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.

Question

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

4.24.2

​seconds, what is the height of the​ cliff?

Answer 1

The easiest way to solve this is to set up a ratio:

3 sec/144.9 feet = 4.24 sec/x feet and cross multiply and solve for x

x = 204.79 feet

Answer 2

d = kt² direct variation as to the square

144.9 = a(3²)

144.9 = 9a

16.1 = a

d = (16.1)(4.2)²

Can you complete and answer?