Chapter 3.3, Problem 75E

Rolling a Ball Bearing A ball bearing is placed on an inclined plane and begins to roll. The angle of elevation of the plane is $\theta$. The distance (in meters) the ball bearing rolls in t seconds is $s(t)=4.9(\sin \theta )t^2$.

(a) Determine the speed of the ball bearing after t seconds.

(b) Complete the table and use it to determine the value of $\theta$ that produces the maximum speed at a particular time.

$\theta$	0	$\pi /4$	$\pi /3$	$\pi /2$	$2\pi /3$	$3\pi /4$	$\pi$
$s^{\text{'}}(t)$