A child in an inner tube is bobbing up and down in the ocean and notices that after a wave crest passes, four more crests pass in a time of 38.4 s and the distance between the crests is 32 m. If possible, determine the following properties for the wave. (If not possible, enter IMPOSSIBLE.)(a) Period (s)(b) Frequency (Hz)(c) Wavelength (m)(d) Speed ( m/s)(e) Amplitude (m)

Explanation:

Given:

Four more crests pass in a time of 38.4 s and the distance between the crests is 32 m.

We have to determine five terms.

Lets start with one-one basis.

a.  

Period = Time taken by a wave to pass though.

⇒  

⇒

⇒

b.  

Frequency = Reciprocal of time period in Hertz.

⇒

⇒

⇒

c)

Wavelength = Distance between two consecutive trough and crest.

⇒

d.

Speed (v) = Product of frequency and wavelength.

⇒

⇒

⇒

e)

Amplitude = The maximum displacement or half the distance from crest to trough.

⇒ Here it can't be determined.

⇒ Impossible.

see the picture for the vector

the magnitude of the vector by pythagorean theorem

r = √( (-10)^2 + (3)^2 ) = √109

magnitude = √109 units

the direction angle between vector and x-axis is

tan^(-1)(3/10) = 16.699

so the direction is approximately 16.7 degrees north of west