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Projectile Motion
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• Projectile- Object that is launched by a force and continues to move by its own inertia
• Trajectory- parabolic path of a projectile
• Projectile motion involves an object moving in 2D (horizontally and vertically) but only vertically is influenced by gravity.
• The X and Y components act independently from each other and will be separated in our calculations.
The equations for uniform acceleration, from unit one, can be written for either x or y variables: the kinematic equations
• If we push the ball harder, giving it a greater horizontal velocity as it rolls off the table, the ball would take _________ time to fall to the floor.
Horizontal and vertical movement is independent
• If we push the ball harder, giving it a greater horizontal velocity as it rolls off the table, the ball would:– Y axis: take the same time to fall to the floor. – X axis: It would just go further.
Horizontal and vertical movement is independent
• Horizontal uniform (no acceleration due to gravity) use this equation
• Vertical accelerated by gravity (use kinematic equations)
X and Y are independent
• X axis has uniform motion since gravity does not act upon it.
X and Y are Independent
• Y axis will be accelerated by gravity: 10 m/s2
• Combined, a projectile with voy = 0 follows this path.
• Wording that means Voy = 0• rolled of a table• thrown horizontally
Solving Simple Projectile Motion Problems• You will have only enough information to deal with the y
or x axis first
• You cannot use the Pythagorean theorem since X and Y-axes are independent
• Time will be the key: The time it took to fall is the same time the object traveled vertically.
• dx = (vx)(t) is the equation for the horizontal uniform motion.
• If you don’t have 2 of three x variable you will have to solve for t using gravity and the y axis
Equations Solving Simple Projectile Motion Problems
• Do not mix up y and x variables
• dy – height
• dx – range (displacement x)
For all projectile motion problems
• Draw a diagram• Separate the X and Y givens• Something is falling in these problems
X Givens Y Givens
dX = a = -10 m/s
vX = …t = …
…
Example Problem 1
• A stone is thrown horizontally at 7.50 /s from a cliff that is 68.4 m high. How far from the base of the cliff does the stone land?
Write out your x and y givens separately
• A stone is thrown horizontally at 7.50 /s from a cliff that is 68.4 m high. How far from the base of the cliff does the stone land?
X givens Y givens
• A stone is thrown horizontally at 7.50 m/s from a cliff that is 68.4 m high. How far from the base of the cliff does the stone land?
X givens Y givens