The Mike O’Callaghan-Pat Tillman Memorial Bridge spanning the Colorado River opened on October 16, 2010. Having a span of 1900 feet, it is the longest arch bridge in the Western Hemisphere, and its roadway is 890 feet above the Colorado River.
Here, the motion occurs along a vertical line with the positive direction downward.
If a rock falls from the roadway, the function \(s=\) \(f(t) =16t^{2}\) gives the distance \(s\), in feet, that the rock falls after \(t\) seconds for \(0 ≤ t ≤ 7.458\). Here, \(7.458\) seconds is the approximate time it takes the rock to fall \(890\) feet into the river. The average velocity of the rock during its fall is \[ \dfrac{\Delta s}{\Delta t}=\dfrac{f( 7.458) -f(0) }{7.458-0}=\dfrac{890-0}{7.458}\approx 119.335\; \hbox{feet per second} \]