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3 years ago

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A fisherman notices that his boat is moving up and down periodically, owing to waves on the surface of the water. It takes 2.5 s

for the boat to travel from its highest point to its lowest, a total distance of 0.62 m. The fisherman sees that the wave crests are spaced 6.0 m apart. (a) How fast are the waves traveling? (b) What is the amplitude of each wave? (c) If the total vertical distance traveled by the boat were 0.30 m but the other data remained the same, how would the answers to parts (a) and (b) be affected?

1 answer:

blondinia [14]3 years ago

8 0

Answer:

1.2 m/s

0.31 m

0.15 m

Explanation:

Time period is

$T=2.5\times 2\\\Rightarrow T=5\ s$

Frequency is

$f=\dfrac{1}{T}\\\Rightarrow f=\dfrac{1}{5}\\\Rightarrow f=0.2\ Hz$

Velocity is given by

$v=f\lambda\\\Rightarrow v=0.2\times 6\\\Rightarrow v=1.2\ m/s$

The waves are traveling at 1.2 m/s

Amplitude is given by

$A=\dfrac{d}{2}\\\Rightarrow A=\dfrac{0.62}{2}\\\Rightarrow A=0.31\ m$

Amplitude is 0.31 m

If d = 0.3 m

$A=\dfrac{0.3}{2}=0.15\ m$

The amplitude would be 0.15 m. The speed would remain the same.

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<em>b. Approved. He will get cold but he should be able to make it across</em>

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a.

The explorer wants to swim across a river to his campsite, as shown in the image below. The river has a velocity vr and the explorer can swim at ve in still water. If he swam directly to the campsite, he would end up in a point below it because the river would push him down. He must swim with a velocity such that he overcomes the stream but he advances to its objective. Let's call the angle he must swim at respect to the shoreline to achieve his goal. The explorer's velocity can be decomposed in its rectangular components vx and vy. To overcome the river's velocity:

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