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<blockquote data-quote="jossip10" data-source="post: 1591907" data-attributes="member: 620581">...the rim of the front wheel? assume the wheel has radius 10in and the bike is moving at a rate of 20pi in/sec in the direction counterclockwise. As the bike moves from left to right in the picture below, the reflector will trace out a path in the imposed coordinate system: x(t)= 20pi t +10cos(-2pi t - pi/2) &amp; y(t) = 10 + 10sin(-2pi t - pi/2) where t is in units of sec and the coordinate system has units of inches on the axes. a portion of the graph is pictured below for 0&lt;_t&lt;_2.a)Compute horizontal &amp; vertical velocities of motion of the reflector x&#039;(t) and y&#039;(t)b)Compute x&#039;(t) and y&#039;(t) at t=0, 0.25, 0.5, 0.75, 1 sec. c)When will horizontal velocity be a maximum(minimum)? what is the maximum(min) horizontal velocity? Where is reflector in picture when this happens?d)When will vertical velocity be a max(min)? What is the max(min) vertical velocity? Where is the reflector in the pic when this happens?e)The speed of moving reflector at time t is defined by equation s(t) = sq root of [x&#039;(t)]^2 + [y&#039;(t)]^2.&nbsp; compute s(t). During the first 2 sec, how many times will the speed be equal to 50in/sec?</blockquote>

[QUOTE="jossip10, post: 1591907, member: 620581"] ...the rim of the front wheel? assume the wheel has radius 10in and the bike is moving at a rate of 20pi in/sec in the direction counterclockwise. As the bike moves from left to right in the picture below, the reflector will trace out a path in the imposed coordinate system: x(t)= 20pi t +10cos(-2pi t - pi/2) & y(t) = 10 + 10sin(-2pi t - pi/2) where t is in units of sec and the coordinate system has units of inches on the axes. a portion of the graph is pictured below for 0<_t<_2. a)Compute horizontal & vertical velocities of motion of the reflector x'(t) and y'(t) b)Compute x'(t) and y'(t) at t=0, 0.25, 0.5, 0.75, 1 sec. c)When will horizontal velocity be a maximum(minimum)? what is the maximum(min) horizontal velocity? Where is reflector in picture when this happens? d)When will vertical velocity be a max(min)? What is the max(min) vertical velocity? Where is the reflector in the pic when this happens? e)The speed of moving reflector at time t is defined by equation s(t) = sq root of [x'(t)]^2 + [y'(t)]^2. compute s(t). During the first 2 sec, how many times will the speed be equal to 50in/sec? [/QUOTE]

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