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

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 wave-length 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 wave-length 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

Wave Properties

Wave properties such as wavelength and frequency are fundamental in analyzing periodic disturbances in a medium. The wavelength, which is the spatial period of the wave, combined with the relative motion between the observer (the ship) and the wave crests, allows one to calculate the time intervals between successive encounters. This underscores the relationship between the spatial structure of a wave and the timing of observed events when there is relative motion.

Relative Motion

This concept involves analyzing how the velocities of two objects or phenomena combine when observed from a specific frame of reference. In the context of the problem, the ship and the wave crests are moving in opposite directions (or the same direction after turning around), and the effective or relative speed at which the ship meets the crests is determined by adding or subtracting these speeds appropriately. This understanding helps determine the rate at which successive wave crests are encountered.

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