Bellaire High School Advanced Physics - Chapter 3 - Projectile Motion
Review of Vectors
Scalars and Vectors
Recall a scalar does not have a direction
A vector has BOTH magnitude and direction
Vectors can be added graphically
When adding vectors, the units must match
It would be meaningless to add a force vector to a
They are essentially apples and oranges
When vectors do have the same units, we
may add or subtract the vectors
A student is walking to school. First, the
student walks 350m to a friend’s house. The
two then both walk 740 m to school.
The method to add the vectors is called the tail
to tip method. The vector we find is called
the resultant vector.
Vectors can be moved parallel to each other
Does not matter where the vectors are, as long as
they are addable, tail to tip
Push a toy car across a moving sidewalk
Say the sidewalk is moving at 1.5 m/s
The car is pushed .8 m/s
Vector Addition and Subtraction
Vector addition is commutative
The order the vectors are added does not matter
To subtract a vector, simply add the opposite
Multiplying and Dividing Vectors
Multiplying or Dividing vectors by scalars
results in vectors
Lets say we have the velocity of a race car
We want to examine the properties of the car when it is
traveling twice as fast
If vi is v, what is twice vi?
What is half of vi
What would be the new v if the car drove twice as fast in
the opposite direction?
Up to this point, we have only needed one
dimension to study our situations
What if we wanted to study a ball being thrown at
45o above the ground?
That path of motion does not fit any of our current
We will have to use a combination of the two axis
Note: Orientation of the axis is up to you.
Determining the Resultant
Trigonometry is very useful to find the
The Pythagorean Theorem
Think of a tourist in Egypt walking up the side of a
Are they walking vertical?
Are they walking horizontal?
It is a combination of the two motions that produces one
final motion, somewhere between horizontal and vertical
The resultant of two vectors is also a vector
That means the resultant must have:
It is not enough to say the magnitude of the
resultant, it must have direction also.
We will use the trig functions of sine, cosine
or tangent to find the direction
Any vector may be broken into x and y
That is to say any vector may be RESOLVED into
its component vectors
A horizontal vector has a 0 y component
A vertical vector has a 0 x component
A vector at 45o has equal x and y vectors
Until now, all of our vectors have been
perpendicular to each other
Things in real life are much, much less rigid
Lets say a plane travels 50 km at an angle of
35o, then levels out and climbs at 10o for 220
These vectors are not perpendicular, we cannot
use the Pythagorean Theorem, yet
Resolve the vectors
Two Dimensional Motion
In the last section, we resolved vectors into x
and y components.
We will apply the same ideas to something
thrown or flying in the air
Think of a long jumper
When she approaches her jump, she has only an
When she jumps, she has both x and y
Analyze Projectile Motion
We can break the motion into the two
component vectors and apply the kinematic
equations one dimension at a time
Any object thrown or launched into the air
that is subject to gravity is said to have
Projectiles follow a path called a parabola
A common mistake is to assume projectiles fall
Since there is vxi, there must be continuous
Neglecting air resistance, is there anything to stop the
projectile in the horizontal direction?
Velocity in the horizontal direction is constant
In real life, horizontal velocity is not constant, but for our
purposes we will assume uniform, constant velocity
Projectile motion is simply free fall with horizontal
If two similar objects fall to the ground from the
same height, one straight down while the other is
thrown out to the side, which hits first?
It is very important to realize motion in the x
direction is completely independent of motion in the
A projectile has horizontal velocity until the
object stops (hits the ground)
A projectile will have a vertical velocity that is
ever changing due to gravity, until the
projectile stops (hits the ground)
What is the only factor that is consistent in
the x AND y directions?
Sample Pg 101, Practice Pg 102
Objects Launched at an Angle
When an object is launched at an angle, the
object has both horizontal and vertical
This is similar to the motion of an object
thrown straight up with an initial vertical
Example pg 103, Practice pg 104
Frames of Reference
Velocities are different in different frames of
You are in a train traveling at 40 km/h
Relative to the train, how fast are you moving?
Someone outside sees the train pass, how fast do they
see you moving?
The velocities are different because the
reference frames were different
You – Train, Outside observer - Earth
You are driving on the interstate at 80 km/h
and a car passes you at 90 km/h
How fast does it seem the passing car is moving
to you? To someone on the side of the road?
A semi-truck driving west at 85 km/h passes
a car on the other side of the road, driving
east at 75 km/h. To the trucker, how fast is
the car moving?
A person standing on top of a train traveling at 20 km/h. They
throw a baseball. How fast does it look like the ball is moving to
a person standing on the ground when:
The ball is thrown 10 km/h forward
The ball is thrown 40 km/h backward
The ball is thrown 20 km/h backward
The ball is thrown straight up
Example pg 108, Practice pg 109