UNIT 2
Two Dimensional Motion
And Vectors
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ConcepTest 3.6c
A projectile is launched
from the ground at an
angle of 30o. At what
point in its trajectory does
this projectile have the
least speed?
Dropping the Ball III
1) just after it is launched
2) at the highest point in its flight
3) just before it hits the ground
4) halfway between the ground and
the highest point
5) speed is always constant
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ConcepTest 3.6c
A projectile is launched from
the ground at an angle of
30o. At what point in its
trajectory does this projectile
have the least speed?
Dropping the Ball III
1) just after it is launched
2) at the highest point in its flight
3) just before it hits the ground
4) halfway between the ground and
the highest point
5) speed is always constant
The speed is smallest at
the highest point of its
flight path because the ycomponent of the velocity
is zero.
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ConcepTest 3.10a
Shoot the Monkey I
You are trying to hit a friend with a
water balloon. He is sitting in the
window of his dorm room directly
across the street. You aim straight
at him and shoot. Just when you
shoot, he falls out of the window!
Does the water balloon hit him?
1) yes, it hits
2) maybe – it depends on
the speed of the shot
3) no, it misses
4) the shot is impossible
5) not really sure
Assume that the shot does have
enough speed to reach the dorm4
across the street.
ConcepTest 3.10a
Shoot the Monkey I
You are trying to hit a friend with a
water balloon. He is sitting in the
window of his dorm room directly
across the street. You aim straight
at him and shoot. Just when you
shoot, he falls out of the window!
Does the water balloon hit him?
Your friend falls under the
influence of gravity, just like the
water balloon. Thus, they are
both undergoing free fall in the
y-direction. Since the slingshot
was accurately aimed at the
right height, the water balloon
will fall exactly as your friend
does, and it will hit him!!
1) yes, it hits
2) maybe – it depends on
the speed of the shot
3) no, it misses
4) the shot is impossible
5) not really sure
Assume that the shot does have
enough speed to reach the dorm5
across the street.
ConcepTest 3.10b
Shoot the Monkey II
You’re on the street, trying to hit a
friend with a water balloon. He sits
in his dorm room window above
your position. You aim straight at
him and shoot. Just when you
shoot, he falls out of the window!
Does the water balloon hit him??
1) yes, it hits
2) maybe – it depends on
the speed of the shot
3) the shot is impossible
4) no, it misses
5) not really sure
Assume that the shot does
have enough speed to6reach
the dorm across the street.
ConcepTest 3.10b
Shoot the Monkey II
You’re on the street, trying to hit a
friend with a water balloon. He sits
in his dorm room window above
your position. You aim straight at
him and shoot. Just when you
shoot, he falls out of the window!
Does the water balloon hit him??
This is really the same
situation as before!! The only
change is that the initial
velocity of the water balloon
now has a y-component as
well. But both your friend and
the water balloon still fall with
the same acceleration -- g !!
1) yes, it hits
2) maybe – it depends on
the speed of the shot
3) the shot is impossible
4) no, it misses
5) not really sure
Assume that the shot does
have enough speed to7reach
the dorm across the street.
Thursday September 29
Projectiles: Launch At Any Angle
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TODAY’S AGENDA
Thursday, September 29
 Projectile Motion
 Mini-Lesson: Launch At Any Angle
 Hw: Complete Projectile Motion Worksheet p15
UPCOMING…
 Thurs: More Projectile Motion
Problems @ the Boards
 Fri:
Problem Quiz 2 Projectile Motion
 Access to Reading Quizzes ENDS @ 11:30pm
 Mon: Problems @ the Boards
 Tues: CH 3 TEST
 Wed: Lab 3 Report Due
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Demonstration with Dr. Walter Lewin
Two Dimensional Cannon on Cart
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Projectile Motion Equations
Horizontal
Velocity
Eq 1
Vertical
Velocity
Eq 2
Eq 3
Horizontal
Displacement
Eq 4
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Projectile Motion Equations
Vertical
Displacement
Eq 5
Range
Eq 6
Time to
the Top
Eq 7
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Solving Projectile Motion Outline
1) If vi is launched at an angle, break the vi into x- and y- components.
2) If vi is launched at 0° angle, go to step 3.
3) If time of flight is not given, solve for time first.
4) Considering the given information, decide which component
equations (x or y) can best solve for time of flight.
5) If the variable you are solving for is in the y-direction, use
only the y-component equations. If the variable you are solving
for is in the x-direction, use only the x-component equations.
6) Finally, if the projectile begins and ends at the same y-position, you
can use the Range equation for what you need.
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Sample Problem
A baseball is thrown with an initial speed of 15.0 m/s.
If the ball’s horizontal displacement is 17.6 m, at what angle
with respect to the ground is the ball pitched?
Ө = 25.1°
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Sample Problem
A football is kicked so that its initial speed is 23.1 m/s.
If the football reaches a maximum height of 16.9 m, at
what angle with respect to the ground is the ball kicked?
Ө = 52.0°
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Sample Problem
Jackie Joyner-Kersee’s record long jump is 7.49 m.
Suppose she ran 9.50 m/s to jump this horizontal distance.
At what angle above the horizontal did she jump?
Ө = 27.3°
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Sample Problem
A ball is thrown from a roof with a speed of 10.0 m/s and
an angle of 37.0° with respect to the horizontal.
What are the vertical and horizontal components of the
ball’s displacement 2.5 s after it is thrown?
Δx = 20 m
Δy = -16 m
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Sample Problem
A downed pilot fires a flare from a flare gun. The flare has
an initial speed of 250.0 m/s and is fired at an angle of
35.0° to the ground.
How long does it take for the flare to reach its maximum
altitude?
t = 15 s
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Sample Problem
In 1991, Doug Danger rode a motorcycle to jump a horizontal
distance of 76.5 m.
Find the maximum height of the jump if his angle with
respect to the ground at the beginning of the jump was 12.0°.
Δymax = 4.07 m
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Sample Problem
A scared kangaroo once cleared a fence by jumping with a
speed of 8.42 m/s at an angle of 55.2° with respect to the
ground.
If the jump lasted 1.40 s, how high was the fence?
What was the kangaroo’s horizontal displacement?
Δx = 6.73 m
Δy (fence) = 2.44 m
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Sample Problem
Measurements made in 1910 indicate that the common flea is
an impressive jumper, given its size. Assume that a flea’s
initial speed is 2.2 m/s, and that it leaps at an angle of 21°
with respect to the horizontal.
If the jump lasts 0.16 s, what is the magnitude of the flea’s
horizontal displacement?
How high does the flea jump?
Δx = 0.33 m
Δy = 0.032 m
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END
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