10. [-I22 Points] | DETAILS I | MY NOW A bicyclist is interested in the motion of a point on the tread of her tire, so she marks the tread at one point with chalk. She then rides the bike along a at, level road. She imposes a coordinate system as shown in the gure 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 70x 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: yaxie dixoc \"on of travel xaxie chalk mark The parametric equations for the path of the chalk mark are x(t) = 707dL + 35cos(-27rt - 7r/2) y(t) = 35 + 355in(-2nt - am A portion of the path (on the time interval [0,2]) is shown in this gure: Give EXACT ANSWERS to all questions below; use pi to denote the number . (a) The horizontal velocity is (b) The vertical velocity is (c) Compute x'(t) at these times: t = 0sec t = 0.25sec t = 0.5sec t = 0.75sec t = 1 sec (d) Compute y'(t) at these times: t = 0sec t = 0.25sec t = 0.5sec t = 0.75sec t = 1 sec(e) When is the rst time the horizontal velocity will be a maximum? |:| (f) When is the first time the horizontal velocity will be a minimum? |:| (Q) What is the maximum horizontal velocity? |:| (h) What is the minimum horizontal velocity? |:| (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? |:| (I) What is the minimum vertical velocity? |:| (m) The speed of the moving chalk mark at time t is defined by the equation s(t) = View? + (y'(t))2}. (n) During the first 2 seconds, how many times will the speed be equal to 50 cm/sec? |:|