Projectile Motion Vectors Part 2Vectors Part 2PVHS PhysicsPVHS Physics
Essential Questions
What is a vector? What is the difference between a scalar
and a vector? How do you add and subtract vectors? What are the horizontal and vertical
components of a vector? What is projectile motion? How can the motion of a projectile be
described by its horizontal and vertical vector components?
What we know…
A scalar has magnitude but no direction
A vector has magnitude and direction The resultant is a vector representing
the sum of two or more vectors Vectors can be added graphically
using the triangle or the parallelogram methods
Try this…
An A-10 normally flying at 80 km/hr encounters wind at a right angle to its forward motion (a crosswind). Will the plane be flying faster or slower than 80 km/hr?
60 km/hr
Crosswind
80 km/hr
Is the resultant greater than or less than 80 km/hr?
80 km/hr
60 km/hr
Add the vectors
Resultant
hr
km100
6080Resultant 22
Vectors
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2-D Coordinate System
In 2-D, a good reference is the x-y coordinate plane
X
Y
Remember… we can move a vector as long as we don’t change magnitude or direction
2-D Coordinate System
X
Y
Once you establish a coordinate system or frame of reference, you can begin to analyze vectors mathematically
First, resolve the vector into its x-component and its y-component
Determining Magnitude
The component vectors can represent the change in x and the change in y for the vector
To find the magnitude, d, of the vector, we use the Pythagorean Theorem:
X
Y
x
y
22
222
yxd
,or
yxd
d
Determining Direction
Once we have a frame of reference, the vector will make an angle, with the x-axis
We can use the tangent function to determine the value of
X
Y
x
yd
x
ytan
,orx
ytan
1
If using a calculator, be sure to set degrees or radians as appropriate
Try this…
While following directions on a map, a pirate walks 45.0m north then 7.5m east. What single distance and direction could he have walked to reach the treasure?
While following directions on a map, a pirate walks 45.0m north then 7.5m east. What single distance and direction could he have walked to reach the treasure?
o..
tan
m..d
58057
45
6455745
1
22
X
Y
45.0m
7.5m
d
Component Vectors
Just as we can add two vectors to create a resultant…
80 km/hr
60 km/hr
Resultant
Component Vectors
Any vector can be broken down into two vectors that are at right angles to one another These vectors are
called “component vectors”
The process of determining the components is called “Resolution”
Velocity
VerticalComponent
HorizontalComponent
Resolving Components
If we know the magnitude, d, and direction, we can also find the x and y components
X
Y
x
yd
cos
sin
,
cossin
dx
dy
ord
xand
d
y
Try this…
How fast must a truck travel to stay directly beneath and airplane that is moving 105 km/hr at an angle of 25 degrees to the ground?
X
Y
V=105 kph
Vtruck=?
hr/kmcos
cosvvtruck
9525105
Adding Vectors
Algebraically
Demo
Vector A=4.5m/s @ 35 degrees Vector B=6.5m/s @ -40 degrees Find A+B
Try this…
A ranger leaves his base camp for a ranger tower. He drives 35o south of east for 25.5 km and then drives 65o north of east for 41.0 km. What is the displacement from the base camp to the tower?
What we know…
What is a vector? What is the difference between a
scalar and a vector? How do you add and subtract
vectors? What are the horizontal and vertical
components of a vector?
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Questions?
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