Question

A stationary boat in the ocean is experiencing waves from a storm. The waves move at 59 km/h and have a wavelength of 145 m . The boat is at the crest of a wave. .How much time elapses until the boat is first at the trough of a wave?

Answer 1

Answer:

The time elapses until the boat is first at the trough of a wave is 4.46 seconds.

Explanation:

Speed of the wave, v = 59 km/h = 16.38 m/s

Wavelength of the wave, $\lambda=145\ m$

If f is the frequency of the wave. The frequency of a wave is given by :

$v=f\lambda\\\\f=\dfrac{v}{\lambda}\\\\f=\dfrac{16.38\ m/s}{145\ m}\\\\f=0.112\ Hz$

The time period of the wave is given by :

$T=\dfrac{1}{f}\\\\T=\dfrac{1}{0.112\ Hz}\\\\T=8.92\ s$

We need to find the time elapses until the boat is first at the trough of a wave. So, the time will be half of the time period of the wave.

$T=\dfrac{8.92}{2}\\\\T=4.46\ s$

Hence, this is the required solution.