The tube rotates in the horizontal plane at a constant rate of = 4 rad/s. If

The tube rotates in the horizontal plane at a constant rate of θ̇ = 4 rad/s. If a 0.2-kg ball B starts at the origin O with an initial radial velocity of ṙ = 1.5 m/s and moves outward through the tube, determine the radial and transverse components of the ball's velocity at the instant it leaves the outer end at C, r = 0.5 m. Show that the equation of motion in the r direction is  r̈ - 16r = 0. The solution is of the form r = Ae^-4t + Be^4t. Evaluate the integration constants A and B, and determine the time t when r = 0.5 m. Proceed to obtain v_r, and v₀.

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x N 6 = 4 rad/s B 0.5 m C y