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13 June, 20:36

A horse on the merry-go-round moves according to the equations r = 8 ft, u = (0.6t) rad, and z = (1.5 sin u) ft, where t is in seconds. Determine the cylindrical components of the velocity and acceleration of the horse when t = 4 s.

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  1. 13 June, 20:50
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    velocity = 0.664 ft/s, acceleration = 0.365 ft/s²

    Explanation:

    z = 1.5 sin 0.6t

    angular velocity = dz/dt = d (1.5sin0.6t) / dt

    = 0.9cos0.6t

    at t=4

    =0.9cos (0.6*4)

    = - 0.664 ft/s

    Acceleration = dv/dt

    = d (0.9cos0.6t) / dt

    = - 0.54sin0.6t

    at t=4

    acceleration = - 0.54sin (0.6**4)

    = 0.365 ft/s²
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