The distance that an object falls varies directly as the square of the time the object is in motion. If an object falls for 3 seconds, it will fall 144.9 feet. To estimate the height of a cliff, a person drops a stone at the edge of the cliff and measures how long it takes for the stone to reach the base. If it takes 2.3 seconds, what is the height of the cliff?

85.2 feet

Step-by-step explanation:

Let the distance be 'd' and time be 't'.

Given:

Distance varies directly as the square of the time the object is in motion.

So,

Where, 'k' is constant of proportionality.

Now, also given:

When d = 144.9 ft, t = 3 s

Plug in these value in the above equation to find 'k'. This gives,

Now, we need to find 'd' when time 't' equals 2.3 s.

So, plug in the given values in the above equation to get the value of 'd'. This gives,

Therefore, the distance traveled by the object to reach base is nothing but the height of cliff. So, height of cliff is 85.2 ft.

0.50 , 0.75

step-by-step explanation: