A prototype of an adaptive bowling device is a simple ramp next to a wheelchair. For the initial design, the $20-$lb ramp has small rollers on its bottom. The $15-$lb bowling ball has a diameter of $8\mathrm{.}500$ in$.$ and can be modeled as a solid sphere. The athlete nudges the ball slightly from a height of h$=3$fth$=3$ft $,$ and the ball rolls down the ramp without sliding. It hits the bowling lane, and after slipping for a short distance, it begins to roll again. Know that the ball does not bounce as it hits the lane. The angle of the ramp, $,$ is $40$ degrees.

Determine the velocity of the mass center of the ball immediately after it leaves the bottom of the ramp. $($Round the final answer to four decimal places.$)$

The velocity of the mass center of the ball is ft$/$sft$/$s $$

Required information

A prototype of an adaptive bowling device is a simple ramp next to a wheelchair. For the initial design, the $20-$lb ramp has small rollers on its bottom. The $15-$lb bowling ball has a diameter of $8\mathrm{.}500$ in $.$ and can be modeled as a solid sphere. The athlete nudges the ball slightly from a height of $\backslash ($ h$=3\backslash$mathrm$\{$ft$\}\backslash ),$ and the ball rolls down the ramp without sliding. It hits the bowling lane, and after slipping for a short distance, it begins to roll again. Know that the ball does not bounce as it hits the lane. The angle of the ramp, $\backslash (\backslash$theta $\backslash ),$ is $40$ degrees.

Determine the velocity of the mass center of the ball immediately after it leaves the bottom of the ramp. $($Round the final answer to four decimal places.$)$

The velocity of the mass center of the ball is