To define the difference between scalar
and vectorial quantities.
 To
understand and use vectorial
addition.
 To state and understand the concept of
relative velocities.

A quantity such as a velocity, which has a direction as well as magnitude is a
vector quantity. Some example of vector quantities are force, displacement
and momentum.
However, many quantities have no direction like mass, time and temperature
and are called scalar quantities.
The number of
grapes is a scalar
quantity, the
number of blocks
and direction to a
place is a vector
quantity.
When a vector quantity is handwritten its represented with an arrow over
the letter representing it.
Simple arithmetic cannot be used to add vectors that are not along the
same line. They also must have the same units.
Vectors can be added geometrically or algebraically.
To add a vector to vector
geometrically you must draw them to some
𝐵
scale. The resultant vector
tip of
𝐵
𝐴
𝑅
is the vector drawn from the tail of
as shown in the figure.
𝐴
to the
Adding vectors graphically is not sufficiently accurate and not useful for
vectors in three dimensions.
A vector
𝐴
can be expressed as the sum of two other vectors called the
components. They are usually chosen to be along two perpendicular
directions.
Using trigonometric functions we can find the components are:
We can now add vectors using components. First solve each vector
into its components. Then the sum of the x components equals the
x component of the resultant and similarly for y. So for
𝑅
= +
𝐴
𝐵
The components of a vector form the sides of a right triangle having an
hypotenuse with magnitude A that correspond to the magnitude of the
resultant vector.
Using the Pythagorean Theorem and the definition of a Tangent we find
that:
And to solve the angle of the resultant vector we can then use:
• A rural mail carrier leaves the post office and drives 22.0 km in a
northerly direction. She then drives in a direction 60.0 degrees south of
east for 47.0 km. What is her displacement from the post office?
Solution: 30.0 km. 38.5 degrees southeast.
• An airplane trip involves three short trips with two stopovers. The first is
due east for 620 km; the second is southeast (45 degrees) for 440 km;
and the third is at 53 degrees south of west for 550 km. What is the
plane’s total displacement?
Solution: 960 km. 51 degrees south of east.
• While exploring a cave, a spelunker starts at the entrance and moves the
following distances: 75m north, 250m east, 125m at an angle 30 degrees
north of east, and 150m south. Find the resultant displacement from the
cave entrance.
Solution: 358.47m 1.998 degrees south of east
• The eye of a hurricane passes over Grand Bahama Island in a direction
of 60 degrees north of west with a speed of 41.0 km/h. Three hours later
it shifts due north and its speed slows to 25.0 km/h. How far from grand
Bahama is the hurricane after 4.5 hours?
Solution: 157 km.
Statistics from treasure hunting.
 12 Teams.
 2 treasure marks found.
 6 treasure marks not found but
end point being within an average
of 6.4 m.
 4 treasure marks not found due to
wrong set of instructions.
Why wasn’t the mark found?
What were the most common errors on the activity?
How can these mistakes be minimized?
Watch the following video about vector addition.
After watching it. A set of questions will be given to you and you must answer
them individually.
http://www.youtube.com/watch?v=UeQNnfY0BQA
http://www.youtube.com/watch?v=6zfMENV_tak&feature=relmfu
 What was the first problem the Myth Busters encountered when using a
conveyor belt?
 What is the grid pattern on the back for?
 Why Grant decided to place a marker to know when to shoot ?
 What was the reason for choosing the air pressure cannon over the other
devices?
 Briefly explain how Kari overcame the measuring problem of the truck
speed.
 Write a brief description of another way of proving vector addition you can
think about.
The measured velocity of an object depends on the velocity of the observer
with respect to the object.
For example: On highways cars are moving in the same direction at high
speed relative to earth, but with respect to each other they hardly move at
all.
But if velocities are not along the same line we must use vector addition to
find the relative velocity.
𝑉𝑅𝐸 = Velocity of the river
with respect to earth.
𝑉𝐵𝑅 = Velocity of the boat
with respect to the river.
𝑉𝐵𝐸 = Velocity of the boat
with respect to earth.
• A train is traveling with a speed of 15m/s with respect to earth. A
passenger standing at the end of the train throws a baseball with a
speed of 15m/s relative to the train, in direction opposite the motion of
the train. What is the velocity of the baseball relative to the earth?
Solution: 0 m/s
• A rowboat crosses a river with a velocity of 3.3 mi/h at an angle of 62.5
degrees north of west relative to the water. The river is 0.505 mi wide
and carries and eastward current of 1.25 mi/h. How far upstream is the
boat when it reaches the opposite shore?
Solution: 0.26 miles upstream
• Two canoeists in identical canoes exert the same effort paddling and
hence maintain the same speed relative to the water. One paddles
directly upstream (and moves upstream), whereas the other paddles
directly downstream. With downstream being the positive direction, an
observer on the shore determines the velocities of the two canoes to be
-1.2m/s and 2.9m/s, respectively. (a) What is the speed of the water
relative to the shore? (b) What is the speed of each canoe relative to the
water.
Solution: 0.85m/s , 2.05m/s
• A jet airliner moving initially at 300mi/h due east enters a region where
the wind is blowing at 100mi/h in a direction 30 degrees north of east.
What is the new velocity of the aircraft relative to the ground?
Solution: 389.82 mi/h at 7.37 degrees north of east
• Giancoli , Douglas C. Physics Sixth Edition. USA Pearson 2005
• Serway, Raymond A. Essentials of College Physics. USA Thomson 2007