Question

1. 16 pts) The position r of an object in an xy plane varies as r (-sini+1-cos n) j. where r is in seconds and r in meters. (Set your calculators in radians for trig functions.) (a) What is the displacement vector of this object between 1-0 and 2n (b) What is the distance (or are length) travelled by this object between 1-0 and 2? Hint sin'e-(1/211-cos 200 (c) What are the object's speed and direction of motion at /6

Answer 1

R^rightarrow = (t - sin t) i + (1 - cos t) j t is in second r is in meters (a) Let position of object at t = 0 is r, r_1 rightarrow = (0 - sin 0) i + (1 - 1) j r_1 rightarrow = 0 Position of object at t = 2 pi r_2 rightarrow = (2 pi - sin 2 pi) i + (1 - cos 2 pi)j r_2 rightarrow = (2 pi - 0) i + (1 - 1) j r_2 rightarrow = 2 pi i displacement r rightarrow = r_2 rightarrow - r_1 rightarrow r rightarrow = 2 pi i \r\n (b) r rightarrow = (t - sin t) i + (1 - cos t) j distance = squareroot (t - sin t)^2 + (1 - cos t)^2 = squareroot t^2 - 2t sin t + 2 - 2 cos t at = 0 at t = 2 pi S_1 = 0, S_2 = 2 pi