Transcript Projectile Motion - My Teacher Pages

QOD
• The Royal Gorge Bridge in Colorado rises
321 m above the Arkansas River.
Suppose you kick a rock horizontally off
the bridge. The rock hits the water such
that the magnitude of its horizontal
displacement is 45.0 m. Find the speed at
which the rock was kicked.
What is Projectile
Motion?
Example
• Every March, the swallows return to San Juan
Capistrano, California after their winter in the
south. If the swallows fly due north and cover
200 km on the first day, 300 km on the second
day, and 250 km on the third day, draw a vector
diagram of their of their trip and find their total
displacement for the three-day journey.
Example
• Suppose a car pulling forward with a force
of 20,000 N was pulled back by a rope that
Joe held in his teeth. Joe pulled the car
with a force of 25,000 N. Draw a vector
diagram of the situation and find the
resultant force.
Projectiles
• Any object that moves through the air or
space, acted on only by gravity
– Near Earth, follow a curved path
– Can be broken down into two components.
• Vertical
• Horizontal
Horizontal
Component
• Like horizontal motion of a ball rolling
freely on a level surface
• Friction is negligible, rolling ball moves at a
constant velocity
• Ball covers = distance in = time intervals
• If no horizontal force acts on the ball, there
is not horizontal acceleration
• Same is true for projectiles.
“When no horizontal force acts on a
projectile, the horizontal velocity remains
constant.”
Example
• If New York Yankee, Mark Texeria hits a
baseball due west with a speed of 50.0
m/s, and the ball encountered a wind that
blew it north at 5.00 m/s, what was the
resultant velocity of the baseball?
Example
• The Maton family begins a vacation trip by
driving 700 km west. Then the family
drives 600 km south, 300 km east, and 400
km north. Where will the Matons end up in
the relation to their starting point. Solve
graphically.
Example
• Ralph is mowing the backyard with a push
mower that he pushes downward with a
force of 20.0 N at an angle of 30.0o to the
horizontal. What are the horizontal and
vertical components of the force exerted by
Ralph
Homework
1.
2.
3.
4.
Some Antarctic explorers heading due south toward the pole travel 50.
km during the first day. A sudden snow storm slows their progress and
they move only 30. km on the second day. With plenty of rest they travel
the final 65 km the last day and reach the pole. What was the explorers’
displacement?
Erica and Tony are out fishing on the lake on a hot summer day when
they both decide to go for a swim. Erica dives off the front of the boat
with a force of 45 N, while Tony dives off the back with a force of 60. N.
a) Draw a vector diagram of the situation. b) Find the resultant force on
the boat.
Derek pulls a horses’ bridle from the front with a force of 200.N and Dan
pushes the horse from behind with a force of 300. N. a) Draw a vector
diagram of the situation. b) What is the resultant force on the horse?
Shareen finds that when she drives her motorboat upstream she can
travel with a speed of only 8 m/s, while she moves with a speed of 12
m/s when she heads downstream. What is the current of the river?
Homework (con’t)
5.
6.
Amit flies due east from San Francisco to Washington, D.C., a
displacement of 5600. km. He then flies from Washington to
Boston, a displacement of 900. km at an angle of 55.0o east of
north. What is Amit’s total displacement?
Marcie shovels snow after a storm by exerting a force of 30.0 N on
her shovel at an angle of 60.0o to the vertical. What are the
horizontal and vertical components of the force exerted by Marcie?
Vertical Component
•
•
•
•
•
Resembles that of free falling objects.
Force due to gravity in vertical direction
Projectile accelerated downwards
Velocity changes with time v = at
Increased speed in vertical direction
causes greater distance to be covered with
each successive time interval
• Horizontal Component TOTALLY
independent from vertical component.
• Combined effects generate the curved
paths projectiles follow.
Horizontal + Vertical = Curved Path
Types of Projectile
Motion
• Horizontal
– Motion of a ball rolling freely along a
level surface
– Horizontal velocity is ALWAYS
constant
• Vertical
– Motion of a freely falling object
– Force due to gravity
– Vertical component of velocity
changes with time
• Parabolic
– Path traced by an object accelerating
only in the vertical direction while
moving at constant horizontal velocity
Simultaneous Balls
Dropped
• One ball launched
horizontally
• One ball simply
dropped
• Analyze the path by
considering
horizontal and
vertical components
separately
Horizontal
• Ball moves same horizontal distance in =
time intervals
• Happens because no horizontal
component of force acts on it.
• The balls horizontal component of motion
remains the same
Vertical
• Ball’s vertical
component of motion
remains the same
• Both balls fall the same
vertical distance in the
same time
 Vertical distance
fallen has nothing to
do with horizontal
component of
acceleration
 Downward motion of
horizontally
projected balls is the
same as free fall
Examples of Projectile
Motion
• Launching a Cannon ball
QOD
• A hiker walks 25.5 km from her base camp
at 35o south of east. On the second day,
she walks 41.0 km in a direction 65o north
of east, at which point she discovers a
forest ranger’s tower. Determine the
magnitude and direction of her resultant
displacement between the base camp and
the ranger’s tower.
Example
• In her physics lab, Melanie rolls a 10 g.
marble down a ramp and off the table with
a horizontal velocity of 1.2 m/s. The
marble falls in a cup placed 0.51m from the
table’s edge. How high is the table?
Example
• Bert is standing on a ladder picking apples
in his grandfather’s orchard. As he pulls
each apple off the tree, he tosses it into a
basket that sits on the ground 3.0 m below
at a horizontal distance of 2.0 m from Bert.
How fast must Bert throw the apples
(horizontal) in order for them to land in the
basket?
• Path traced by a projectile accelerating only
in the vertical direction while moving at
constant horizontal velocity is called a
parabola.
Upwardly Launched
Projectiles
• Cannonball follows
curved path and
hits the ground
because of gravity.
• If no gravity,
cannonball follows
a straight line path
shown by dotted
line.
Because of Gravity…
• Cannonball continually falls beneath
imaginary line until it hits ground
• Vertical distance it falls beneath any point
on dashed line is same vertical distance it
would fall if it dropped from rest and had
fallen for the same amount of time.
• Distance can be measured by d = ½ at2
• Since there is no horizontal acceleration,
the cannonball moves = horizontal
distances per time interval.
Example
• A famous human cannonball of the
Ringling Bros. and Barnum & Bailey
Circus, was fired out of a cannon with a
speed of 24.0 m/s at an angle of 40.0o to
the horizontal. If he landed in a net 56.5 m
away at the same height from which he
was fired, how long was he in the air?
Example
• On May 20, 1999, Robbie Knievel
successfully jumped 69.5 m over a Grand
Canyon gorge. Assuming that he started
and landed at the same level and was
airborne for 3.66 s, what height from his
starting point did he achieve?
QOD
• Abby Brown hates baseball, so she kicks a
soccer ball at an angle of 25.0o relative to
the ground at a speed of 23.0 m/s. If the
ball was stopped by the goalie 42.0 m
away, how long was it in the air? How high
was the tallest spot in the ball’s path?
Vectors
• Vectors represent
• Resultant velocity
both vertical and
vector represented by
horizontal
rectangle formed by
components for a
component parts.
projectile on a
• Velocity at top of path
parabolic path.
= horizontal
• Horizontal component
component because
always the same
vertical velocity is
zero
same magnitude/value
Factors Affecting
Projectile Motion
• What two factors would affect projectile
motion?
– Angle
– Initial velocity
Initial Velocity
Angle
Projectiles Shot at
Steeper Angles
• Initial velocity has greater vertical
component than when projectiles angle is
less
• Greater vertical component results in
higher path
• Horizontal component is less, therefore the
range is less
Things to Note
• Same range obtained
for two different
projectile angles –
angles that add up to
90 degrees.
• Thrown at 60
degrees, will land in
the same place as
object thrown at a 30
degree angle with
same speed.
• Smaller angle remains
in air for shorter
amount of time.
Air Resistance
• If air resistance is not negligible, range of
projectile is smaller and path is not a true
parabola.
• If there is no air resistance…
1)Projectile rises to maximum height in some time
in same time it takes to fall from height to ground.
2)Deceleration due to gravity going up =
acceleration due to gravity coming down
3)Object hits ground at the same speed it had
originally left ground
Fast Moving Objects
• If an object were
thrown so fast that is
clears the horizon, it
would then orbit the
Earth and become an
Earth Satellite.
• Earth Satellite –
projectile moving fast
enough to fall around
the earth rather than
into it.
Class Exercise
An object is fired from the ground at 100. meters per
second at an angle of 30.0o degrees with the
horizontal
Calculate the horizontal and vertical components
of the initial velocity
What is the maximum height achieved?
What is the maximum distance achieved?
After 2.00 seconds, how far has the object
traveled in the horizontal direction?
How high is the object at this point?
Solution
• Part a
 s cos 30   87 m s
 v sin   100 m sin 30   50 m
s
s
vix  vi cos   100 m
viy
• Part b
0
0
i
x
vix 
t

x  v x t  87 m
• Part c
y  viy t 
s
2.0s   174m
  



1
1
2
g t 2  50 m 2.0s   9.8 m 2 2.0s 
s
s
2
2
Applications
Any Ideas?
LAB TIME!!!