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

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

Step-by-step 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=(v)/(\lambda)\\\\f=(16.38\ m/s)/(145\ m)\\\\f=0.112\ Hz`

The time period of the wave is given by :

`T=(1)/(f)\\\\T=(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=(8.92)/(2)\\\\T=4.46\ s`

Hence, this is the required solution.