
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Resolve vectors into components.
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Add vectors that are NOT perpendicular
If the original displacement vectors do not form a right triangle 1. Resolve each vector into its x- and y-
components 2. Find the sum of the x- and y-components 3. Use the Pythagorean Theorem to find the
magnitude of the resultant 4. Use the tangent function to find the direction of
the resultant
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Adding non-perpendicular vectors
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Adding non-perpendicular vectors
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Practice #1
A hiker walks 27.0 km from her base camp at 35 south of east. The next day, she walks 41.0 km in a direction 65 north of east and discovers a forest ranger’s tower. Find the magnitude and direction of her resultant displacement between the base camp and the tower.
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Check you work!
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1. a) 23 km
b) 17 to the east
2. 45.6 m at 9.5° east of north
3. 15.7 m at 22° to the side of downfield
4. 1.8 m at 49° below the horizontal
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Check your work!
Page 92
1. 95 km/h
2. 44 km/h
3. x=21 m/s, y=5.7 m/s
4. x=0 m , y=5m
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Practice #1
A bullet travels 85 m before it glances off a rock. It ricochets off the rock and travels for an additional 64 m at an angle of 36 degrees to the right of its previous forward motion. What is the displacement of the bullet during this path.
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Make physics YOUR
business. Try
problems 1-4 on pages
94.
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Dr. Miller says: Time for some practice! Try pages 89 & 92.
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Check your work!
Page 94
1. 49 m at 7.3° to the right of downfield2. 7.5 km at 26° above the horizontal3. 13.0 m at 57° north of east4. 171 km at 34° east of north
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Problem 3C
1. 216.5 m at 30.0 north of east
2. 2.89 Χ 104 m at 21.7 above the horizontal
4. 1320 km at 3.5 east of north
5. 221 km at 11.2 north of east
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Add and subtract vectors by using the graphical method.
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Multiply and divide vectors by scalars.
Multiplying or dividing vectors by scalars results in _________________.
You are in a cab traveling 25 mph east. You tell the cab driver to drive twice as fast. Your new velocity is ____________________.
You are in a cab traveling 25 mph east. You tell the cab driver to drive twice as fast in the opposite direction. Your new velocity is ________________.
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Add and subtract vectors by using the graphical method.
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Add and subtract vectors by using the graphical method.
T / F Vectors can be added in any order. T / F Vectors can be moved parallel to
themselves in diagrams. Let’s see:
http://www.physicsclassroom.com/mmedia/vectors/ao.cfm
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Calculate the magnitude and direction of a resultant vector.
http://www.physicsclassroom.com/Class/vectors/u3l1b.cfm