The distance that a free falling object falls is directly proportional to the square of the time it falls (before it hits the ground). If an object fell 71ft in 5 seconds, how far will it have fallen by the end of 9 seconds

Step-by-step explanation:

If two variables are directly proportional, it means that an increase in the value of one variable would cause a corresponding increase in the other variable. Also, a decrease in the value of one variable would cause a corresponding decrease in the other variable.

Given that distance, d varies directly with square of the time, t, if we introduce a constant of proportionality, k, the expression becomes

d = kt²

If d = 71 when t = 5, then

71 = k * 5² = 25k

k = 71/25

k = 2.84

The equation becomes

d = 2.84t²

Therefore, when t = 9 seconds, then

d = 2.84 * 9² = 230.04 ft