As the wheel of radius r cm in the figure rotates, the rod of length L attached to point P drives a piston back and forth in a straight line. Let x be the distance from the origin to point at the end of the rod as shown. (a) Use the Pythagorean Theorem to show that L² = (x - r cos 0)² + ² sin²0. (b) Differentiate the equation in part (a) with respect to t to show that 0= = 2(x - r co - r cos 0) (+r sind) + 2r² sin (c) Calculate the speed of the piston when and the wheel rotates at 4 revolutions per minute. L de cos 0 dt. = , assuming that r = 10 cm, L = 30 cm, Piston moves back and forth

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