Question

Use the following information. The average speed of an object \(S\) (in feet per second) that is dropped a certain distance \(d\) (in feet) is given by the following equation. Falling object model: \(S=\frac{d}{\frac{\sqrt{d}}{4}}\) Use either equation to find the average speed of an object that is dropped from a height of 400 feet.

Short answer

The average speed of an object that is dropped from a height of 400 feet is 80 feet per second.

Step-by-step solution

Identify the Variables

In the given problem, the distance \(d\) that the object is dropped from is 400 feet.

Plug in the Given Value

Substitute this value into the equation \(S=\frac{d}{\frac{\sqrt{d}}{4}}\). This gives \(S=\frac{400}{\frac{\sqrt{400}}{4}}\).

Simplify the Equation

Now, simplify the fraction inside the main denominator. The square root of 400 is 20, so you get \(S=\frac{400}{\frac{20}{4}}\).

Simplify Further

Divide 20 by 4 to simplify the denominator which results in \(S=\frac{400}{5}\).

Final Calculation

Finally, divide 400 by 5 to get 80. So \(S=80\) feet per second.