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Projectile Motion Chapter 3

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Vector and Scalar Quantities Vector Quantity – Requires both magnitude and direction Velocity and Acceleration = vector quantities Thrown Baseball Scalar Quantity – Requires magnitude only Scalars can be added, subtracted, multiplied and divided like normal numbers

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Velocity Vectors An arrow is used to represent magnitude and direction of a vector quantity These arrows may be combined (as in combining two or more velocities) These are very useful when we get an object (airplane) moving a certain velocity and another (wind) moving at a different velocity

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Velocity Vectors Should be drawn to scale Must meet head to tow. Draw examples Cars, planes, arrows

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Vector Addition

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Vectors in other Directions When the vectors are not in the same direction, there are a few ways to figure out the resulting velocity. The easiest way is to box the two vectors and use the Pythagorean theorem For a perfect square, the hypotenuse is the square root of 2.

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Vector Addition The hypotenuse, or line drawn between the two vectors, is called the resultant Any vector can be broken down into its parts

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Vector Components

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Try These An airplane is moving North at a velocity of 80 km/hr and there is a wind blowing West at 60 km/hr. What is the resulting velocity? A motor boat traveling 4 m/s, East encounters a current traveling 3.0 m/s, North. What is the resultant velocity of the motor boat? If the width of the river is 80 meters wide, then how much time does it take the boat to travel shore to shore? What distance downstream does the boat reach the opposite shore?

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Try These A motor boat traveling 15 m/s, East encounters a current traveling 8.0 m/s, North. What is the resultant velocity of the motor boat? If the width of the river is 450 meters wide, then how much time does it take the boat to travel shore to shore? What distance downstream does the boat reach the opposite shore?

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Now Try These In your book, page 40, 1-6, 19- 26, and 29-34.

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Projectile Motion What is a projectile? – Throw ball Projectiles near the surface of Earth follow a curved path This path is relatively simple when viewed from its horizontal and vertical component separately The vertical component is like the free fall motion we already covered The horizontal component is completely independent of the vertical component (roll ball) These two independent variables combined make a curved path!

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Projectile Motion

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No GravityWith Gravity

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Projectile Motion

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Horizontally Launched Projectile (initial speed (vx) = 25 m//s) Time Horizontal Displacement (x) 0s0m 1s25m 2s50m 3s75m 4s100m 5s125m Tsv xt Vertical Displacement (y) 0m 25m 50m 75m 100m 125m ½ gt 2

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Horizontally Launched Projectiles What will hit the ground first, a projectile launched horizontally, a projectile dropped straight down, or a project fired up?

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The Plane and the Package

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Upwardly Launched Projectiles Toss a projectile into the air at some angle; without gravity, the projectile would keep moving further away in a straight-line path Instead, the projectile is found directly below that point (d = 5t² to be exact) as if it had been dropped from there for that many seconds. Remember that there is no horizontal acceleration, so the projectile always moves equal horizontal distances in equal times The projectile always lands at the same angle that it was released at

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Upwardly Launched Projectiles Draw cannonball, with parabolic arc and straight line (without gravity). The cannonball would move in a straight line with constant speed, and under every second would be the cannonball, a distance of 5t 2

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Upwardly Launched Projectiles Draw the cannonball with vectors, noticing that the horizontal component stays in the same direction. At the top, the vertical component approaches zero.

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Upwardly Launched Projectiles We have been assuming that the angle of launch has been 45’ What if the angle was other than that? Assuming no air resistance, all would be perfect parabolas with different heights and different distances traveled Angles fired at complements of 90’ will travel the same distance, but different heights

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Upwardly Launched Projectiles This is all considered without air resistance, which results in a significantly shorter parabola. Without air resistance, 45’ makes for the farthest flying object.

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Upwardly Launched Projectiles

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Baseball A boy throws a baseball from a height of 5m. It travels 20 m. How fast did he throw the ball?

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Truck and Ball Imagine a pickup truck moving with a constant speed along a city street. In the course of its motion, a ball is projected straight upwards by a launcher located in the bed of the truck. Imagine as well that the ball does not encounter a significant amount of air resistance. What will be the path of the ball and where will it be located with respect to the pickup truck?

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Fast-Moving Projectiles—Satellites What if a ball were thrown so fast that the curvature of Earth came into play? If the ball was thrown fast enough to exactly match the curvature of Earth, it would go into orbit Satellite – a projectile moving fast enough to fall around Earth rather than into it (v = 8 km/s, or 18,000 mi/h) Due to air resistance, we launch our satellites into higher orbits so they will not burn up

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Satellites Launch Speed less than 8000 m/s Projectile falls to Earth Launch Speed less than 8000 m/s Projectile falls to Earth Launch Speed equal to 8000 m/s Projectile orbits Earth - Circular Path Launch Speed greater than 8000 m/s Projectile orbits Earth - Elliptical Path

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Now Try These In your book Page 40, numbers 8-18, 27-28, and 34-46.

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