Kinematics Problem: Speed of Current, Velocity, Direction

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Homework Help Overview

The problem involves a swimmer crossing a river while being affected by a current. The swimmer's speed in still water is given, along with the width of the river and the downstream displacement upon reaching the opposite bank. The discussion focuses on determining the speed of the current, the swimmer's velocity relative to the shore, and the necessary direction to swim directly across the river.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the swimmer's displacement downstream and the time taken to cross the river. Questions arise regarding the relationship between the swimmer's speed, the current's effect, and the calculation of time and velocity.

Discussion Status

Some participants have provided insights into calculating the time taken for the swimmer to cross the river and how to use that information to find the speed of the current. There is an ongoing exploration of the components of motion and the implications of swimming directly across versus at an angle.

Contextual Notes

Participants are considering the effects of the current on the swimmer's trajectory and the implications of different swimming angles. The discussion reflects a need for clarity on the definitions of displacement and components of motion in this context.

ellusion
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A swimmer who can swim at a speed of 0.8 m/s in still water heads directly across a river 86m wide. the swimmer lands at a position on the far bank 54m downstream from the starting point. determine:

a) the speed of the current
b) velocity of swimmer relative to the shore
c) the direction of departure that would have taken the swimmer directly across river

so far i drew myself a picture and found the distance he covered and the time it took him. from there I am just stuck, how do i find the speed of the current.
 
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ellusion said:
A swimmer who can swim at a speed of 0.8 m/s in still water heads directly across a river 86m wide. the swimmer lands at a position on the far bank 54m downstream from the starting point. determine:

a) the speed of the current
b) velocity of swimmer relative to the shore
c) the direction of departure that would have taken the swimmer directly across river

so far i drew myself a picture and found the distance he covered and the time it took him. from there I am just stuck, how do i find the speed of the current.
How far down the stream (a component of his total distance--be careful) did the current move him (displacement) and how long did it take to displace him that distance?
 
the current moved him 54m down the stream hwo would i get the time

what do you mean by a component of his total distance?
 
Last edited:
if he were to swim across and there is no current his time would be 107.5s
so could i just plug that to find the velocity of the current
v=d/t
= 54/107.5
=0.50m/s

can i do that
 
ellusion said:
if he were to swim across and there is no current his time would be 107.5s
so could i just plug that to find the velocity of the current
v=d/t
= 54/107.5
=0.50m/s

can i do that
Yes. Since the swimmer is heading directly across the river, his crossing time is unaffected by the current. If he swam so that he moved directly across the river, his heading would be upstream and that would change his crossing time.
 

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