The​ distance, d, that an object falls is directly proportional to the square of the​ time, t, it has been in free fall. An object that has been in free fall for 5 seconds has fallen 400 feet. Determine the distance the object has fallen if it has been falling for 3 seconds.

Answer 1

We can set up a proportion based on the given information:

\(d \propto t^2\)

We know that when \(t = 5\), \(d = 400\).

So, we have:

\(\frac{d}{t^2} = \frac{400}{5^2}\)

Simplifying the right side:

\(\frac{d}{t^2} = \frac{400}{25}\)

\(\frac{d}{t^2} = 16\)

Now we can find the value of \(d\) when \(t = 3\):

\(\frac{d}{3^2} = 16\)

\(\frac{d}{9} = 16\)

Multiplying both sides by 9:

\(d = 16(9)\)

\(d = 144\)

Therefore, if the object has been falling for 3 seconds, it has fallen 144 feet.