The distance, d, that an object falls is directly proportional to the square of the time, t, it has been in free fall. An object that has been in free fall for 8 seconds has fallen 1024 feet. Determine the distance the object has fallen if it has been falling for 3 seconds.
d= ___ ft
I think its 384 can someone confirm
To determine the distance the object has fallen if it has been falling for 3 seconds, we can use the information given in the problem.
We are told that the distance, d, is directly proportional to the square of the time, t, in free fall. This can be represented as the equation d = k * t^2, where k is the constant of proportionality.
We are given that when the object has been in free fall for 8 seconds, it has fallen 1024 feet. Using this information, we can substitute these values into the equation and solve for k:
1024 = k * 8^2
1024 = k * 64
To find the value of k, we divide both sides of the equation by 64:
k = 1024 / 64
k = 16
Now that we have the value of k, we can use it to find the distance when the object has been falling for 3 seconds:
d = k * t^2
d = 16 * 3^2
d = 16 * 9
d = 144
Therefore, the distance the object has fallen if it has been falling for 3 seconds is 144 feet.
too bad you didn't show your work ...
d = kt^2, so
64k = 1024
k = 16
16*9 = 144
and in fact, g = 32 ft/s^2, so d = 1/2 g t^2 = 16t^2