UNIT 2
Two Dimensional Motion
And Vectors
ConcepTest 3.4a
A small cart is rolling at
constant velocity on a flat
track. It fires a ball straight
up into the air as it moves.
After it is fired, what happens
to the ball?
Firing Balls I
1) it depends on how fast the cart is
moving
2) it falls behind the cart
3) it falls in front of the cart
4) it falls right back into the cart
5) it remains at rest
ConcepTest 3.4a
A small cart is rolling at
constant velocity on a flat
track. It fires a ball straight
up into the air as it moves.
After it is fired, what happens
to the ball?
In the frame of reference of
the cart, the ball only has a
vertical component of
velocity. So it goes up and
comes back down. To a
ground observer, both the
cart and the ball have the
same horizontal velocity,
so the ball still returns into
the cart.
Firing Balls I
1) it depends on how fast the cart is
moving
2) it falls behind the cart
3) it falls in front of the cart
4) it falls right back into the cart
5) it remains at rest
when
viewed from
train
when
viewed from
ground
Thursday/Friday September 22-23
Projectiles: Zero Launch Angle
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TODAY’S AGENDA
Thursday, September 22
 Projectile Motion
 Mini-Lesson: Zero Launch Angle
 Problem Quiz 1 Vectors
 Hw: Complete Practice C Problems (all)
UPCOMING…
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


Fri:
Mon:
Tues:
Wed:
More Zero Launch Angle
Projectile Motion @ any angle
LAB 3: Projectile Motion
Problem Quiz 2 Projectile Motion
Projectile Motion
Something is fired, thrown, shot, or hurled near
the earth’s surface.
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One Dimensional Projectile
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Two Dimensional Projectile
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Horizontal Component of Velocity
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Horizontal Component of Velocity
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Vertical Component of Velocity
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Horizontal and Vertical Motion
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Horizontal and Vertical Motion
Perpendicular
components of
motion are
independent of
each other.
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Launch Angle
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Launch Angle
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Zero Launch Angle
Vo
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Sample Problem
1) The Zambezi River flows over Victoria Falls in Africa. The falls
are approximately 108m high. If the river is following horizontally
at 3.60 m/s just before going over the falls, what is the final
velocity of the water when it hits the bottom? Assume the water
is in freefall as it drops.
Find the time of flight
Find the final vertical velocity
𝟏 𝟐
𝒚 = 𝒗𝒐 𝒕 − 𝒈𝒕
𝟐
𝒗𝒇𝒚 = 𝒗𝒊𝒚 − 𝒈𝒕
𝟏 𝟐
𝒚 = − 𝒈𝒕
𝟐
𝒗𝒇𝒚 = −𝒈𝒕
−𝟏𝟎𝟖 𝒎 = −(𝟒. 𝟗𝟏)𝒕𝟐
𝒕 = 𝟒. 𝟔𝟗 𝐬
𝒗𝒇𝒚 = (−𝟗. 𝟖𝟏)(𝟒. 𝟔𝟗𝒔)
𝒎
𝒗𝒇𝒚 = −𝟒𝟔. 𝟎
𝒔
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1) continued… Find the time of flight
Find the final vertical velocity
Ө
Final horizontal velocity
𝒗𝒇 =
𝟑. 𝟎𝟔𝟐 + (−𝟒𝟔. 𝟎𝟐 )
𝜽 = tan−𝟏
−𝟒𝟔. 𝟎
𝟑. 𝟔𝟎
𝒕 = 𝟒. 𝟔𝟗 𝐬
𝒎
𝒗𝒇𝒚 = −𝟒𝟔. 𝟎
𝒔
𝒎
𝒗𝒇𝒙 = 𝟑. 𝟔𝟎
𝒔
𝒎
𝒗𝒇 = −𝟒𝟔. 𝟏
𝒔
𝜽 = −𝟖𝟓. 𝟓°
𝒎
𝒗𝒇 = −𝟒𝟔. 𝟏
@ 𝟖𝟓. 𝟓° 𝒃𝒆𝒍𝒐𝒘 𝒕𝒉𝒆 (−𝒙) 𝒂𝒙𝒊𝒔
𝒔
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Sample Problem
2)
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Sample Problem
3)
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Sample Problem
4) A lunch pail is accidently kicked off a steel beam on a building
under construction. Suppose the initial horizontal speed is
1.50 m/s.
a) How far does the lunch pail fall after it travels 3.50 m
horizontally?
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Sample Problem
4) A lunch pail is accidently kicked off a steel beam on a building
under construction. Suppose the initial horizontal speed is
1.50 m/s.
b) If the building is 2.50 x 102 m tall, and the lunch pail is
knocked off the top floor, what will be the horizontal
displacement of the lunch pail when it reaches the ground?
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Sample Problem
4) A lunch pail is accidently kicked off a steel beam on a building
under construction. Suppose the initial horizontal speed is
1.50 m/s.
c) If the building is 2.50 x 102 m tall, and the lunch pail is knocked
off the top floor, what is the final velocity the lunch pail when
it reaches the ground?
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Sample Problem
5) The LZ N07 is a newly designed airship in the manner of the old
Zeppelin airships built in Germany between 1908 and 1940. This
airship can travel with a horizontal speed of 1.30 x 102 km/h.
If a parcel is dropped from this airship, so that it lands 135 m in
front of the spot over which it was released, how far above the
ground is the airship?
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Sample Problem
6) A squirrel on a limb near the top of the tree loses its grip on a nut,
so that the nut slips away horizontally at a speed of 10.0 cm/s.
If the nut lands at a horizontal distance of 18.6 cm, how high above
the ground is the squirrel?
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END
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