A hawk flying at a height of 60 feet spots a rabbit on the ground. If the hawk dives at a speed of 55 feet per second, how
long will it take the hawk to reach the rabbit?
(Hint: A model for the vertical motion of a projected object is given by the equation h = -16t2 + vt + s, where h is the height
in feet, t is the time in seconds, v is the initial velocity in feet per second, and s is the starting height of the object in feet. Use
this equation to find the time taken by the hawk to reach the rabbit.)

When the hawk reaches the rabbit on the ground, its height should have become zero. The goal is to find the [tex]t[/tex] that ensures [tex]-16\,t^2 + v\, t + s = 0[/tex].

The hawk is initially [tex]60[/tex] feet above the ground. Therefore, [tex]s = 60[/tex].

The initial speed of the hawk is [tex]55[/tex] feet per second. However, since the hawk is diving, it is moving downwards, so that its speed should be negative. That is: [tex]v = -55[/tex].

The equation [tex]-16\,t^2 + v\, t + s = 0[/tex] becomes [tex]-16\,t^2 + (-55)\, t + 60 = 0[/tex].

Solve this quadratic equation for [tex]t[/tex]. Keep in mind that the [tex]t[/tex] here stands for time and is supposed to positive. After discarding the negative root, [tex]t \approx 0.87[/tex].

In other words, it would take approximately [tex]0.87\;\rm s[/tex] for the hawk to reach the ground.