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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?

Verified Answer :

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Direct variation:
\(y=kx^2\)
y - the distance, x - the time

The object falls 144 feet in 3 seconds.
\(144=k \times 3^2 \\ 144=9k \\ k=\frac{144}{9} \\ k=16 \\ \Downarrow \\ y=16x^2\)

The object falls y feet in 17 seconds.
\(y=16 \times 17^2 \\ y=16 \times 289 \\ y=4624\)

In 17 seconds the object will fall 4624 feet.

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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.

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