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Projectile motion

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**Examples: cannonballs when shot out of a cannon. **

PROJECTILE – any object that is launched into the air and continues to travel w/o any added input. The parabola shaped path is called the Trajectory Examples: cannonballs when shot out of a cannon. Bomb dropped from plane

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**Horizontally: Vertically:**

In order to get the arch, an object must move in 2 ways at the same time. Horizontally: Vertically: Even though both happen at the same time, we look at each direction separately.

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The Horizontal speed stays constant (it will not change through the whole trip because there is nothing to change it.) WHAT is the HORIZONTAL ACCELERATION? ______ Vertically the object behaves as if it were in free fall. The speed decreases evenly going up, stops and increases evenly down because of the force of gravity. WHAT IS THE ACCELERATION DOING? _____ WHICH WAY DOES IT POINT? _______

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When shot at an angle, The initial velocity vector (vo) will get broken down into its components you will use those components in the motion equations V0x = v0 cos θ V0y = V0 sin θ This is because some of the velocity is horizontal and some is vertical.

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**Use the motion equations in each direction**

Horizontal direction vx = v0x + axt vx2 = v0x2 + 2axd x = x0 + v0xt + ½ axt2 The time is the same for all equations. Vertical direction vy = v0y + gt vy2 = v0y2 + 2gd y= y0 +v0y t+ ½gt2

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**t = the time to go through the entire parabola**

(the time in flight) Use half of the time when finding the highest point because object has only gone through half of the path. The time to go up = the time to come down

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**Shot up and down Origin is at take off location**

For range (horizontal distance) use: R = (V0 2 sin 2θ) / g Use negative g (-9.8 m/s2) because go up then down Use components in the motion equations.

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**When projected off a cliff**

If projected off a cliff, choose the origin at the top where object is released. Use positive gravity (9.8 m/s2) because falling down x = the horizontal distance (range) Voy = 0 because not falling down until released.

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**In a case where the object lands lower than it takes off, the final height (y) is negative.**

Angles that add up to 90 degrees have the same range 45 degrees has the maximum range when you start and land at the same level.

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