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Vectors and Projectile Motion

Vectors and Projectile Motion. Vectors and Scalars. Scalar: any type of quantity that only has an amount (magnitude) Ex. mass, volume, time, speed. Vectors and Scalars. Vector: any type of quantity that has both an amount (magnitude) and direction Ex. Velocity and Acceleration. Vectors.

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Vectors and Projectile Motion

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  1. Vectors and Projectile Motion

  2. Vectors and Scalars • Scalar: any type of quantity that only has an amount (magnitude) • Ex. mass, volume, time, speed

  3. Vectors and Scalars • Vector: any type of quantity that has both an amount (magnitude) and direction • Ex. Velocity and Acceleration

  4. Vectors • Any type of vector is represented by an arrow • The size of the arrow indicates the magnitude, and the way it is pointing indicates the direction

  5. Velocity Vectors Ex. 20 m/s east 30 m/s east

  6. Adding vectors • When two vectors act in the same direction on an object, they are added together • When two vectors act in opposite directions on an object, they are subtracted • When two or more vectors are combined, the final vector is called a resultant

  7. Adding vectors at angles • Suppose two vectors act on the same object at right angles to each other. How is the resultant obtained?

  8. Adding vectors at angles • Ex. A plane is flying at 80 km/hr to the north, and a wind is blowing 60 km/hr to the east. What is the planes resultant speed?

  9. Adding vectors at angles First, draw the two vectors head to tail. 60 km/hr east 80 km/hr north

  10. Adding vectors at angles Draw in the resultant: 60 km/hr east 80 km/hr north

  11. Adding vectors at angles Use the Pythagorean theorem to determine the size of the resultant: Resultant: 100 km/hr 80 km/hr north 60 km/hr east

  12. Components of vectors • Two vectors can be combined into one to find a resultant; the opposite can also be done, one vector can be split into two • These are known as component vectors; they make a right angle with each other

  13. Components of vectors Ex. A ball has a velocity of 20 km/hr northwest; what are the horizontal (west) and vertical (north) components of this velocity?

  14. Components of vectors First, draw out the original vector: 20km/hr northwest

  15. Components of vectors Next, draw out the two components: North component 20km/hr northwest West component

  16. Components of Vectors • How do you tell how big each component is? • Measure with a ruler (when drawn to scale) or use trig functions (sin, cos, tan) • A ruler will be easier, but trig functions will be more accurate

  17. Projectile Motion • Projectile motion: motion of objects (projectiles) as they move through the air (both horizontally and vertically) under the influence of gravity

  18. Projectile Motion • Horizontal motion of a projectile: • When friction is ignored, a projectile moves horizontally with constant velocity

  19. Projectile Motion • Vertical motion of a projectile: • When friction is ignored, a projectile moves vertically with constant acceleration

  20. Projectile Motion • When these two vectors are put together, they form the path of a projectile, which is parabolic in shape. Constant velocity Constant acceleration

  21. Projectiles launched at an angle • When an object is launched at an angle, it also follows a parabolic path (if air friction is ignored) • The distance that the projectile follows is determined by the angle at which it was launched • Horizontal velocity: stays the same • Vertical velocity: goes to zero, then increases

  22. Satellite motion • When an object moves fast enough horizontally so that its path matches the curve of the Earth, the object is said to be in orbit

  23. Keplers Laws of Planetary Motion • Johannes Kepler: 1571-1630 • Formulated three laws of planetary motion

  24. Keplers Laws of Planetary Motion • Based his ideas on data obtained from Tycho Brahe (Court Astronomer for King Frederick II of Denmark) • 20 years worth of data

  25. Keplers 1st law of planetary motion • The paths of all of the planets are ellipses, not circles, with sun at one focus of the ellipse

  26. Keplers 1st law of planetary motion • Most planetary orbits are fairly circular; if they are not perfectly circular, the orbit has a certain amount of eccentricity (off center) • Most eccentric orbits: Mars and Pluto

  27. Keplers 2nd law of planetary motion • An imaginary line from the sun to a planet (or from a planet to a moon) sweeps out equal areas in equal times.

  28. Keplers 2nd law of planetary motion • What equal areas in equal times means for planet movements: • When you are closer to the sun, you go faster • When you are farther from the sun, you go slower

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