Projectile Motion. Objects in projectile motion follow a parabolic path called a trajectory.
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Transcript of Projectile Motion. Objects in projectile motion follow a parabolic path called a trajectory.
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Projectile Motion
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Objects in projectile motion follow a parabolic path called a trajectory.
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If released at the same instant, a bullet shot from a gun will hit the ground at the same time as a bullet dropped from the same height.
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The horizontal and vertical motions of a projectile are independent, meaning they do not affect each other.
Horizontal motionVertical motion
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The 2-D motion of a projectile can be separated into two 1-D motions: horizontal and vertical.
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HPM: Horizontal Projectile Motion
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The horizontal motion of a projectile is always constant, if we neglect air resistance.
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For projectiles shot at 0°, all of the initial velocity is in the x direction. Thus, Vyi = 0 m/s.
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For projectiles shot at 0°, vertical displacement and velocity will always be negative.
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To hit the target, when should you release the package?
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Rules for Projectile Motion
• Treat horizontal and vertical as two separate sides of the problems
• TIMETIME 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
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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
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Example problem
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APM: Angled Projectile Motion
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For projectiles shot at an angle, initial velocity is both vertical and horizontal.
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Horizontal velocity and initial vertical velocity can be found using trig functions.
Vx = Vi Cos θ Vyi
Vx
Vi
θ Vyi = Vi Sin θ
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At the end of the problem, you can recombine horizontal and vertical velocity to get the total 2-D velocity.
Vx
Vyf
Vf
Vx
VyfVf
Vf2 = Vx
2 + Vyf2θ
θ = tan-1(Vyf / Vx)
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For APM, vy at any height is the same while going up and coming down except for direction.
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Velocities of projectile motion
Note: Vy = 0 at the highest point.
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With air resistance, the actual path is shorter.
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Angled 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
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Example ProblemExample ProblemHappy 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 = -9.81 m/s2
•∆x = ?
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vi = 55.0 m/s ay = -9.81 m/s2 ∆x = ?θ = 50.0°
• Find vx and vyi
vx = vi Cos θ = 55.0 m/s Cos (50.0°) = 35.4 m/s
vyi = vi Sin θ
= 55.0 m/s Sin (50.0°)
= 42.1 m/s
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vi = 55.0 m/s ay = -9.81 m/s2 ∆x = ?θ = 50.0° vyi = 42.1 m/s vx = 35.4 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
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vi = 55.0 m/s ay = -9.81 m/s2 ∆x = ?θ = 50.0° vyi = 42.1 m/s vx = 35.4 m/s∆t = 8.58 s
• Now we can find ∆x
• ∆x = vx ∆t
= (35.4 m/s)(8.58 s)
= 304 m
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Where Should We Aim the Cannon?Where Should We Aim the Cannon?
At or Above the monkey?
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Above the MonkeyAbove the Monkey
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At the MonkeyAt the Monkey
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Explanation of monkey experiment
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Ranges of projectiles versus angle.
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Another interesting application
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If speed is great enough…
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That’s how the space shuttle and satellites orbit the earth.