1. Projectile Motion
Horizontal
Angular

2. Rules for Projectile Motion
Treat horizontal and vertical as two separate sides of the problems
TIME is the key, and the only variable that can be used for both horizontal and vertical
Horizontal Motion is always constant
vx is constant
ax = 0 m/s2
Objects follow a parabolic shape
ay = g = m/s2

3. Horizontal Projectile Motion
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4. Horizontal Projectile Motion
All of the initial velocity is in the x direction, vyi = 0 m/s
Vertical displacement and velocity will always be negative

5. Interesting Applications
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6. Angular Projectile Motion
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7. Angular Projectile Motion
Initial velocity is both vertical and horizontal
Use trig functions to find vyi and vx
vx = vi Cos θ
vyi = vi Sin θ
Remember clues
vy at the top is 0 m/s
vy at any height is the same while going up and coming down except for direction
∆y = 0 m if ending at the same height as it started

8. Example Problem
Happy Gilmore hits his shot at 55.0 m/s with an angle of 50.0° to the ground. How far did the ball travel before it lands?
vi = 55.0 m/s
θ = 50.0°
ay = m/s2
∆y = 0 m
vyf = -vyi
∆x = ?

9. vi = 55.0 m/s ay = -9.81 m/s2 ∆x = ? θ = 50.0° ∆y = 0.0 m vyf = - vyi -
vi = 55.0 m/s ay = m/s2 ∆x = ? θ = 50.0° ∆y = 0.0 m vyf = - vyi
Find vx and vyi
vx = vi Cos θ
= 55.0 m/s Cos (50.0°)
= 55.0 m/s (0.643)
= 35.4 m/s
vyi = vi Sin θ
= 55.0 m/s Sin (50.0°)
= 55.0 m/s (0.766)
= 42.1 m/s

10. What do we need to find ∆x? Time! Find time from the vertical side -
vi = 55.0 m/s ay = m/s2 ∆x = ? θ = 50.0° ∆y = 0.0 m vx = 35.4 m/s vyf = m/s vyi = 42.1 m/s
What do we need to find ∆x?
Time! Find time from the vertical side
∆y = vyi ∆t + ½ ay ∆t2
0 m = (42.1 m/s) ∆t + ½ (-9.81 m/s2) ∆t2
- (42.1 m/s) ∆t = ½ (-9.81 m/s2) ∆t2
(42.1 m/s) = ½ (9.81 m/s2) ∆t
∆t = 8.58 s

11. Now we can find ∆x ∆x = vx ∆t = (35.4 m/s)(8.58 s) = 304 m - + -
vi = 55.0 m/s ay = m/s2 ∆x = ? θ = 50.0° ∆y = 0.0 m vx = 35.4 m/s ∆t = 8.58 s vyf = m/s vyi = 42.1 m/s
Now we can find ∆x
∆x = vx ∆t
= (35.4 m/s)(8.58 s)
= 304 m

12. Where Should We Aim the Cannon?
At or Above the monkey?
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13. Above the Monkey
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14. At the Monkey
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15. At the Monkey (Faster)
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