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A 240m wide river flows East at 1.40m/s. A swimmer is caplable of swimming at 2.40m/s...

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l70295100 | Student, Grade 12 | (Level 1) Honors

Posted July 10, 2013 at 2:42 AM via web

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A 240m wide river flows East at 1.40m/s. A swimmer is caplable of swimming at 2.40m/s in still water.

a. Determine the velocity of the swimmer if the swimmer followed the shortest distance (in m/s)

b. Dtermine the time it would take to cross the river if the swimmer followed the shortst distance (in minutes)

c. Determine the time it would take if the swimmer was trying to cross in the shortest time (in minutes)

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aruv | High School Teacher | (Level 2) Valedictorian

Posted July 10, 2013 at 3:19 AM (Answer #1)

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Velocity of flowing water = 1.40 m/s

Velocity of swimmer in still water= 2.4 m/s  (let us assume swimmer wants to cross river from North to south)

Thus resultant velocity of swimmer

 `sqrt(1.4^2+2.4^2)=2.78` m/s  and direction will SE.

angle which swimmer's resultant velocity be

`tan(theta)=2.4/1.4=1.71`

`theta=59.74`

Since he wants to cross river in short distance= 240 `sec(59.74)` 

=`476.31`

b. time=`476.31/2.78=171.22`   (approx)

c .  time (in min) =`171.22/60=2.85 min.`  (approx.)

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