On the surface of the moon, astronomers notice that the distance traveled by an object falling freely is proportional to the square of the time passed after the release of the object. If the object travels 3.2 meters in 2 seconds, how many seconds would it take to travel 15 meters?

If the object travels 3.2 meters in 2 seconds, it would take 4.34 seconds to travel 15 meters.

Step-by-step explanation:

Hi, to answer this question we have to analyze the information given:

The distance traveled by an object falling freely is proportional to the square of the time passed after the release of the object.

Mathematically speaking:

d = k t²

Where:

d = distance

t = time

k = constant

We have to find the value of "k", using the values of "d" and "t" given .

3.2 = k 2²

3.2 = k 4

3.2 / 4 =k

0.8 = k

Finally, to find the time that takes travel 15 meters:

d = 0.8 t²

15 = 0.8 t²

15/0.8 = t²

√18.75 =t

t= 4.34 seconds

If the object travels 3.2 meters in 2 seconds, it would take 4.34 seconds to travel 15 meters.