Answer:
Approximately [tex]0.87\;\rm s[/tex].
Step-by-step explanation:
In this question, this hawk acts like a projectile. According to the hint, the height (in feet) of this hawk at time [tex]t[/tex] would be
[tex]-16\,t^2 + v\, t + s[/tex].
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.
