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The vectors are used here to represent the forces acting on the plane.
The lift is balanced by the weight and the drag by the thurst.
The plane has a constant speed and a constant direction. (if thrust = drag)


VECTORS

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INTEGERS: REVIEW

To understand how to add or subtract vectors, review integers.
Horizontal  number line :
If you move to the right, you move toward a positive direction. The numbers increases.
If you move to the right, you move toward a negative direction. The numbers decreases.

The number line can be vertical. If you combine the vertical and the horizontal number lines, you
get a coordinate system.


 Try:
Along the horizontal:
5 - 7  =         plot the point
-3 + 5 =        plot the point
-1 - 2 =         plot the point
Along the vertical:
- 4 + 9 =
9 - 12 =
-3 -1 =


VECTORS

A vector is a quantity that involves both amplitude and direction and obeys the communitative
law for addition. If A and B are vectores we have A + B = B + A

see the figure below/
r is a vector. r could be a displacement if you were to walk from the
tail of the vector to the tip. the length of r could be proportional
(use a scale) to the distance you walked. r gives you also a direction.
The displacement vector tells us "how far" and "which way"
(example: r = 50m@20 degrees NorthEast)

Using a protactor and a ruler, define the vector r:
r = _____@_________

scale: 1cm = 10m




r could be the velocity of you car ("how fast", "which way")
r could be the force acting on a plane (see figure above, the resultant of drag + thrust) ( "how strong", "which way")

IN PHYSICS

Velocity is a vector. Velocity is one of the many quantities that have direction,  magnitude and unit..
Velocity tells you : "which way"and "how fast".  V = 30 mph@30  West of North
Speed is not a vector. The speedometer in the car gives you incomplete infirmation. It says nothing about which way
you are going. speed is a scalar. It has a magnitude and an unit.
Displacement is a vector. "Which way", "how far". D= 3 blocks @ North , Distance is not a vector. It just tells you "how far".
Remember    velocity vs speed and displacement vs distance
What about these quantities:
temperature ? energy ? acceleration ? force ? time ? volume ?


 vectors can be used to represent both the magnitude and
the direction of the velocity of a ball bouncing off the
wall, before and after the collision. Do you thinck
magnitude of V1 = magnitude V2  ? with a base ball ? soft ball ?
why ? Click on the image, use a protactor and give a direction to
each of the vector.
















ADDING PARALLEL VECTORS



 Adding // vectors is easy. Remember the number line?  A positive sign indicates the right and
a negative sign indicates the left. Add the integers together.






1)You walk 3 blocks to the East (write A=+3)  and 8 blocks to the West (write B = -8).
What is you displacement ? (Find A + B).

2)You walk 3 miles to the North and 10 miles to the south what is your displacement ?

3)You walk 10 blocks East and 10 West ?

4) You walk 20 blocks East and 10 West ?
5) you are in a train. the train is going at 100m/s and you walk at 1m/s to the right.
a) what is your velocity (include direction) relative to a cow outside.
b) if you walk now at 1m/s to the left, what is your velocity relative to the cow ?


5)  Praticeadding vectors  with the following applet. Work only in 1D (vectors going to the right/left or up/down)

  click here


6) A boat can travel with a speed of 20.0m/s. If it going against a current of 5.0m/s,
what is the velocity of the boat from a person standing on the shore? Draw the vector representation of this problem before solving.
Use integer: 20.0 m/s right = + 20
                   5.0 m/s left = -5


7) A boat can travel with a speed of 20.0m/s. If it going with a current of 6.0m/s, what is the velocity of the boat from a person standing on the shore? Draw the vector representation of this problem before solving.


8) If Brad is pushing the box with a force of 40.0N to the right, Sam is pushing the box 13N to the left
and Robby is pushing the box 17 N to the left, what force must Max be exerting?
 Draw the vector representation of this problem before solving.

9)What is the angle between A and -A when they are drawn from a common origin ?

10) What  is the minimum number of vectors with equal magnitude whose vector sum can be zero ?


















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