Help Needed: Troubleshooting a Stream Insect Motion Problem

AI Thread Summary
The discussion revolves around troubleshooting a problem related to the motion of a water insect on a stream. The insect moves upstream against the current and then drifts downstream to maintain its position. Users seek guidance on calculating the insect's velocity relative to the water and understanding relative velocity concepts. A suggested formula for relative velocity is v_ab = va - vb, which helps clarify the calculations needed for the problem. The conversation emphasizes the importance of correctly applying formulas to derive the average velocity of the insect relative to the water.
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I've been having difficulty with this problem and can't seem to find where to start. Any help would really be appreciated.

A water insect maintains an average position on the surface of a stream by darting upstream (against the current) then drifting downstream (with the current) to its original position. The current in the stream is 0.540 m/s relative to the shore, and the skater darts upstream 0.510 m (relative to a spot on shore) in 0.770 s during the first part of its motion. Take upstream as the positive direction.
(a) Determine the velocity of the insect relative to the water (i) during its dash upstream

(b) How far upstream relative to the water does the insect move during one cycle of this motion?
m
(c) What is the average velocity of the insect relative to the water?
m/s
 
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Do you know what relative velocity is? You have to show some attempt.

Suppose the skater is still wrt a point on the shore. But the water is flowing past it. What do you think the relative velo of the insect is wrt the flowing water?
 
I don't know how to solve b and c. I don't even know where to start. can anyone point me in the right direction? a formula or some way to think of it other then the way the question states it. I figured out A finally but I never know what equation to use.
 
I thought in order to solve part C. I had to do this:

square root of (.510/.770)^2 + (.540)^2 then divide that answer by 2 to find the average. What did I do wrong?
 
Use this formula: v_ab = va - vb, where v_ab denotes the relative velo of a with respect to b, va and vb are velocities of a and b wrt ground respectively.

Using this, can you find the ans to (a)? Use proper signs.
 
I found the answers to each part but part C. The formula from shooting star is how I found part A. So why would you not add the velocities of the insect relative to the water and divide by 2 in order to find the average velocity of the bug relative to the water for part c?
 
First think about this: what is the averege velocity of the insect wrt the shore?
 

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