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# HW_3 - P112 Spring 2007 Homework#3 Due Friday Feb 9th 2007...

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P112 Spring 2007 Homework #3 Due: Friday Feb 9th, 2007 – At lecture Reading: 3.4, 4.1-4.2, 5.5, 12.1 Not all concepts will be covered in class – you are responsible for all material in the reading and in the homework problems. Warm-up Exercises: (Answer only will be marked) 1. An airplane pilot sets a compass course due west and maintains an airspeed of 220km/h. After flying for 0.500h, she finds herself over a town 120 km west and 20 km south of her starting point. a) Find the wind velocity (magnitude and direction) b) If the wind velocity is 40 km/h due south, in what direction should the pilot set her course to travel due west? Use the same airspeed of 220 km/h c) For both parts, (a) and (b), please include carefully drawn and labeled velocity vector diagrams showing how the airplane's velocity relative to the ground is related to its velocity relative to the air. 2. A tennis ball rolls off the edge of the table 0.750 m above the floor and strikes the floor at a point 1.40 m horizontally from the edge of the table. You can ignore air resistance. a) Find the time of flight, b) Find the magnitude of the initial velocity c) Find the magnitude and the direction of the velocity of the ball just before it strikes the floor. d) Draw x-t, y-t, v x -t and v y -t graphs for the motion. Mathematics Exercises: 3. The coordinates of circular motion of an object around an origin in the xy-plane are given as functions of time by x(t)= R cos ω t and Y(t)= R sin ω t, where R and ω are constants. a) show that the object’s distance from the origin is constant and equal to R. b) show that at every point the object’s velocity is perpendicular to its position vector. c) Show that the magnitude of the object’s velocity is constant and equal to R ω . d) Show that the object’s acceleration is always opposite in direction to its position vector, and that the magnitude is R ω 2 e) Show that the object’s acceleration has constant magnitude v 2 /R. Estimation:

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HW_3 - P112 Spring 2007 Homework#3 Due Friday Feb 9th 2007...

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