Projectile Motion (pages 95 ­101) Date ______
In the last section quantities like displacement and velocity were resolved into two components.
Using these components the motion of objects thrown in the air can be easily understood.
A long jumper's motion can be resolved into two vectors. The jumper runs in a straight line along the x­axis and then jumps. The jumper's velocity after jumping has horizontal and vertical components.
Projectile motion is the motion of objects
that are thrown or launched into the air and are subject only to gravity. The path of a
projectile is its trajectory.
Examples:
1
Horizontal Component of Projectile Motion
Constant velocity is motion in a ________________ line with ____________ speed like a ball rolling on a table.
Each vector arrow is the same length to represent constant velocity.
We will assume that there are no forces acting on the ball. and the velocity would remain constant. Actually, friction would make it slow down and eventually stop.
2
Vertical Component of Projectile Motion
All objects, when ignoring air resistance fall with the same
acceleration, ________________.
Vectors can be used to represent the increasing speed of the
ball in _________ _________.
The distance the ball falls each second increases because
the ball is _____________________.
3
Projectile Motion is the combination of free fall and
constant velocity in the horizontal direction.
A ball rolling off the table would continue in a
straight line if gravity was ignored.
The ball moving at constant horizontal velocity
and the ball in free fall occur at the same time.
The horizontal and vertical vectors are added
together at each time interval.
The trajectory of the ball can be seen by connecting
the resultant vectors.
4
Projectiles follow parabolic trajectories.
When Wile e Coyote runs off a cliff, the cartoon show him falling straight down.
If he has an initial horizontal velocity there will be
a horizontal motion throughout his fall so he will not
fall straight down.
For all our work we will assume the horizontal
velocity of a projectile will be ______________
and the projectile will have an initial ______________
velocity component and ______ initial vertical
component.
5
Projectile launched horizotally.
6
Vertical and Horizontal Components of the Velocity of a Projectile
If air resistance is ignored, the projectile moves equal horizontal distances in equal time intervals. There is no acceleration in the horizontal component.
The vertical component of the velocity changes because of the acceleration due to gravity.
The actual velocity is represented by the resultant vector that forms from the horizontal and vertical components of the velocity.
Vertical component is zero.
7
Projectiles follow parabolic trajectories.
The path of a projectile is a curve called a parabola.
With air resistance the horizontal component of the velocity would not be constant. The range of the projectile and the maximum height are both decreased.
8
How do Satellites Orbit the Earth?
Think about what happens when you throw a ball. The ball
might go 100 feet (30 meters) and then hit the ground. You
put the ball in orbit. The orbit was very short.
Now imagine you shoot a rifle. The bullet might travel 1 mile
(1.6 km) before hitting the ground.
What if you shoot a large cannon at a high initial velocity?
If the Earth was covered with water so there weren't any hill,
the path might look like the picture to the right. The cannonball
is going far enough to follow the curve of the Earth of a period of time before hitting the ground.
On Earth satellites have to get up above the atmosphere into the vacuum of space to orbit for any length of time. To avoid atmospheric interference the satellite must be 200 miles (320 km) above the surface of the Earth. The speed of the satellite is adjusted so that it falls to the Earth at the same rate that the curve of the Earth falls away from the satellite. The satellite is falling, but it never hits the ground.
http://www.fearofphysics.com/Satellite/satellite.html
9
A strobe light photograph of two golf balls released
at the same time shows that the two balls hit the ground at the same time.
The red ball drops and the yellow ball is projected
horizontally.
Why do they hit at the same time?
10
A package drop from an airplane is
like a horizontally projected object.
How would the trajectory change if air
resistance was not ignored?
How would the falling path of the package
look from the air plane if air resistance is ignored?
11