Circular motion Find parametric equations that describe the circular path of the following objects. For Exercises 53–55, assume ( x , y ) denotes the position of the object relative to the origin at the center of the circle. Use the units of time specified in the problem. There are many ways to describe any circle. 54. The tip of the 15-inch second hand of a clock completes one revolution in 60 seconds.
Circular motion Find parametric equations that describe the circular path of the following objects. For Exercises 53–55, assume ( x , y ) denotes the position of the object relative to the origin at the center of the circle. Use the units of time specified in the problem. There are many ways to describe any circle. 54. The tip of the 15-inch second hand of a clock completes one revolution in 60 seconds.
Circular motion Find parametric equations that describe the circular path of the following objects. For Exercises 53–55, assume (x, y) denotes the position of the object relative to the origin at the center of the circle. Use the units of time specified in the problem. There are many ways to describe any circle.
54. The tip of the 15-inch second hand of a clock completes one revolution in 60 seconds.
The center field fence in a ballpark is 7 feet high and 408 feet from home plate. A baseball is hit at a point h = 2.5 feet above the ground. It leaves the bat at an angle of ? degrees with the horizontal at a speed of 110 miles per hour.
Write a set of parametric equations that model the path of the baseball. (Let t be in seconds and let x and y be in feet.)
Find the minimum angle required for the hit to be a home run. (Round your answer to one decimal place.)
You're going for a bike ride and start 7km north of the town and riding on a straight path that leads to a park 3km west of town. It takes 20 minutes to cover this distance. Write parametric equations expressing your motion, with the town being represented by the origin, and t=0 representing your starting point then find your location after 5 minutes using these parametric equations. Then eliminate the parameter to get a rectangular equation for this path and verify algabraically that this equation represents this line and that both the parametric and rectangular equations are the same. Suppose you ride back along the same path, but now t=0 represents the new starting point, which was the original ending point. Explain what changed in the parametrization and if the rectangular equation changed.
Find parametric equations and a parameter interval for the motionof a particle that starts at (a, 0) and traces the circle x2 + y2 = a2 once clockwise
Calculus, Single Variable: Early Transcendentals (3rd Edition)
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