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Understanding Projectile Motion Basics

Projectile motion describes the trajectory of objects thrown or projected into the air. It involves two types of motion: horizontal motion at a constant velocity, and vertical motion under constant acceleration due to gravity. The path of a projectile forms a parabolic curve. Projectile motion can be used to calculate values like maximum height, time of flight, landing point, and final velocity from initial velocity, launch angle, and other variables. Experiments use high-speed cameras to capture projectile motion trajectories.

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Xin Chen
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46 views11 pages

Understanding Projectile Motion Basics

Projectile motion describes the trajectory of objects thrown or projected into the air. It involves two types of motion: horizontal motion at a constant velocity, and vertical motion under constant acceleration due to gravity. The path of a projectile forms a parabolic curve. Projectile motion can be used to calculate values like maximum height, time of flight, landing point, and final velocity from initial velocity, launch angle, and other variables. Experiments use high-speed cameras to capture projectile motion trajectories.

Uploaded by

Xin Chen
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Projectile Motion

• Curve Motion
• Typical Example
Projectile Motion
“throw something off a cliff…”
Constant acceleration:
g (~10 𝑚/𝑠 2 , vertical, the acceleration due to
gravity near the Earth’s surface)
v0
 Certain initial velocity
 First, horizontal 𝑣0 v
(how about 𝑣0 = 0? ) g
g
Coordinate: 2D
• Horizontal
Constant velocity
(straight line)

• Vertical
Free-fall
Experiment

High-speed camera
Overlapped image
Coordinate: 2D
• Decompose
1 2
𝑥 = 𝑣0 𝑡 𝑦 = 𝑔𝑡
2
𝑣𝑥 = 𝑣0 𝑣𝑦 = 𝑔𝑡
• Compose
𝑔𝑡
𝑣𝑡 = 𝑣𝑥2 +𝑣𝑦2 = 𝑣02 + 𝑔2 𝑡 2 𝑡𝑎𝑛𝛽 =
𝑣0
Trajectory Function
• From:
1 2
𝑥 = 𝑣0 𝑡 𝑦 = 𝑔𝑡
2
• Substitute t:
𝑔 2
𝑦= 2𝑥
2𝑣0
 It’s a parabola!
Do they hit?

𝑣0 Free-fall

?
Application
Initial
velocity
(𝑣0 )
Height
(h)
Time
(t)
Maximum
Distance
(𝑥𝑚𝑎𝑥 )
Projectile Motion
𝑣𝑥 = 𝑣0 𝑐𝑜𝑠𝜃
• General 𝑣0
𝑣𝑦 = 𝑣0 𝑠𝑖𝑛𝜃 − 𝑔𝑡
(non-horizontal,
with angle θ) 𝑥 = 𝑣0 𝑡𝑐𝑜𝑠𝜃
1 2
𝑦 = 𝑣0 𝑡𝑠𝑖𝑛𝜃 − 𝑔𝑡
2
𝑣0
𝑣𝑦

𝜃
𝑣𝑥
Example

A ball is shot at a velocity 25 m/s from a


cannon pointed at an angle 𝜃 = 30° above
the horizontal. How far does it travel
before hitting the level ground?

Maximum height?
How long? Final velocity?
More Example
• A ball is thrown from the top of stairs with
𝑣0 = 2 𝑚/𝑠, horizontally. Each step is 0.2 m
high and 0.25 m wide. The question is, which
step will the ball first hit?
v0

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