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Vectors and Projectile Motion: Concepts and Examples

This chapter provides an introduction to vectors, their properties, and how they can be added graphically and algebraically. It also covers the analysis of projectile motion and relative velocity. Examples are included to illustrate the concepts.

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Vectors and Projectile Motion: Concepts and Examples

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  1. Chapter 3 Vectors and Two-Dimensional Motion • Vectors and Scalars • Component of a Vector • Adding Vectors • 2D Motion • Projectile Motion • Relative Velocity

  2. Vector vs. Scalar Review • What is a vector? • Why do we need vectors? • What is a scalar? • How do I represent them?

  3. Properties of Vectors • Equality • Movement • Negative vectors • Resultant vectors • Multiplication and division by a scalar • Components of a vector • Adding vectors

  4. Adding Vectors • I learned addition in kindergarten, why am I learning it again in college? • Graphical method • Algebraic method

  5. Graphically Adding Vectors Head to tail rule Addition is commutative

  6. Components of a Vector • Ax • Ay • Magnitude A • Direction of A

  7. Example Adding Vectors Algebraically

  8. Motion in 2D - Displacement

  9. Velocity and Acceleration Vector forms • Average • Instantaneous • SI units

  10. Acceleration • How can an Object change acceleration?

  11. Projectile Motion • What is a projectile motion? • What assumptions do I make in analyzing this type of motion? • What rules do I need to know to solve projectile motion problems?

  12. Projectile Motion - Analysis

  13. Projectile Motion - Analysis

  14. Example • A stone is thrown upward from the top of a building at an angle of 30.0° to the horizontal and with an initial speed of 20.0 m/s. The height of the building is 45.0 m. • How long is the stone in flight? • What is the speed of the stone just before it strikes the ground?

  15. Example • See problem 73 of text. The determined Wile E. Coyote is out once more to try to capture the elusive roadrunner. The coyote wears a new pair of Acme power roller skates, which provide a constant horizontal acceleration of 15 m/s2, as shown in Figure P3.73. The coyote starts off at rest 70 m from the edge of a cliff at the instant the roadrunner zips by in the direction of the cliff. • If the roadrunner moves with constant speed, find the minimum speed the roadrunner must have in order to reach the cliff before the coyote. • If the cliff is 100 m above the base of a canyon, find where the coyote lands in the canyon. (Assume that his skates are still in operation when he is in "flight" and that his horizontal component of acceleration remains constant at 15 m/s2.)

  16. Relative Velocity • What is relative motion? • Why do I need frame of reference? • Are there any specific equations to learn?

  17. Example Relative Velocity • The boat is heading due north as it crosses a wide river with a velocity of 10.0 km/h relative to the water. The river has a uniform velocity of 5,0 km/h due east. Determine the velocity of the boat with respect to an observer on the riverbank.

  18. Example Relative Velocity • A science student is riding on a flatcar of a train traveling along a straight horizontal track at a constant speed of 10.0 m/s. The student throws a ball along a path that she judges to make an initial angle of 60.0° with the horizontal and to be in line with the track. The student’s professor, who is standing on the ground nearby, observes the ball to rise vertically. How high does the ball rise?

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