Question 914482
Hi, I need help solving this math word problem please.

The distance d that an object falls is directly proportional to the square of the time of the fall, t. A person who is parachuting for the first time is told to wait 19 seconds before opening the parachute. If the person falls 64 feet in 2 seconds, find how far he falls in 19 seconds.

According to my professor, the answer is: 5776 feet

Would you please show me the steps on how my professor got this answer please. Thank you.
<pre>
Based on the scenario, formula is: {{{d = kT^2}}}, with:
d being the fallen distance at a certain time
k being the constant of variation
T being time taken to fall to a certain distance

Thus, {{{d = kT^2}}} becomes:
{{{64 = k(2^2)}}}
64 = 4k
k = {{{64/4}}}, or 16

{{{d = kT^2}}}
{{{d = 16(19^2)}}}
d, or distance he falls = 5,776 ft