Transcript Projectile Motion

Demo
• Horizontally launched ball vs dropped ball
• Which one hits the ground first?
• Laserdisk side B chp 11 & 14
At only 5’7”, he won the
1986 NBA Slam Dunk
Championship where he
defeated many highflying artists that were
more than a foot taller
than him, including
Dominique Wilkins.
In Fact:
Spud Webb holds the
vertical jump world
record at an amazing
1.25 m.
So just how much
“hang time” did he get?
∆y = ½at2
g
t = √2∆y = √2(-1.25)
g
- 9.8
= .50 s
double it
1 second record hang time
Okay, that’s
great… but
Jordan had a
running start!
Hang time depends only on the jumper’s
vertical speed at launch… not horizontal.
Horizontal speed remains constant but
vertical speed undergoes acceleration.
Projectile Motion
Parabolic path
Range (Dx): the horizontal
distance a projectile travels
Height (Dy): the
vertical distance a
projectile travels.
• Read directions and answer 1-5 on
page 83
• Then, Do 1-3 on page 84
• Finish Lab with collection of data and
answer # 2
1.
FBD: ball on table
FBD: ball in trajectory
FN
a
a=0
Fg
Fg
Example
The Basics
Horizontal
SFnety = Fg
ma = mg = -9.8 m/s2
therefore, a = -9.8 m/s2
• Viy = Vfy ; (velocity is changing)
• Use the 3 kinematic equations
•
•
 SFx = Fnet x = 0
 a = 0 m/s2
 From the kinematic
equations, we get
 Vix = Vfx,
Vertical
constant
horizontal velocity
 Therefore, Dx = vixt
• time (ty)
Remember
FBD: Freefall
• time (tx)
a
Fg
The Formulas
Horizontal
Vertical
0
Dx= ½ at2+vixt
• so, Dx = vixt
Remember….. 0
• vfx = vix + axt
0
2
2
• vfx = vix + 2axDx
These last two equations do not
help in finding new unknowns.
• Dy = ½ at2+viyt
• vfy = viy + ayt
• vfy2 = viy 2 + 2ayDy
Here’s how to get the answer
• Picture
• Vertically
• Given
• Viy = ?, Dy = ?
• Unknowns • ay = -9.8m/s2
• Dy = 1/2 at2+viyt
• vf = vi + ayt
Dy
• vf2 = vi 2 + 2ayDy
• Horizontally
• Vix = ?, Dx = ?
• ax = 0
• Dx = vixt
•
•
•
Dx
•
First draw a diagram.
Write out your givens.
First solve for the horizontal. You know that
a in the horizontal Is 0. And that the
change in x=Vit. And that means 9.05=Vit.
We need t so let’s see if we can find it in the
vertical.
You know that a in the vertical is -9.8 and
that the Vi=0. Also change in y is equal to
.5at^2+Vit. So plug that in and you get
-1=.5(-9.8)t^2 + (0)t
So you solve for t and you get t=.452. Then
you have t so you can solve for the
horizontal vi and you get 19.9m/s. Easy!
Warm-up
• In the absence of air resistance, why does
the horizontal component of velocity for a
projectile remain constant, and why does
only the vertical component change?
• Now design a lab to determine the initial
velocity of a tennis ball shot horizontally
from a toy cannon.
FLAT TRAJECTORY
• A bullet shot from a very high velocity
rifle may travel one hundred feet or
more without dropping at all.
A) true
B) false
Explain.
THE DROPPING BULLET
• At the same time that a
high-speed bullet is
fired horizontally from
a rifle, another bullet is
simply dropped from
a) The dropped bullet
the same height.
b) The fired bullet
Which bullet strikes
c) Both strike at the same time
the ground first?
Explain.
Some more fun problems
A dodge ball is
kicked horizontally
at 10 m/s off a 20 m
cliff.
Find:
a) The time it takes for it
to hit the ground.
b) How far from the cliff it
lands.
t = 2.02 s; Δx = 20.2 m
Remember……..
• Picture
• Vertically
• Given
• Viy = ?, Dy = ?
• Unknowns • ay = -9.8m/s2
• Dy = 1/2 at2+viyt
• vf = vi + ayt
Dy
• vf2 = vi 2 + 2ayDy
• Horizontally
• Vix = ?, Dx = ?
• ax = 0
• Dx = vixt
•
•
•
Dx
•
First draw a diagram.
Write out your givens.
First solve for the horizontal. You know that
a in the horizontal Is 0. And that the
change in x=Vit. And that means 9.05=Vit.
We need t so let’s see if we can find it in the
vertical.
You know that a in the vertical is -9.8 and
that the Vi=0. Also change in y is equal to
.5at^2+Vit. So plug that in and you get
-1=.5(-9.8)t^2 + (0)t
So you solve for t and you get t=.452. Then
you have t so you can solve for the
horizontal vi and you get 19.9m/s. Easy!
Projectile Practice
1. A marble is fired via sling shot at a barn
wall 15 m away. The glass spheroid
travels with an initial horizontal
velocity of 33 m/s.
A. How long does it take to reach the barn?
B. How far has it dropped vertically when it
strikes the wall?
t = .4545 s; Δy = -1.01 m
Check this out:
Vfy
VR
Vfx
How can I find out how fast the object is
going when it hits the ground? Or what
angle the object strikes the ground?
You Try!!!
2. Freddie Frog takes a
swan dive from a 13meter board. He leaves
the board at 6.5m/s. If
his initial velocity is
horizontal, at what angle
and at what speed does
Freddie hit the water.
Answer: vf = 17.23 m/s @ 67.84° below the horizontal
Launched Horizontally
Viy = 0 m/s
Launched at an Angle
Viy ≠ 0 m/s
Projectiles-launched at an angle
More fun problems
• A cannon shoots a ball upwards at an angle of 30
degrees from the horizontal. If the Vi is 100 m/s.
a) Find the horizontal vix
*Assume ball
b) the vertical viy
was launched
c) the time
at ground level
d) the ∆x
30º
t = 10.204 s; Δx = 883.7 m
The Answer
• Since the Vi is 100, and the angle is 30°, then the
vertical Vi is 100sin30 and the horizontal Vi is 100cos30.
• Solving for horizontal. You know that the Δx is equal to
Vit. We need t to solve this, so let’s come back to it later.
• Solving for vertical. We know that the Δy is equal to
0.5at2+Vit. So plug the numbers and we get the Δy is
equal to 0.5(-9.8)t2 + 100sin30t. We also know the Δy is
0 because the ball lands where it starts. Factor out a t,
and then solve for it and you get t=10.2 seconds.
• Now we have t so we can get the horizontal
displacement which turns out to be 100cos30*10.2 which
is 883.35 meters.
Critical Thinking
A zoo keeper invents a canon to
shoot bananas to a monkey who
is too shy to come down from
the trees and eat.
If the monkey does not move, should
the zoo keeper aim at, above,
or below the monkey?
If there was no gravity the zoo keeper could
aim right at the monkey…
but in real life there
is gravity so the zoo
keeper should aim
above the monkey!
If the monkey lets go of the branch at
the instant the zoo keeper shoots the
banana, should the zoo keeper aim at,
above, or below the monkey to get the
monkey the banana in mid-air?
If he aims above the
monkey… whoops!
He should aim at
the monkey…
anyone know why?
The Answer:
Because of gravity, the banana (like any
projectile) will fall below this direct straight
line. How far below? As far as the monkey
falls in the same amount of time. So the
monkey and the banana will fall the same
vertical distance in the same time, and midair contact is made.
But doesn’t it matter
how hard he shoots
the banana?
Nope, they’ll
still meet in
mid-air just at
different
vertical
positions
high-speed
shot
medium-speed
shot
low-speed
shot
Steph hits a volleyball straight up from a
height of 0.80 m with an initial velocity of
+7.5 m/s.
a)How high will the volleyball go?
b)How long will it take for the volleyball to
reach its maximum height?
Spud was yelling at his friend when
suddenly his gum flew horizontally out of
his mouth. If his mouth was 1.6 m above
the ground and the gum flew a distance of
8 m,
a) determine the initial velocity of the gum
A football is kicked off a tee at an
angle of 40° to the horizontal with a
velocity of 3 m/s.
a)Determine the time the football is in
the air
b)Determine the range the football
travels.
3. An arrow is shot at an angle and
hits a target 20 m away and is in
the air for 2.5 seconds.
a. Find the initial velocity of the
arrow.
b. Find the maximum height of the
arrow.
Assume ∆y = 0
Vi 14.63 m/s @ 56.8º above horizontal , Δy = 7.66 m
Projectile Warm up
A Football player is trying to kick a field goal
from 35 meters out. If he kicks at an angle of
40 degrees, what initial velocity must be given
to the ball? The goalpost is 3 meters high.
19.69 m/s
Freefall/Projectile Quiz