At the local swimming hole, a favorite trick is to run horizontally off a cliff that is 8.3 m above the water. One diver runs off the edge of the cliff, tucks into a ball, and rotates on the way down with an average angular speed of 1.6 rev/s. Ignore air resistance and determine the number of revolutions she makes while on the way down.

Options

A. 1.6 rev
B. 2.4 rev
C. 0.81 rev
D. 2.1 rev

Answer

To solve the problem of how many revolutions the diver makes while falling from a height of 8.3 meters, we can follow these steps:

### Step 1: Calculate the time of fall
To find the time it takes for the diver to fall, we can use the formula for free fall:

\[ t = \sqrt{\frac{2h}{g}} \]

Where:
- \( h = 8.3 \) m (the height of the cliff)
- \( g = 9.81 \) m/s² (acceleration due to gravity)

Substituting the values:

\[ t = \sqrt{\frac{2 \times 8.3}{9.81}} \approx \sqrt{\frac{16.6}{9.81}} \approx \sqrt{1.69} \approx 1.3 \text{ seconds} \]

### Step 2: Calculate the number of revolutions
The average angular speed of the diver is given as \( \omega = 1.6 \) revolutions per second. The total number of revolutions \( N \) can be calculated using the formula:

\[ N = \omega \times t \]

Substituting the values:

\[ N = 1.6 \text{ rev/s} \times 1.3 \text{ s} \approx 2.08 \text{ revolutions} \]

### Final Answer
The diver makes approximately **2.08 revolutions** while falling.

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