Relative Velocity of a boat Question

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Homework Help Overview

The discussion revolves around a relative velocity problem involving a boat traveling downstream and upstream in a river. The original poster presents a scenario where the boat takes different times to cover the same distance in each direction, prompting questions about the river's flow speed and the boat's velocity relative to the water.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to apply a velocity equation but struggles with the interpretation of the variables involved. Participants engage in clarifying the definitions of the variables and the relationships between them, questioning the calculations made for the boat's velocities in each direction.

Discussion Status

Some participants provide guidance on correctly identifying and applying the variables in the velocity equation. There is an acknowledgment of the need to apply the equation for both legs of the trip, and while the original poster expresses gratitude for the assistance, there is no explicit consensus on the final understanding of the problem.

Contextual Notes

The original poster notes a potential misplacement of the discussion in the forum, indicating a concern about the appropriateness of the topic for the section. There is also mention of confusion regarding the signs of the velocities based on the direction of travel.

jt121
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Homework Statement



A boat takes 4.0 hr to travel 25 km down a river, then 5.0 hr to return.

A. How fast is the river flowing?
B. What is the velocity of the boat relative to the water flow?

Homework Equations



VAC=VAB+VBC

The Attempt at a Solution



For some reason I have trouble thinking in terms of the equation... I keep thinking that I can simply divide the time by distance traveled which yields a velocity of 6.25 km/hr for one direction and 5.0 km/hr for the return. Any help is appreciated.

Thanks.
EDIT: This should probably be in Introductory Physics, sorry. Any help on this section is still appreciated. Thanks =)
 
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You are right about everything you have posted.
So in the formula you posted, what do the three variables stand for?
For which of the three are the numbers you calculated (6.25 and 5.0) values?
 
Thanks for the response, good to know I'm headed in the right direction.

To go further, I tried to identify the variables in the equation as you said.

So far;

Let:
Vwg = Velocity of water relative to the ground
Vbw = Velocity of the boat relative to water
Vbg = Velocity of the boat relative to the ground = 6.25 km/hr and 5 km/hr ?

So if I set this up right,

Vwg = Vbw + Vbg?

Maybe I'm lost.

Thanks again.
 
You got them mixed up in the final line ;)

jt121 said:
So if I set this up right,

Vbg = Vbw + Vwg?

Think of you walking on one of those automatic walkways you see in airports, for example.
Suppose it is moving at Vwg 5 m/s and you are walking at Vyw = 1.5 m/s. Clearly, what is your speed Vyg with respect to someone sitting around, waiting for their flight?
Do you see why you get something like (looking at the subscripts only)
ac = ab + bc​
with the b's in the middle "dropping out"?

Anyway, there are two velocities Vbg, one for the upstream and one for the downstream trip. So you should apply the equation twice. What can you say about Vwg and Vbw in the two cases?
 
Solved the problem, thank you so much for the help! I was hung up on the equation for each "leg" of the trip but you helped me simplify it.
 
jt121 said:
Solved the problem

Good, so you didn't fall into the minus sign traps then (e.g. the velocities are actually +6.25 and -5, if positive direction is downstream.

Well done.
 

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