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Projectile Motion Introduction Horizontal launch
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#1 A ball is dropped from a height of 125 m.
How long does it take the ball to strike the ground? What is the velocity of the ball at the ground? #2 A ball rolls at 15 m/s for 5 seconds. How far does the ball roll? INCLUDE A LIST OF GIVENS FOR EACH motion map
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Projectile motion Projectile – an object with only gravity
acting on it No air resistance (in our examples) No propellant After some initial condition (throwing, etc)
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Projectile motion vo Which ball hits the ground first?
A: dropped B: launched horizontally vo A B
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Projectile motion Perpendicular vectors are independent
They do not directly affect each other Break all 2-D motion into two separate vector components. Choose easy components that make sense
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Projectile motion Gravity pulls down (vertical vector),
so it has no effect on the horizontal vector ***This (vertical) should be a dimension that we analyze “Horizontal” would then be the other (┴)
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Projectile motion Acceleration in the vertical (y) direction will continue to be g = -10 m/s2 ay = m/s2 If air resistance is ignored, there is nothing changing the horizontal velocity* ax = 0 m/s2 vox = vx *This may change in future problems
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Constant acceleration
Projectile motion Horizontal (x) Constant velocity (ax = 0 m/s2) vox = vx Equation: Vertical (y) Constant acceleration (ay = -10 m/s2) Equation:
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Constant acceleration
Projectile motion Horizontal (x) Constant velocity (ax = 0 m/s2) vox = vx Equation: dx = d0x + vx·t Vertical (y) Constant acceleration (ay = -10 m/s2) Equation:
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Constant acceleration
Projectile motion Horizontal (x) Constant velocity (ax = 0 m/s2) vox = vx Equation: dx = d0x + vx·t Vertical (y) Constant acceleration (ay = -10 m/s2) Equation: dy = … vy = …
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Constant acceleration
Projectile motion Horizontal (x) Constant velocity (ax = 0 m/s2) vox = vx Equation: dx = d0x + vx·t Determines: ____ Vertical (y) Constant acceleration (ay = -10 m/s2) Equation: dy = … vy = … Determines: ___
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Constant acceleration
Projectile motion Horizontal (x) Constant velocity (ax = 0 m/s2) vox = vx Equation: dx = d0x + vx·t Determines: ____ Vertical (y) Constant acceleration (ay = -10 m/s2) Equation: dy = … vy = … Determines time
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Constant acceleration
Projectile motion Horizontal (x) Constant velocity (ax = 0 m/s2) vox = vx Equation: dx = d0x + vx·t Determines range Vertical (y) Constant acceleration (ay = -10 m/s2) Equation: dy = … vy = … Determines time
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A ball is rolled horizontally off a 125 meter ledge at a speed of 15 m/s.
What is the range of the ball? (How far will it go horizontally, dx) What is the velocity when it hits the ground? magnitude and direction (angle)
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Projectile Motion Horizontal launch – v0y = 0 m/s
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Projectile Motion Angled launch
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#1 A ball is thrown upward at 30 m/s from
an 80 meter cliff. How long does it take the ball to strike the ground? What is the velocity of the ball at the ground? #2 A ball rolls at 40 m/s for 8 seconds. How far does the ball roll?
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Projectile motion v0 v0 vx v0y
When starting with an angled velocity, show the velocity as a sum of perpendicular components horizontal (x), and vertical (y) v0 v0 vx v0y
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Projectile motion v0 v0y v0y vx vx
Remember, vectors can be moved around v0 vx v0y vx v0y
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A ball is launched off an 80 meter cliff.
The initial velocity of the ball is 50 m/s at an angle of 37º above horizontal. What is the range of the ball? What is the velocity when it hits the ground?
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Motion Map
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Motion Map
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Motion Map
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Projectile Motion Horizontal launch – v0y = 0 m/s Angled launch
Always find vx and voy first Never use the total/vector sum in equations Remember: vy = 0 m/s at max vx is constant position has two coordinates (dx, dy)
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