Question

The distance an object falls when dropped from a tower varies directly as the square of the time it falls. If the object falls 144 feet in 3 seconds, how far will it fall in 17 seconds?

Answer 1

Question

This is a relatively close question, and I have tried multiple times. Can you help?

The distance an object falls when dropped from a tower varies directly as the square of the time it falls. If the object falls 144 feet in 3 seconds, how far will it fall in 18 seconds?

Answer: The one below is correct.

Answer 2

Direct variation:

`y=kx^2`
y - the distance, x - the time

The object falls 144 feet in 3 seconds.

`144=k * 3^2 \\ 144=9k \\ k=(144)/(9) \\ k=16 \\ \Downarrow \\ y=16x^2`

The object falls y feet in 17 seconds.

`y=16 * 17^2 \\ y=16 * 289 \\ y=4624`

In 17 seconds the object will fall 4624 feet.