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.)

Approximately .

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 would be

.

When the hawk reaches the rabbit on the ground, its height should have become zero. The goal is to find the that ensures .

The hawk is initially feet above the ground. Therefore, .

The initial speed of the hawk is feet per second. However, since the hawk is diving, it is moving downwards, so that its speed should be negative. That is: .

The equation becomes .

Solve this quadratic equation for . Keep in mind that the here stands for time and is supposed to positive. After discarding the negative root, .

In other words, it would take approximately for the hawk to reach the ground.