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While vacationing on a tropical island, you find the courage to step off a high cliff and fall for 4 seconds before entering the water below. Exactly 2 seconds into your fall, you glance at the cliff face and see a secret treasure embedded in the rock. When you recover from your plunge, you return to the cliff top and find that treasure ______________________.1 point1/2 the distance down from the cliff top to the water.1/4 the distance down from the cliff top to the water.3/4 the distance down from the cliff top to the water.Slightly above 1/2 the distance down from the cliff top to the water. In other words, about a meter (3 feet) closer to the cliff top than to the water.

Question

While vacationing on a tropical island, you find the courage to step off a high cliff and fall for 4 seconds before entering the water below. Exactly 2 seconds into your fall, you glance at the cliff face and see a secret treasure embedded in the rock. When you recover from your plunge, you return to the cliff top and find that treasure ______________________.1 point1/2 the distance down from the cliff top to the water.1/4 the distance down from the cliff top to the water.3/4 the distance down from the cliff top to the water.Slightly above 1/2 the distance down from the cliff top to the water. In other words, about a meter (3 feet) closer to the cliff top than to the water.

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Solution

The treasure is 1/2 the distance down from the cliff top to the water.

Here's why:

The total time of the fall is 4 seconds. You saw the treasure exactly halfway through your fall, which is 2 seconds into the fall. This means the treasure is halfway down the cliff, because the distance you fall is proportional to the square of the time you've been falling. So if you've been falling for half the total time, you've fallen half the total distance. Therefore, the treasure is 1/2 the distance down from the cliff top to the water.

This problem has been solved

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