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Displacement

Displacement. Defining Position. Position has three properties: Origin, magnitude, direction. 1 dimension 12 feet above sea level. Origin: sea level Magnitude: 12 feet Direction: up. 2 dimensions 65 miles west of Chicago. Origin: downtown Chicago Magnitude: 65 miles Direction: west.

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Displacement

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  1. Displacement

  2. Defining Position • Position has three properties: • Origin, magnitude, direction • 1 dimension 12 feet above sea level. • Origin: sea level • Magnitude: 12 feet • Direction: up • 2 dimensions 65 miles west of Chicago. • Origin: downtown Chicago • Magnitude: 65 miles • Direction: west • 3 dimensions Range 200 m, bearing 270, at 30 altitude. • Origin: observer • Magnitude: 200 meters • Direction: 270 by the compass and 30 up.

  3. Position Graph • Position can be displayed on a graph. • The origin for position is the origin on the graph. • Axes are position coordinates. • The position is a vector. • A set of position points connected on a graph is a trajectory. trajectory y position vector x 2-dimensions (x, y)

  4. Scalar Multiplication • A vector can be multiplied by a scalar. • Change feet to meters. • Walk twice as far in the same direction. • Scalar multiplication multiplies each component by the same factor. • The result is a new vector, always parallel to the original vector.

  5. Reference Point • Displacement is different from position • Position is measured relative to an origin common to all points. • Displacement is measured relative to the object’s initial position. • The path (trajectory) doesn’t matter for displacement. trajectory displacement position origin

  6. Displacement Vector • The position vector is often designated by . • A change in a quantity is designated by Δ (delta). • Always take the final value and subtract the initial value. y x

  7. Two Displacements • A hiker starts at a point 2.0 km east of camp, then walks to a point 3.0 km northeast of camp. What is the displacement of the hiker? • Each individual displacement is a vector that can be represented by an arrow. 3.0 km 2.0 km

  8. Vector Subtraction • To subtract two vectors, place both at the same origin. • Start at the tip of the first and go to the tip of the second.

  9. Component Subtraction • Multiplying a vector by -1 will create an antiparallel vector of the same magnitude. • Vector subtraction is equivalent to scalar multiplication and addition.

  10. Displacement Components • Find the components of each vector, and subtract. • Ax = 2.0 km • Ay = 0.0 km • Bx = (3.0 km)cos45 = 2.1 km • By = (3.0 km)sin45 = 2.1 km • Dx = Bx – Ax = 0.1 km • Dy = By – Ay = 2.1 km next

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