Thex- and y-motions of guides A and B with right-angle slots control the curvilinear motion of the connecting pin P, which slides in both slots. For a short interval, the motions are governed by x = 20+ 0.61t² and y = 21 -0.64t, where x and y are in millimeters and t is in seconds. Calculate the magnitudes of the velocity v and acceleration a of the pin for t = 1.9 s. Sketch the direction of the path and indicate its curvature for this instant.

A rodeo horse is running around a corral at a speed of 300 ft/s. Let x(t) be the distance of the horse from the third barrel and y(t) his distance from the fourth. (see figure; note that the distance between barrels is 900 řt). At what rate is the horse's distance from the fourth barrel changing at the instant when he is 200 ft from the third? 2 1 3 4

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A rotating fan completes 1180 revolutions every minute. Consider the tip of a blade, at a radius of 20.0 cm. (a) Through what distance does the tip move in one revolution? What are (b) the tip's speed and (c) the magnitude of its acceleration? (d) What is the period of the motion? (a) Number i Units (b) Number i Units

A helicopter blade spins at exactly 115 revolutions per minute. Its tip is 6.50 m from the center of rotation. (a) Calculate the average speed (in m/s) of the blade tip in the helicopter's frame of reference. m/s (b) What is its average velocity (in m/s) over one revolution? m/s

A squirrel runs along an overhead telephone wire that stretches from the top of one pole to the next. It is initially at position x: = 2.01 m, as measured from the center of the wire segment. It then undergoes a displacement of Ax = -6.// m. What is the ' sauirrel's final position xe?

A golfer launches a tee shot down a horizontal fairway and it follows a path given by r(t) = (at, (85-0.1a)t, - 5t² +60t), where t≥0 measures time in seconds and r has units of feet. The y-axis points straight down the fairway and the z-axis points vertically upward. The parameter a is the slice factor that determines how much the shot deviates from a straight path down the fairway. a. With no slice (a = 0), sketch and describe the shot. How far does the ball travel horizontally (the distance between the point the ball leaves the ground and the point where it first strikes the ground)? b. With a slice (a = 0.2), sketch and describe the shot. How far does the ball travel horizontally (along the y-axis)? c. How far does the ball travel horizontally (along the y-axis) with a = 2.5?