# Math

a man can swim with a speed of 4 km per hr in still water. How long does he take to cross a river 1 km wide if the river flows steadily at 3 km per hr and he makes his strokes normal to the river current? How far down the river does he go when he reaches the other bank?

Ans: the speed of the swimmer will be approx 1 km

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1. Are you studying vectors?

the resulting velocity vector is (4,0) + (0,3)
= (4,3)
magnitude of vector = √(4^2+3^2)
= √25 = 5

time to go 1 km at 5 km/h
= 1/5 hours or 12 minutes

angle between the resultant an normal:
tanØ = 3/4
Ø = 36.87°

for distance down the river where he lands:
tanØ = x/1
x = tanØ = .75

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posted by Reiny

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