Sure, let's solve this step-by-step.
1. Understand the given values:
- Wavelength ([tex]\(\lambda\)[/tex]) = 37.0 meters
- Speed ([tex]\(v\)[/tex]) = 5.00 meters per second (m/s)
2. Use the relationship between speed, wavelength, and frequency:
The speed [tex]\(v\)[/tex] of a wave is the product of its wavelength [tex]\(\lambda\)[/tex] and its frequency [tex]\(f\)[/tex]:
[tex]\[
v = \lambda \cdot f
\][/tex]
3. Rearrange the formula to solve for frequency:
To find the frequency [tex]\(f\)[/tex], we rearrange the formula:
[tex]\[
f = \frac{v}{\lambda}
\][/tex]
4. Substitute the given values into the formula:
[tex]\[
f = \frac{5.00 \text{ m/s}}{37.0 \text{ m}}
\][/tex]
5. Calculate the frequency:
[tex]\[
f \approx 0.13513513513513514 \text{ Hz}
\][/tex]
The frequency of the boat bobbing up and down is approximately 0.135 Hz, meaning it bobs 0.135 times per second.
6. Convert the frequency to times per minute:
Since there are 60 seconds in a minute, multiply the frequency by 60 to find the number of bobs per minute:
[tex]\[
\text{Times per minute} = 0.13513513513513514 \text{ Hz} \times 60 \text{ s/min}
\][/tex]
7. Calculate the times per minute:
[tex]\[
\text{Times per minute} \approx 8.108108108108109
\][/tex]
Therefore, the boat bobs up and down approximately 8.11 times per minute on the ocean waves.
