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Projectile Motion
Notes
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Projectile Motion
Definition
• Movement in 2 dimensions rather than 1
2 models
• Horizontal launch
• Kicking a stone off a bridge
• Angled launch
• Golf/base/football
• Artillery shell
• In both models, the only effect on the
projectile, after leaving the launch, is g↓
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Horizontal Launch
Basic premise
• In the absence of air
resistance…
• The objects are in
free fall!
• Both objects reach
the ground at the
same time
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Horizontal Launch
Analysis technique• Break the model down into vertical (y) and
horizontal (x) component columns• Vertical (y) ↓
• vo = 0 (drop model)
• g = 9.8 (always on Earth!)
• dy = height
• t = time to fall
• Horizontal (x) →
• dx = range
• vx = initial velocity in horizontal direction
• t = time to fall
vx
dy
dx
![Page 5: Projectile Motion - augusta.k12.va.us · Projectile Motion Vertical (y) Horizontal (x) g = 9.8 d x = range v o = 0 v x = initial velocity in x direction d y = height t = t = TOOL:](https://reader034.vdocument.in/reader034/viewer/2022052612/5f09c23b7e708231d4285fe4/html5/thumbnails/5.jpg)
Projectile Motion
Vertical (y) Horizontal (x)
g = 9.8 dx = range
vo = 0 vx = initial velocity in x direction
dy = height t =
t =
TOOL: dy = vot + ½ g t2 (iii) TOOL: dx = vx*t
vx
dy
dx
Identify the target parameter, and start in the opposite column.
ex. If vx (horizontal column) is requested, start solving in the
vertical column
Use the time (t) value as common to both axes – the time taken to
follow the parabolic path is the same as a simple drop!
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Ex. Horizontal
A baseball rolls off a 0.7 m high desk and
strikes the floor 0.25 m away from the base
of the desk.
How fast was it rolling?
vx
dy
dx
![Page 7: Projectile Motion - augusta.k12.va.us · Projectile Motion Vertical (y) Horizontal (x) g = 9.8 d x = range v o = 0 v x = initial velocity in x direction d y = height t = t = TOOL:](https://reader034.vdocument.in/reader034/viewer/2022052612/5f09c23b7e708231d4285fe4/html5/thumbnails/7.jpg)
Solution
1) vertical
• dy = vot + ½ g t2
• 0.7 = 0 + ½ (9.8) t2
• t = 0.38 seconds (use in the “other” column)
2) horizontal
• dx = vx*t
• 0.25 = vx* 0.38
• vx = 0.66 m/s
vx
dy
dx
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Practice
Your turn!
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What if the projectile is launched
at an angle to the horizontal?
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Angled Launch Projectile Motion
Definition
• The motion of the projectile is uniquely
defined by:
• Its launch angle (Ө) and
• its initial velocity (vo)
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Angled Launch Parameters
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Angled Launch
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Angled Launch – refer to sheet
Max Height:
• dymax = (V0 sin )2/2g
Range:
• d xmax= V02 sin (2 ) / g
Time to max height:
• t = (V0 sin )/g
Total time in air (hang time)
• (time up=time down)
• ttotal = 2 (V0 sin )/g
![Page 14: Projectile Motion - augusta.k12.va.us · Projectile Motion Vertical (y) Horizontal (x) g = 9.8 d x = range v o = 0 v x = initial velocity in x direction d y = height t = t = TOOL:](https://reader034.vdocument.in/reader034/viewer/2022052612/5f09c23b7e708231d4285fe4/html5/thumbnails/14.jpg)
Comparing Trajectories
Max range angle
Which angle provides the maximum down range (x) distance?
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Practice time
Your turn!