Regents Physics

1
Regents Physics

• Vectors and Scalars
• What is a Vector? A scalar?
• A vector is a quantity that has both magnitude
  and direction
• A scalar has only magnitude
• For example
• Distance vs. Displacement
• Speed vs. velocity

2
Drawing Vectors

• A vector has magnitude and direction
• each vector is drawn to scale and includes a tip,
  indicating a direction

N
V 100.0 m/s east
Tip
Tail
E
W
The length is defined by creating a scale
S
Scale 1.0 cm 10.0 m/s
The coordinate axis system defines the direction
of the vector
3
Tip to Tail Triangle Method..How do we
graphically add/subtract vectors
Tail of V2 to tip of V1
Resultant Vector (R) V1 V2
V2
V1
The resultant vector is an equal expression of
vectors V1 , V2
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Tip to Tail...
V1 east
N
V2 north
R
Put on axis and use tip to tail method
V2 north
W
E
V1 east
Measure the length of the resultant!
S
5
Vector addition example

• A person walks 24.0 m north and 12.0 m east.
  Determine the position and magnitude of the
  resultant vector of this motion.
• First, make a scale for the vectors
• Draw a coordinate axis
• Draw and the label the vectors
• Draw and measure the resultant vector!

6
Vector addition problem 2

• A plane flies at 200.0 miles per hour north when
  it encounters a crosswind of 80.0 miles per hour
  from the west. Determine the position and
  magnitude of the resultant vector of this motion.

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These are equal expressionsright?!
8
Notice both vectors start at the same origin
This method can also be used when we are not
using tip to tail addition and we also get the
same results!
9
Example

• Find the resultant vector of the following two
  vectors

We use dashed lines to represent the mirror
images of the vectors
10
Rotate green A vector 180 degrees and give it a
negative sign! Just remember..tip to tail
B
A
Our resultant vector is now B - A and has a
different magnitude and direction!
11
A car drives 100.0 km at an angle of 35 degrees
north of east. Find the vectors d1 east
and d2 north of this motion.
What if we START with the resultant?
V2 north
35
V1 east
Just draw and measure the vectors!
12
Practice Problem...

• A package is dropped from a plane and is off
  target by 100ft to the west. If the distance to
  the ground is 500ft.
• (a) What is the resultant vector of this motion?
• (b) What is the angle from the negative y - axis
  of the resultant vector?

end
13
Vectors

• Relative Velocities
• The Boat and the Plane

14
The Boat

• If a motor boat were to head straight across a
  river, it would not reach the shore directly
  across from its starting point.
• The river current influences the motion of the
  boat and carries it downstream.
• The motor boat may be moving with a velocity of 4
  m/s, but
• While the speedometer of the boat may read 4 m/s,
  its speed with respect to an observer on the
  shore will be greater than 4 m/s.

15
The Plane

• We can apply the same logic to a plane