A boat at anchore is rocked by waves whose crests are `100m` apart and velocity is `25 m//s` The boat bounces up once in every

Options

A. 2500 s
B. 75s
C. 4s
D. `0.25` s

Explanation

To solve the problem step by step, we will use the information given about the wave and the boat.

### Step 1: Identify the given data
- Wavelength (λ) = 100 m (the distance between two crests)
- Velocity (v) = 25 m/s (the speed of the wave)

### Step 2: Use the wave speed formula
The relationship between speed (v), wavelength (λ), and frequency (f) of a wave is given by the equation:
\[ v = f \cdot \lambda \]

### Step 3: Rearrange the equation to find frequency
We can rearrange the equation to find the frequency:
\[ f = \frac{v}{\lambda} \]

### Step 4: Substitute the known values
Now, substitute the values of velocity and wavelength into the equation:
\[ f = \frac{25 \, \text{m/s}}{100 \, \text{m}} \]

### Step 5: Calculate the frequency
Perform the calculation:
\[ f = \frac{25}{100} = 0.25 \, \text{Hz} \]

### Step 6: Determine the time period
The time period (T) is the reciprocal of the frequency:
\[ T = \frac{1}{f} \]
Substituting the frequency we found:
\[ T = \frac{1}{0.25} = 4 \, \text{seconds} \]

### Conclusion
The boat bounces up once every 4 seconds.

### Final Answer
The boat bounces up once in every **4 seconds**.

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