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AP Unit I A 2

AP Unit I A 2. Motion in two dimensions. Objectives. I A 2. a) Students should know how to deal with displacement and velocity vectors so they can: (1) Relate velocity, displacement, and time for motion with constant velocity.

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AP Unit I A 2

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  1. AP Unit I A 2 Motion in two dimensions

  2. Objectives • I A 2. • a) Students should know how to deal with displacement and velocity vectors so they can: • (1) Relate velocity, displacement, and time for motion with constant velocity. • (2) Calculate the component of a vector along a specified axis, or resolve a vector into components along two specified mutually perpendicular axes. • (3) Add vectors in order to find the net displacement of a particle that undergoes successive straight-line displacements. • (4) Subtract displacement vectors in order to find the location of one particle relative to another, or calculate the average velocity of a particle . • (5) Add or subtract velocity vectors in order to calculate the velocity change or average acceleration of a particle, or the velocity of one particle relative to another

  3. c) Students should understand the motion of projectiles in a uniform gravitational field so they can: • (1) Write down expressions for the horizontal and vertical components of velocity and position as a function of time, and sketch or identify graphs of these components. • (2) Use these expressions in analyzing the motion of a projectile that is projected above level ground with a specified initial velocity

  4. Graphical vectors • By scale drawing: A + B = R(Bold represents a vector) Vector B or V2 4 m/s E Vector A or V1 3 m/s N R or VR Resultant vector

  5. Components of a vector • A vector A at an angle θ to the horizontal can be expressed as the sum of two vectors, Ax, parallel to the x axis (horizontal component), and Ayparallel to the y axis (vertical component). • Hence the magnitude (unbolded) of the components of A are • Ax = A cos θ Ay = A sin θ • θ = tan -1 (Ay/ Ax) A Ay θ Ax

  6. Adding Vectors • 1. Calculate the following resultant velocity vector: • A plane traveling at 40 m/s north is blown by a wind of 20 m/s from the south west, calculate the resultant velocity R of the plane. B = 20 m/s θ = 45° A = 40 m/s N R

  7. Subtracting Vectors • Two boats both traveling at 45 m/s leave the pier at the same time. Boat A travels north, boat B travels north east. Calculate the velocity of boat B relative to A. R R = A - B -B A A B R

  8. Projectile motion • Rocket projected with initial velocity of 340 m/s at an angle of 30° to the ground. • Calculate time of flight, range, and maximum height reached. v0 Indicate horizontal and vertical components of velocity on each quarter of the trajectory. Where is the acceleration? θ =30°

  9. Calculations • 1. Read Chapter 3 • 2. Answer Multi Choice 1-5 • 3. Answer conceptual questions 1-5 • 4. Answer problems Chapter 3 1,7,16,24,31,41,51,61.

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