The distance an object falls?

Question

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

Answer 1

8 seconds

d ~ a t^2

using the given info solve for a, which is 36.

2304 = 36 t^2

t = 8 seconds!

Answer 2

yes

h= 0.5 g t^2

or  as you have put it

h= kt^2   where k = h/t^2= 1296/(6)^2

then

t2=sqrt( h2/k)

t2= sqrt (2304 / [1296/(6)^2])

t2= 8 sec

Answer 3

Time . . .. . . . .  Distance

t seconds . . . . 2304 feet

6 seconds . . . .1296 feet

(t/6)² = 2304/1296

t / 6 = sqrt(2304/1296)

t = 6 sqrt(16/9)

t = 6 x 4/3

t = 8 s