A jet skier is moving at 8.4 m/s in the direction in which the waves on a lake are moving. Each time he passes over a crest, he feels a bump. The bumping frequency is 1.2 Hz, and the crests are separated by 5.8 m. What is the wave speed?

Options

A. 1.4m/s
B. 2.1m/s
C. 7.0m/s
D. 8.4m/s

Answer

To solve the problem, we need to find the wave speed using the information given about the jet skier and the waves on the lake. Here's a step-by-step solution:

### Step 1: Understand the Given Information
- The jet skier's speed (v_j) = 8.4 m/s (in the direction of the wave)
- The bumping frequency (f) = 1.2 Hz (the frequency at which the skier passes over the crests)
- The distance between crests (wavelength, λ) = 5.8 m

### Step 2: Calculate the Speed of the Jet Skier with Respect to the Waves
The speed of the jet skier with respect to the waves (v_jw) can be calculated using the formula:
\[ v_{jw} = f \cdot \lambda \]

Substituting the values:
\[ v_{jw} = 1.2 \, \text{Hz} \times 5.8 \, \text{m} \]
\[ v_{jw} = 6.96 \, \text{m/s} \]

### Step 3: Determine the Wave Speed
Since the jet skier is moving in the same direction as the wave, the wave speed (v_w) can be found using the relationship:
\[ v_w = v_j - v_{jw} \]

Substituting the values:
\[ v_w = 8.4 \, \text{m/s} - 6.96 \, \text{m/s} \]
\[ v_w = 1.44 \, \text{m/s} \]

### Conclusion
The speed of the wave on the lake is approximately **1.44 m/s**.

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