# dx = v x t dy = v y t + ½ at 2 - PowerPoint PPT Presentation

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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 + ½ at 2

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## dx = vxtdy = vyt + ½ at2

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).

### 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

• 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

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

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

• 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

• 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

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….

• 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…