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.

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