Question

The distance s that an object falls is directly proportional to the square of the time t of the fall. If an object falls 16 feet in 1 second, how far will it fall in 4 seconds? How long will it take an object to fall 144 feet?

Answer 1

In this case, we'll have to carry out several steps to find the solution.

Step 01:

Data:

distance = s

time = t

Step 02:

directly proportional:

s = kt²

k:

s = 16 ft

t = 1 s

16 ft = k * (1 s)²

16 ft = k * 1 s²

16 ft / s² = k

distance, t = 4 s:

s = 16 ft / s² * (4 s)² = 16 ft / s² * 16 s² = 256 ft

time, s = 144 ft:

144 ft = 16 ft / s² * t²

`\begin{gathered} \frac{144\text{ ft}}{16\text{ ft / s}^2}=\text{ t}^2 \\ \\ \sqrt{9\text{ s}^2}=t \\ \\ 3\text{ s = t } \end{gathered}`

The answer is:

distance, t = 4 s:

s = 256 ft

time, s = 144 ft:

t = 3 s