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A large goose lands in a lake and bobs up and down for a short time. A fisherman notices that the first wave crest created by the goose reaches the shore 7.9 s after the goose first contacts the water. The distance between two wave crests is 60 cm, and in 2.2 s he sees four wave crests hit the shore. Determine how far from the shore the goose landed?

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Answer:

11.85m

Explanation:

For the development of this problem we must resort to the concepts of the basic kinematic equations that define the distance of a body, such as speed for a certain time, that is,

[tex]D=v*t[/tex]

From the information provided we say that the distance between the cretas is 0.6m,

[tex]D_{crest} = 0.6m[/tex]

In our information we have also that the length between the first and latest wave is in time terms of 2.2s. They are 4 waves in 3 intervals then

[tex]D_{T} = D_{crest}*3= 0.6*4 = 2.4m[/tex]

[tex]t=1.6s[/tex]

[tex]\upsilon = \frac{D_{T}}{t} = \frac{2.4}{1.6}[/tex]

[tex]\upsilon = 1.5 m/s[/tex]

Then the distance from the shore is given by the speed of the waves for the total time. That is

[tex]X = \upsilon*T\’[/tex]

[tex]X = 1.5*7.9[/tex]

[tex]X= 11.85m[/tex]

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