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