Question

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 2 seconds has fallen 64 feet. Determine the distance the object has fallen if it has been falling for 4 seconds. d= ft ...​

Answer 1

The distance an object falls is directly proportional to the square of the time it has been in free fall.

By using the given values and the formula d = kt^2, the distance the object has fallen after 4 seconds is 256 feet.

Step-by-step explanation:

The given problem states that the distance an object falls is directly proportional to the square of the time it has been in free fall.

We can express this relationship using the formula d = kt^2, where d is the distance fallen, t is the time in free fall, and k is the constant of proportionality.

Given that the object has been in free fall for 2 seconds and has fallen 64 feet, we can substitute these values into the formula to solve for k:

64 = k * 2^2
64 = 4k
k = 16

Now that we know the value of k, we can determine the distance the object has fallen after 4 seconds:

d = 16 * 4^2
d = 16 * 16
d = 256 feet.