HW_4 - P1112 Fall 2008 Homework #4, total of 3 pages! (The...

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P1112 Fall 2008 Homework #4, total of 3 pages! (The strobe diagram in a separate file.) Due : the 2nd session in the week of September 22. Reading: 4.3-4.6, 5.1, 5.2 Not all concepts will be covered in class – you are responsible for all material in the reading and in the homework problems. 1. 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. 2. Consider Figure 3.24 in your textbook (“Monkey and Zookeeper”). Suppose the departure angle α 0 is 42.0 0 and the distance d is 3.00 m. Where will the dart and the monkey meet if the initial speed of the dart is a) 12.0 m/s Ans: 2.15 m b) 8.0 m/s Ans: 1.45 m c) what will happen if the initial speed of the dart is
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HW_4 - P1112 Fall 2008 Homework #4, total of 3 pages! (The...

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