Question

lauren dove into a swimming pool from a 15- foot high diving board with an initial upward velocity of 8 feet per second. find the time t seconds it took lauren to enter the water. use the model for vertical motion given by the equation h=-16t^2 + by +s is the initial height in feet.

Answer 1

It would take 1.25 seconds.

The equation would be $0=-16t^2+8t+15$, since the original velocity is 8 and the original height is 15.  Using the quadratic formula we have

$t=\frac{-8\pm \sqrt{8^2-4(-16)(15)}}{2(-16)} \\ \\=\frac{-8\pm \sqrt{64--960}}{-32}=\frac{-8\pm \sqrt{1024}}{-32} \\ \\=\frac{-8\pm 32}{-32}=\frac{-8+32}{-32}\text{ or } \frac{-8-32}{-32} \\ \\=\frac{24}{-32}\text{ or }\frac{-40}{-32}=-0.75\text{ or }1.25$

Since negative time makes no sense, the time is 1.25 seconds.