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Velocity and Coriolis Acceleration of a Problem

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Problem 15.118 attached here from the textbook named " Mechanics for Engineers" Dynamics 4th ed. Ferdinand P.Beer & E.Russell Johnston, Jr. Although I knew the answers as shown yet but I want an explanation that how to find velocity and acceleration both of magnitude and direction. For clarity v= 706 mm/s and 40.9 degree from positive x-direction, Coriolis a = 5.45 m/s^2 and 51.6 degree counterclockwise from negative x-direction.

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The solution determines the velocity and coriolis acceleration of a problem.

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