# The parametric equations for the path of the chalk

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The parametric equations for the path of the chalk mark arex(t) = 70πt+ 35cos(–2πtπ/2)y(t) = 35 + 35sin(–2πtπ/2)A portion of the path (on the time interval [0,2]) is shown in this figure:Give EXACT ANSWERS to all questions below; use pi to denote the numberπ(a) The horizontal velocity is\$\$70π+70πsin(2πt−π2).(b) The vertical velocity is\$\$70πcos(2πt−π2).
12/14/16, 4(08 PMhw14S3.5.(c) Computex'(t)at these times:
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(d) Computey'(t)at these times:
12/14/16, 4(08 PMhw14S3.5t = 0.5sec\$\$0t = 0.75sec\$\$70πt = 1sec\$\$0(e) When is the first time the horizontal velocity will be a maximum?
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(f) When is the first time the horizontal velocity will be a minimum?
(g) What is the maximum horizontal velocity?
(h) What is the minimum horizontal velocity?
12/14/16, 4(08 PMhw14S3.5(i) When is the first time the vertical velocity will be a maximum?
Page 14 of 1711.14/14 points |Previous AnswersAn object is moving in the plane according to these parametric equations:
(j) When is the first time the vertical velocity be a minimum?
(k) What is the maximum vertical velocity?
(l) What is the minimum vertical velocity?
(m) The speed of the moving chalk mark at timetis defined by the equations(t) ={(x'(t))2+ (y'(t))2}.Compute s(t).
(n) During the first 2 seconds, how many times will the speed be equal to 50 cm/sec?
12/14/16, 4(08 PMhw14S3.5Page 15 of 17x(t) =πt+ cos(4πt+π/2)y(t) = sin(4πt+π/2)A portion of the "cycloidal" path (on the time interval [0,1]) is shown in this figure:At timet=0, the object is located at (0,1). Give EXACT ANSWERS to all questions below; use pi todenote the numberπ(a) The horizontal velocity at time t is\$\$π−4πsin(4πt+π2).(b) The vertical velocity at time t is\$\$4πcos(4πt+π2)..(c) The slope of the tangent line to the path at timetis\$\$4cos(4πt+π2)14sin(4πt+π2)(d) The equation of the tangent line to the path at timet=1/6isy =\$\$23
12/14/16, 4(08 PMhw14S3.5Page 16 of 17

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