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dx = v x t dy = v y t + ½ at 2. Projectile Motion. Projectile. Object given an initial velocity, that then moves only under the force of gravity. Trajectory. The path that a projectile traces. Parabolic (neglecting the effect of wind resistance).

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### dx = vxtdy = vyt + ½ at2

Projectile Motion

Object given an initial velocity, that then moves only under the force of gravity.

Trajectory

The path that a projectile traces. Parabolic (neglecting the effect of wind resistance).

Horizontal and Vertical components of motion are independent of one another, only when they act in concert do we get a true parabolic trajectory.

NOTE: ag = -9.8m/s2

• The horizontal and vertical components are added to form the velocity vector for the projectile.

• Combination of constant and horizontal acceleration produces a trajectory that has the shape of a parabola.

Begin

Acceleration in the x direction = 0

Constant velocity in the X direction

(note the constant size of the vector)

End

Acceleration in the Y direction = -9.8 m/s2

Increase velocity in the Y direction (note the increasing size of vectors)

A stone is thrown horizontally from the top of a cliff which is 44m high at a velocity of 15m/s.

a) How long does it take for the stone to reach the bottom of the cliff?

b) How far from the base of the cliff does the stone strike the ground?

• vx= 15m/s

• y = 44m

• Vy = 0m/s

• a = -9.8 m/s2

• t = ?

• x = ?

Formulasx = vxty = vyt + ½ at2

How fast is it moving at the instant before it hits the ground?Solve for vy, then use the Pythagorean Theorem

Vy = at

= (-9.8 m/s2)(3s)

Vy = -29 m/s

-29 m/s

vx2 + vy2 = v2

-292 + 152 = v2

841 + 225 = v2

1066 = v2

V = 33 m/s

15 m/s (given)

Practice Problems ground?

• A stone is thrown horizontally at a speed of 5 m/s from the top of a cliff 78.4 m high.

• How long does it take the stone to reach the bottom of the cliff?

• How far from the base of the cliff does the stone hit the ground?

What if it isn’t thrown horizontally? What if the object is thrown at an angle??

Vector

Decomposition!

*Break v up into vx and vy

vx= vcos

vy= vsin

PRACTICE PROBLEM is thrown at an angle??

A ball is thrown into the air with an initial velocity of 20m/s at an angle of 60º above the horizontal.

a) How long does the ball take to land?

b) How high did the ball fly?

c) What was its range?

Mythbusters…. occurs.

• If two identical objects are thrown and dropped at the same time, they will hit the ground at the same time.

• Don’t believe me? Maybe you’ll believe these guys…