Tennis ball Golf ball Football Softball Soccer ball Bullet Hockey puck Basketball Volleyball Arrow Shot put Javelin These are all examples of things that are projected then go off under the ID: 648461
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Slide1
PROJECTILE MOTIONSlide2
Projectile Examples
Tennis ball
Golf ballFootballSoftballSoccer ballBullet
Hockey puckBasketballVolleyballArrowShot putJavelin
These are all examples of things that are
projected
, then go off under the
influence of gravitySlide3
Not projectiles
Jet plane
RocketCar (unless it looses contact with ground)Slide4
The key to understanding
projectile motion is to realize that gravity acts vertically
it affects only the vertical part of the motion, not thehorizontal part of the motionUnderstanding ProjectilesSlide5
Demonstration
We can see that the horizontal and vertical motions are independent
The red ball falls vertically
The yellow ball was given a kick to the right.They track each other vertically step for step and hit the ground at the same timeSlide6
In the absence of gravity a bullet
would follow a straight line forever.
With gravity it
FALLS AWAY
from
that straight line!
Projectile PathsSlide7
Shoot the MonkeySlide8
Sample Problem
A zookeeper finds an escaped monkey hanging from a light pole. Aiming her tranquilizer gun at the monkey, she kneels 10.0 m from the light
pole,which is 5.00 m high. The tip of her gun is 1.00 m above the ground. At the same moment that the monkey drops a banana, the zookeeper shoots.
If the dart travels at 50.0 m/s,will the dart hit the monkey, the banana, or neither one?Slide9
1 . Select a coordinate system.
The
positive y-axis points up, and the positive x-axis points along the ground toward the pole. Because the dart leaves the gun at a height of 1.00 m, the vertical distance is 4.00 m.
Sample ProblemSlide10
2 . Use the inverse tangent function to find the angle that the initial velocity makes with the
x
-axis.
Sample ProblemSlide11
3 . Choose a kinematic equation to solve for time.
Rearrange the equation for motion along the
x-axis to isolate the unknown Dt, which is the time the dart takes to travel the horizontal distance.
Sample ProblemSlide12
4 . Find out how far each object will fall during this time.
Use the free-fall kinematic equation in both cases.
For the banana,
vi = 0. Thus:
D
y
b
=
½
a
y
(
D
t
)
2
=
½(–9.81 m/s2)(0.215 s)2 = –0.227 m
Sample ProblemSlide13
The dart has an initial vertical component of velocity equal to
v
i sin q
, so:Dyd = (v
i
sin
q
)(
D
t
) +
½
a
y
(
D
t
)2
Dyd
= (50.0 m/s)(sin 21.8)(0.215 s) +
½(–9.81 m/s2)(0.215 s)2
Dyd = 3.99 m – 0.227 m = 3.76 m
Sample ProblemSlide14
5 . Analyze the results.
Find the final height of both the banana and the dart.
ybanana
, f
=
y
b,i
+
D
y
b
= 5.00 m + (–0.227 m)
y
banana
,
f = 4.77 m above the ground
Sample ProblemSlide15
The dart hits the banana.
The slight difference is due to rounding.
y
dart
, f
=
y
d,i
+
D
y
d
= 1.00 m + 3.76 m
y
dart
, f
= 4.76 m above the ground
Sample ProblemSlide16
No gravity is good for kickersSlide17
Newton’s First Law of Motion
“Every object continues in its state of rest, or of uniform motion in a straight line, unless it is compelled to change that state of motion by forces impressed upon it ”
The tendency of matter to maintain its state of motion is known as INERTIA. Slide18
Basketball – without gravitySlide19
Hitting the target – aim high, not directly at the target
BULLSEYE!Slide20
Path of the Projectile
v
Distance downfield
(range)
Height
rising
falling
projectile
g
Horizontal velocity
Vertical
velocity
vSlide21
Horizontal MotionSlide22
Vertical MotionSlide23
Projectile motion – key points
The projectile has both a vertical and horizontal component of velocity
The only force acting on the projectile once it is shot is gravity (neglecting air resistance)At all times the acceleration of the projectile is g = 9.8 m/s2 downward
The horizontal velocity of the projectile does not change throughout the pathSlide24
Key points, continued
On the rising portion of the path gravity causes the vertical component of velocity to get smaller and smaller
At the very top of the path the vertical component of velocity is ZEROOn the falling portion of the path the vertical velocity increasesSlide25Slide26
More key points
If the projectile lands at the same elevation as its starting point it will have the same vertical SPEED as it began with
The time it takes to get to the top of its path is the same as the time to get from the top back to the ground.The range of the projectile (where it lands) depends on its initial speed and angle of elevationSlide27Slide28
A
2.00 m tall basketball player wants to make a basket from
a distance of 10.0 m. If he shoots the ball at a 450 angle, atwhat initial speed must he throw the ball so that it goes through the hoop without striking the backboard?
y
x
y
0
Sample ProblemSlide29
Equations
to Choose fromSlide30
Maximum Range
When an artillery shell is fired the initial speed of the projectile depends on the explosive charge – this cannot be changed
The only control you have is over the angle of elevation.You can control the range (where it lands) by changing the angle of elevationTo get maximum range set the angle to 45°Slide31
Interactive
http://galileo.phys.virginia.edu/classes/109N/more_stuff/Applets/ProjectileMotion/jarapplet.html
http://jersey.uoregon.edu/vlab/Cannon/Slide32
Imagine trying to
throw a rock around
the world. If you give it a large horizontal velocity,it will go into orbitaround the earth!
The ultimate
projectile: Orbit