Dx v x t dy v y t at 2
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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 v x t dy v y t at 2

dx = vxtdy = vyt + ½ at2

Projectile Motion


Projectile

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).


Independence of horizontal and vertical motion

Independence of horizontal and vertical motion.

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


Projectile launched horizontally

Projectile Launched Horizontally

  • 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.


Projectiles launched horizontally

Projectiles Launched Horizontally

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)


Practice problem

PRACTICE PROBLEM

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?


Givens

Givens

  • vx= 15m/s

  • y = 44m

  • Vy = 0m/s

  • a = -9.8 m/s2

  • t = ?

  • x = ?

Formulasx = vxty = vyt + ½ at2


Dx v x t dy v y t at 2

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

Practice Problems

  • 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

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 problem1

PRACTICE PROBLEM

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?


Label maximum height maximum range and where time occurs

Label maximum height, maximum range and where ½ time occurs.


Mythbusters

Mythbusters….

  • 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…

  • http://www.youtube.com/watch?v=D9wQVIEdKh8


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