Two boats are anchored in the harbor, separated by a horizontal distance of 30 m. The boats bob up and down as waves enter the harbor. When one boat is at its highest point, the other is at its lowest point and there is one wave crest between them. Each boat makes exactly 3 complete up-and-down cycles every 18.0 s. The vertical distance between a boat's highest and lowest position is 3.8 m.

Explanation:

Given:

Horizontal distance = 30 m

Note that Wavelength, lambda is the distance between two consecutive crests/troughs. Since,

One boat is at trough, the other is at crest.

The distance between a crest and a trough next to it = lambda/2

Complete cycles = 3 cycles

Time taken for the 3 cycles = 15 s

Vertical distance = 3.8 m

Wavelength, lambda = 2 × horizontal distance

= 2 × 30

= 60 m

Amplitude = vertical distance from the extreme loint to the mid point

= y/2

= 3.8/2

A = 1.9 m

In one cycle = 18/3

= 6 s/cycle

frequency, f = 1/T

= 1/6 = 0.17 Hz

speed,v = lambda × frequency

= 60 × 0.17

= 10 m/s

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