# The distance an object falls is directly proportional to the square of the time it has been falling. After 6seconds it has fallen 1296 feet. How long will it take to fall 2304 feet?

Jul 7, 2016

8 seconds

#### Explanation:

Let distance be $d$
Let time be $t$
Let 'directly proportionate to' be $\alpha$
Let the constant of proportionality by $k$

$\implies d \text{ " alpha" } {t}^{2}$

$\implies d = k {t}^{2}$
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Given condition is at $t = 6 \text{; } d = 1296 f t$

$\implies 1296 = k {\left(6\right)}^{2}$

$\implies k = \frac{1296}{36} = 36$

So $\textcolor{b l u e}{d = 36 {t}^{2}}$
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Find t for a distance of 2304 ft

$d = 36 {t}^{2} \to t = \sqrt{\frac{d}{36}}$

$\implies t = \sqrt{\frac{2304}{36}} = \frac{48}{6} = 8 \text{ seconds}$