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point with chalk. She then rides the bike along a flat, level road. She imposes a coordinate system as shown in the figure below such that the chalk mark is touching the ground at the point (0,0) at time t=0 . The radius of her wheels is 35 cm and the bike moves at 70 π cm/sec in the direction indicated. As the bike moves from left to right in the picture below, the chalk mark will trace out a path in the imposed coordinate system: The parametric equations for the path of the chalk mark are x ( t ) = 70 π t + 35cos(–2 π t π /2) y ( t ) = 35 + 35sin(–2 π t π /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 number π (a) The horizontal velocity is . .
2/21/14, 2:44 PM Chapter 3.5 HW Page 11 of 14 (b) The vertical velocity is (c) Compute x'(t) at these times: t = 0 sec t = 0.25 sec t = 0.5 sec t = 0.75 sec t = 1 sec (d) Compute y'(t) at these times: t = 0 sec t = 0.25 sec t = 0.5 sec t = 0.75 sec t = 1 sec (e) When is the first time the horizontal velocity will be a maximum? (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? .
2/21/14, 2:44 PM Chapter 3.5 HW Page 12 of 14 (i) When is the first time the vertical velocity will be a maximum? (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 time t is defined by the equation s ( 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? 11. 14/14 points | Previous Answers An object is moving in the plane according to these parametric equations: x ( t ) = π t + cos(4 π t + π /2) y ( t ) = sin(4 π t + π /2) A portion of the "cycloidal" path (on the time interval [0,1]) is shown in this figure: At time t=0 , the object is located at (0,1). Give EXACT ANSWERS to all questions below; use pi to denote the number π (a) The horizontal velocity is (b) The vertical velocity is . . .
2/21/14, 2:44 PM Chapter 3.5 HW Page 13 of 14
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