Kinematics Problem: Speed of Current, Velocity, Direction

AI Thread Summary
The discussion focuses on a kinematics problem involving a swimmer crossing a river with a current. The swimmer, who swims at 0.8 m/s in still water, ends up 54m downstream after crossing an 86m wide river. Participants analyze how to calculate the speed of the current, which is determined to be 0.50 m/s by using the time it would take to swim across without current interference. The conversation emphasizes that the swimmer's direction must be adjusted upstream to swim directly across the river. The calculations and understanding of displacement and time are crucial for solving the problem accurately.
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?
 
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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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