Question 128639
First write the equation of variation:
{{{d = kt^2}}} k is the constant of variation, d is the distance, and t is the time the object has been falling.
To find the value of k, substitute the given values of t = 6 secs. and d = 1296 ft.
{{{1296 = k(6)^2}}}
{{{1296 = 36k}}} Divide both sides by 36.
{{{k = 36}}} Now write the equation as:
{{{d = 36t^2}}} Substitute the given values of d = 2304 ft.
{{{2304 = 36t^2}}} Divide both sides by 36.
{{{t^2 = 64}}} Take the square root of both sides.
{{{t = 8}}} Use only the positive value.
It will take 8 seconds for the object to fall 2304 feet.