A container ship is traveling westward at a speed of 5.00 m / s. The waves on the surface of th

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A container ship is traveling westward at a speed of 5.00 m...

A container ship is traveling westward at a speed of $5.00 \mathrm{~m} / \mathrm{s}$. The waves on the surface of the ocean have a wavelength of $40.0 \mathrm{~m}$ and are traveling eastward at a speed of $16.5 \mathrm{~m} / \mathrm{s}$. (a) At what time intervals does the ship encounter the crest of a wave? (b) At what time intervals will the ship encounter wave crests if it turns around and heads eastward?

A container ship is traveling westward at a speed of $5.00 \mathrm{~m} / \mathrm{s}$. The waves on the surface of the ocean have a wavelength of $40.0 \mathrm{~m}$ and are traveling eastward at a speed of $16.5 \mathrm{~m} / \mathrm{s}$. (a) At what time intervals does the ship encounter the crest of a wave?
(b) At what time intervals will the ship encounter wave crests if it turns around and heads eastward?

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Key Concepts

Time Interval Calculation

The time interval between encountering successive wave crests is found by dividing the wavelength by the relative speed between the ship and the wave crests. This method reveals how the direction and speed of the ship, relative to the wave propagation, influence how often the crests are met.

Relative Motion

Relative motion refers to the effective speed between two moving objects. In this context, it involves calculating how fast the wave crests approach or recede from the ship by vectorially combining the velocity of the ship and the velocity of the waves. The relative speed determines the frequency with which the ship encounters consecutive wave crests.

Wavelength

Wavelength is the spatial period of the wave—the distance between one crest and the next. It is a fundamental attribute of wave phenomena and directly affects the time interval between successive encounters with wave crests when combined with the relative speed of the observer (the ship).

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