Question

A hawk dives toward a snake. When the hawk is at a height of 200 feet the snake sees the hawk, which is diving at 105 feet per second. Estimate the time the snake has to escape.

Short answer

The snake has approximately 1.9 seconds to escape.

Step-by-step solution

Identify known variables

Firstly, we should identify the variables given in this exercise. We know that the distance \(d\) is 200 feet as this is the height from which the hawk is diving. The speed \(s\) at which the hawk is diving is given as 105 feet/second.

Apply distance-speed-time formula

Secondly, we have to apply the formula for time which is \(t = d/s\), where \(t\) is the time, \(d\) is the distance that the hawk has to cover and \(s\) is the speed at which the hawk is diving.

Substitution and calculation

Substitute \(d = 200\) feet and \(s = 105\) feet/second into the equation. The resulting calculation \(t = 200/105\), gives us the time in seconds that it takes for the hawk to reach the ground, and hence, the time the snake has to escape.