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There will be another question later building on this one. Be sure to save your computations for referencing later. A 8-centimeter rod is attached at one end to a point A rotating counterclockwise on a wheel of radius 4 cm. The other end B is free to move back and forth along a horizontal bar that goes through the center of the wheel. At time t=0 the rod is situated as in the diagram at the left below. The wheel rotates counterclockwise at 1.5 revolutions per second. Thus, when t=1/9 sec, the rod is situated as in the diagram at the right below. Note that the wheel has its center at the origin. (a) When t=1/9 sec, Point A has coordinates ( , ) and point B has coordinates ( ,0). (b) The angular velocity for the circular motion of the point A is m: radians per second (c) Express the x and y coordinates of point A as a function oft: X= and y: (d) Express the X-coordinate of the right end of the rod at point B as a function of t: (e) Express the velocity of the right end of the rod as a function of t: centimeters per second. This question builds on an earlier problem. The randomized numbers may have changed, but have your work for the previous problem available to help with this one. A 6-centimeter rod is attached at one end to a point A rotating counterclockwise on a wheel of radius 3 cm. The other end B is free to move back and forth along a horizontal bar that goes through the center of the wheel. At time t=0 the rod is situated as in the diagram at the left below. The wheel rotates counterclockwise at 1.5 rev/sec. At some point, the rod will be tangent to the circle as shown in the third picture. ai some Instant. the piston will be tangent to the circle (a) Express the x and y coordinates of point A as functions oft: x: 3 cos(31rt) and y: 3 sin(31tt) w / (b) Write a formula for the slope of the tangent line to the circle at the pointA at time t seconds: cot(3nt) V/ (c) Express the x-coordinate of the right end of the rod at point B as a function of t: (d) Express the slope of the rod as a function oft: tan(31tt) X 1 (c) Find the rst time when the rod is tangent to the circle: E seconds. X (d) At the time in (c), what is the slope of the rod? (e) Find the second time when the rod is tangent to the circ e: seconds. (f) At the time in (e), what is the slope of the rod