QUIZ VIII
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Problem 1.
Problem 2.
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Quiz 8 Solution - Vector Geometry | MATH 1224, Quizzes of Vector Analysis
Material Type: Quiz; Class: Vector Geometry; Subject: Mathematics; University: Virginia Polytechnic Institute And State University; Term: Unknown 1989;
Typology: Quizzes
Pre 2010
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Problem 1.
Problem 3.
Problem 6.
QUIZ VIII Problem 1. Given the velocity vit) = (e-?*)i + (#7 + #*)j + (cos(4 Ak, find the trajectory r(t) if r(1) = Oi + Oj + Ok. ca ih = deh a ( : Pi A sins 1k. + rh = Cle? i + (+ Sj + (= sin - 2 eS UtG 4 ob rhe cy +40?) + (36 4°45 £5 -11)j + (16 sin(4 f) +16 sin(4))k. e cc r(t) = +e? i + (484 #5 2)j + (sin(4)— sin(4 AIK. od. rit) = Ge?) + (364945 F5)j + (6 sind A). Ce rit) = ei + (484 #5)j + Csin(4 PK. of. y= ry al Pou ito sing ty — 2 rh) = (pS - t (SS - t+ (sing t)- . ze 65 307% ‘€! Use the initial condition r(1) when integrating to find the position r(t). Problem 2. A particle that passes the point P = (245,161, —3) at time t = 3 is moving with velocity vit) = <12 %, 8 #3, O>. Find the parametric equations for its motion. ca. xsiett, y=s8t!, z=0 cb x=3f8-2, yoa2rtsl 225 9 =3f'+2, ys2rt-t, cod. x=3f, ys2t*, zal 9 2 x j =l2t'+2, y=8f'-1, z= -4 cf. xsiatt-2, y=srte za4 In this problem the initial condition is at t = 3 rather than at t =O. It still te: can be used to set the integration constants. Parametric equations of motion just means the trajectory r(t), written in components.