MAT-2130 Midterm: MATH 2130 App State Spring2016 Test2 answer key
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|r (t)| (cid:19) t(t) +(cid:18) |r (t) r (t)| r (t) = (cid:18) r (t) r (t) x ds,zc y ds,zc z ds(cid:19) P = ( 1, 2, 1) and q = (2, 1, 0). Initially its velocity is v0 = 3i 4j (meters per second) and it begins at position r0 = i + j (meters). Find the position function r(t) for this particle (t is measured in seconds). What is the particle"s initial speed? (meters per second): (10 points) let c be the circle (x + 3)2 + (y 2)2 = 4. Parameterize c and then compute its arc length. It will only end in tears. : (14 points) consider the curve parameterized by r(t) = h4t, 3 cos(t), 3 sin(t)i. (a) parameterize a line tangent to r(t) at t = . (b) find the tnb-frame for r(t). Show v + w and v w are perpendicular.
