MATH 222 Midterm: Kansas State MATH 222 222t1f99
7 Mar 2019
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To receive credit you must show your work. (25) 1. Given the three points p (1, 0, 2) , q(2, 2, 1) and r(0, 1, 4) , let p qr denote the triangle having p , q and r as vertices. An object is moving around the ellipse x2+2y2 = 100 in the xy-plane . It is moving at a constant speed of 3 ft/sec. An object is moving in 3-space in such a way that its acceleration vector as a function of time is ~a = 2~j (sin t)~k . Suppose that at time t = 0 we know that ~v(0) = ~i + ~j and ~r(0) = ~i . Find the velocity vector and the position vector as functions of the time t and then give the parametric equations for the motion. An object is moving in 3-space according to the parametric equations x = sin t , y = cos t , z = sin 2t .
