What Is the Speed of a Wave If a Jetskier Moves at 8.30 m/s?

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Homework Help Overview

The problem involves a jetskier moving at a speed of 8.30 m/s in the same direction as the waves on a lake. The scenario includes a bumping frequency of 1.17 Hz and a wavelength of 5.30 m, leading to a question about determining the wave speed.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the relationship between the jetskier's speed and the wave speed, questioning the use of the bump frequency as it relates to the wave frequency. Some suggest drawing diagrams to visualize the problem, while others explore the concept of relative velocity between the jetskier and the waves.

Discussion Status

The discussion is active, with participants offering different perspectives on how to approach the problem. There is an exploration of the relative motion of the jetskier and the waves, and some participants express confusion about the concepts being discussed, indicating a lack of consensus on the interpretation of the problem.

Contextual Notes

Participants are grappling with the implications of relative velocity and the timing of wave crests as the jetskier moves. There is an emphasis on understanding the relationship between the frequency of bumps experienced by the skier and the actual wave frequency.

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Homework Statement



A jetskier is moving at 8.30 m/s in the direction in which the waves on a lake are moving. Each time he passes over a crest, he feels a bump. The bumping frequency is 1.17 Hz, and the crests are separated by 5.30 m. What is the wave speed?

Jetski's Speed = 8.30m/s with the waves
ƒ of waves= 1.17
wavelength = 5.30m

Homework Equations



v = (wavelength)ƒ

The Attempt at a Solution



when i tried the equation above i got an answer of 6.201m/s which turned out to now be right. What am i missing here?

v = ƒ(wavelength)
v = (1.17)(5.30)
v = (6.201m/s)
 
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The waves are moving forward at the same time that the boat is, so the frequency of the bumps that the skier feels is not the frequency of the wave.

I suggest that you draw a diagram showing a wave at some starting time (zero is a good number), with the jetski at a wavecrest. The jetski will hit the following wavecrest at a time consistent with the given bump frequency. So, draw another wave below the first but shifted over to reflect that the wave has moved during that time interval. See if you can't work out the wave speed from there.
 
It is easy to solve this problem by using the relative velocity of the skier with respect to the waves. If the velocity of the waves is V, the relative velocity of the skier is 8.3-V (m/s), as they move in the same direction. You can imagine a standing wave pattern with crests 5.30 m apart. The skier travels this distance with its relative velocity in 1/f time (f is the frequency of the bumps). Just use the relation "distance = speed times time".

ehild
 
ehild said:
It is easy to solve this problem by using the relative velocity of the skier with respect to the waves. If the velocity of the waves is V, the relative velocity of the skier is 8.3-V (m/s), as they move in the same direction. You can imagine a standing wave pattern with crests 5.30 m apart. The skier travels this distance with its relative velocity in 1/f time (f is the frequency of the bumps). Just use the relation "distance = speed times time".

ehild

Why would it be 8.3 - V if they go in the same direction? wouldn't they add up? Also how does the skier have two relative velocities? (8.3 - v) and (1 / ƒ)
I'm still not getting it.
 
Imagine you sit on a train and another train travels beside you with the same velocity Does it seem moving at all?

The skier moves with velocity v(rel)=8.3-v during a time interval T=1/f. The distance traveled is 5.3 m.

ehild
 
Okay, yeah that makes sense now, i don't know how that didn't click before, thanks for your help man.
 

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