Question

A container ship is traveling westward at a speed of 5 m/s. The waves on the surface of the ocean have a wavelength of 40 m and are traveling eastward at a speed of 16.5 m/s. At what time intervals does the ship encounter the crest of a wave?

a. 1.9

b. 2.3

c. 1.4

d. 2.2

Answer 1

(16.5 m/s + 5 m/s) ÷ (40 m) = 0.5375 Hz

1 ÷ 0.5375 Hz = 1.86 s

round up and you get 1.9 s, so the answer would be A.

Answer 2

Answer: Option (a) is the correct answer.

Step-by-step explanation:

It is known that frequency is velocity or speed divided by wavelength.

Mathematically, f =
`(v)/(\lambda)`

where v = speed or velocity

`\lambda` = wavelength

Therefore, total speed of ship will be (5 + 16.5) m/s = 21.5 m/s. Firstly calculate the frequency as follows.

f =
`(v)/(\lambda)`

=
`(21.5 m/s)/(40 m)`

= 0.537 Hz

Also it is known that frequency is inversely proportional time. Hence calculate the time interval of ship encountering the crest of a wave as follows.

f =
`(1)/(T)`

or, T =
`(1)/(f)`

=
`(1)/(0.537)`

= 1.86 s

= 1.9 (approx)

Thus, we can conclude that time intervals at which the ship encounter the crest of a wave is 1.9 s.