Question 1032106

The distance that a free falling object falls is directly proportional to the square of the time it falls (before it hits the ground).  If an object fell 50 ft in 5 seconds, how far will it have fallen by the end of 9 seconds?  (Leave the variation constant in fraction form or round to at least 2 decimal places.  Round your final answer to the nearest foot.) 
<pre>With D being distance, k: constant of proportionality, and T, time (in seconds), we get: 
{{{D = kT^2}}}
{{{50 = k(5)^2}}}
{{{matrix(1,5, 50/5^2 = k, or, 50/25 = k, or, k = 2)}}}

{{{D = kT^2}}}
{{{D = 2(9)^2}}}
D = 2(81), or {{{highlight_green(matrix(1,2, 162, feet))}}}