• Take out physics supplies.
• Label a clean sheet “Projectiles”
• Make a line down the center to form 2 columns.
• On the right, list what you know about
projectiles.
• On the left, list what you think you know, or
your associations with projectiles.
Projectile Demo:
1. Sketch the path.
2. Does this example describe linear 1 dimensional
motion? Explain.
3. Is there any acceleration? Explain.
4. What force(s) are acting on the object?
5. Where during its flight is the velocity the slowest?
6. Where during its flight is the velocity the fastest?
Projectiles
objects move vertically & horizontally, 2
dimensional, at same time. The only force acting
on them is gravity!
They accelerate in the vertical direction.
They have constant forward velocity in the
(horizontal direction).
For projectiles launched horizontally – (no
initial vertical velocity) the projectile moves
forward & down at the same time.
The forward & vertical v are separate – they
occur independently.
The Resultant v is the vector sum of the
perpendicular X(horz) & Y(vector) vector
components.
Horizontal Launch Demo
• How does the launch velocity affect the
time in the air?
• Once launched it’s X (forward or horizontal)
v stays constant.
• What about the Y (vertical) component?
• The Y v is accelerated motion with a = g.
• The Y v increases as the object falls.
• What about as it rises?
German Project clip 4.5 min.
ting ting.
• https://www.youtube.com/watch?v=z24_ihi
kEqQ&list=PL3B2111CE2F7C797B
Demo Horz launch vs drop.
• Strobe position vs. Time 6 seconds.
• https://www.youtube.com/watch?v=z24_ihi
kEqQ&list=PL3B2111CE2F7C797B
Cannonballs
Shoot with no gravity, object
moves at const. v forever.
Trajectory with gravity. Object
drops as it falls.
Can solve 2 motion equations to find
resultant distance, velocity.
Resultant trajectory (path) =
parabola.
Launch w/ no vertical vi
V horiz stays const. Vvert starts at
zero & increases.
Hewitt 9 min with handout
• http://www.youtube.com/watch?v=e_L_vm
aCvxo&list=PLF062072FFCB1607F
Drop from plane no viy
vhoriz same as plane. Object stays
below plane as it falls.
Running off a cliff
A cannon fires a cannonball parallel to the
ground.
What factors control trip time for a
horizontal launch?
PHET Launch
http://phet.colorado.edu/sims/proj
ectile-motion/projectileDemo
motion_en.html
Height Only
For a horizontal launch the total trip
time is controlled by the launch height!
What variable is always the
same for horizontal and vertical
projectile motion?
The only
variable that
is always the
same in the
X and Y
direction is
the trip time!
Vocabulary
Projectile – object moving in 2 dimensions
with constant horizontal velocity and
accelerating vertically with gravity.
Trajectory – the path of the projectile.
Parabola – the shape of the trajectory.
Range – the horizontal distance traveled.
Worksheet.
• Link Intro Projectiles ~ 9 min.
• With Questions
•
Youtube: Project Horizontal launch
•
http://www.youtube.com/watch?v=e_L_vmaCvxo&feature=relmfu
Horizontal Launch Problems
Horizontal Launch v is constant
use
v = d/t.
Accl g in vertical. Use an
acceleration equation.
1. A cannonball is shot horizontally from a 125 m cliff. Its
horizontal velocity is 75 m/s.
List the known & unknown horizontal & vertical
variables.
How long was the cannonball in the air?
What was the range of the cannonball?
2. An airplane traveling parallel to the ground
at 100 m/s drops a package from 3000-m.
• Calculate the time to hit the ground.
• How far in front of the target must the
package be dropped?
• t = 25 s.
• d = 2500 m
3. A unicorn runs off a high diving board with a
horizontal velocity of 2.8 m/s and lands in
the water 7.3 meters in front of the board.
• How high is the
platform?
• 33 m
• Hwk MC packet and pg 102 Text
Do Now:
• For a projectile launched at a constant speed,
what variable(s) determine the total trip time?
height
• For a projectile launched at a constant speed,
what variable(s) determine how far forward
(range) the projectile will travel?
vx, trip time
Projectiles Launched at Angles
Resultant Velocity
The initial velocity is forward & up.
The velocity has a horizontal & vertical
component at every point - including the initial
launch velocity.
If we know vx &
vy, at a point, we
can calculate the
total resultant v,
from Pythagorean
v2 = vx2 + vy2.
Resolution of Resultant to Components
• Any 2-d vectors (velocity, force, etc) can be
described as the sum of perpendicular vectors
• v2 = vx2 + vy2.
• Often, instead of adding vector components to give
resultant, we take resultant & resolve it (break it )
into perpendicular components.
If plane takes off at an angle it has a forward and
upward velocity component like a projectile.
It is useful to break or “resolve” the velocity vector
into horizontal & vertical components.
Make a rough sketch of its velocity vector relative to
the ground.
Vector a can be broken down, or resolved
into 2 perpendicular components: ay & ax.
Ex 1: How fast must a car be moving to stay beneath a
plane taking off at 105 km/h at 25o to the ground?
• Need horizontal component of plane v.
• vx = v cos q.
• vx = 105 km/h cos 25 = 95 km/h
b. What is the vertical plane velocity from
the previous example?
• vy = v sin q
• 105 km/h sin 25o
• 44 km/h
Ex 2: The landing speed of the space shuttle is
99.7 m/s. If the shuttle is landing at an angle of
15o to the horizontal:
a. How fast is it descending?
b. What is its horizontal velocity?
• a. 25.8 m/s
• b. 96.3 m/s
Hwk pg Text pg 94 #2-7.
Finish Horz Projectile Prac Sheet.
Need
Rifle & Ammunition
• Bookbags between you & neighbors.
What assumptions can you
make??
Velocity Vectors
• V2 = vx2 + vy2
• viy ± 0.
• vx = Vcos q.
• viy = V sin q.
For projectiles launched at angles, the viy IS NOT zero.
The total resultant v is a combination of vx & vy.
Find vtot from V2 = vx2 + vy2 .
Given vtot we resolve the initial total v into X and Y
components.
vx = v cos q
viy = v sin q.
Other Assumptions needed.
•
•
•
•
•
•
vx = constant velocity v = d/t.
Vertical (Y) motion is accelerated a = g.
vy top = 0. This can be vf or vi.
t up = t down.
viy = - vfy. Same altitude.
vy up = vy down. Same altitude.
Ex: A cannonball is launched at a 30o angle with a
vertical velocity of 20 m/s and a horizontal velocity
of 80 m/s.
•
Make a rough vector sketch of the cannonball.
• Calculate its initial resultant velocity.
• Calculate the time to reach the high point in its
trajectory.
• If it lands at the same height as it was launched,
calculate its horizontal range.
1. A cannonball is launched at a 55o angle to the horizontal at
a velocity of 150 m/s. It lands at the same height from
which it was fired.
Make a sketch of path of the cannonball and on your
sketch make vector arrows to show the horizontal and
vertical velocity, and acceleration at 3 different points.
Find the initial horizontal & vertical velocity.
Find the maximum height.
Find the total time of the trip.
How far horizontally did it travel? (range).
• viy = 150 m/s (sin 55) = 123 m/s
• vx = 150 m/s (cos 55) = 86 m/s
• Max height vf2 = vi2 + 2ad
• 771 m= h.
• Tot trip time t = Dv/a
• (123m/s) - (- 123 m/s) /-9.81 m/s2.
• 25 s.
• 2156 m.
Finish Projectiles the Sequel
• Film Mechanical Universe “Falling Bodies”
Hewitt Angle Projectile Launch
http://www.youtube.com/watch?v=H-Y4PcV_mto
Hanging Monkey Problem
Hwk Rev Book pg 37 “Try It” Prb AND
Text pg 114 #26, 28, and pg 117 #58a.