20. The function s(t)=16t^2 models the distance, s(t) in feet, that an object falls in t seconds. Find the number of seconds a sky diver is in free fall after jumping from a plane and falling 1584 feet before opening a parachute. Express answers in simplified radical form.

To find the number of seconds a sky diver is in free fall, we need to solve the equation $s(t) = 1584$ for $t$.<br /><br />Given the function $s(t) = 16t^2$, we can substitute $s(t)$ with 1584 and solve for $t$:<br /><br />$16t^2 = 1584$<br /><br />Divide both sides by 16:<br /><br />$t^2 = 99$<br /><br />Take the square root of both sides:<br /><br />$t = \sqrt{99}$<br /><br />Simplify the radical:<br /><br />$t = 3\sqrt{11}$<br /><br />Therefore, the sky diver is in free fall for $3\sqrt{11}$ seconds.