Question

A river is flowing due east with a speed 3 m/s. A swimmer can swin in still water at a speed of 4 m/s (Fig.).
(a) If swimmer starts swimming due north, what will be his resultant velocity (magnitude and direction)?
(b) If he wants to start from point A on south bank and reach opposite point B on north bank.
(i) which direction should he swim?
(ii) what will be his resultant speed?
(c) From two different cases as mentioned in (a) and (b) above, in which case will he reach opposite bank in shorter time.

Answer 1

Answer:

Explanation:

A river is flowing due east with a speed 3 m/s. A swimmer can swin in still water at a speed of 4 m/s

Resultant Speed = √3² + 4² = √9 + 16 = √25 = 5 m/s

Direction =  tan⁻¹(4/3)  (53°)  wrt E toward North

so he will reach East of point B

If he wants to start from point A on south bank and reach opposite point B on north bank.  

He should swim North west

in such a way that west component cancel East Component.

If he swims with 4 m/s

4cosθ = 3  (to cancel impact of stream) ( θ is  angle from west  toward north)

cosθ = 3/4  

Sinθ = √1 - Cos²θ  = √1 -(3/4)²  = √7 /4

resultant speed = 4 Sinθ = 4√7 /4  = √7  m/s = 2.65 m/s

in second case he will reach point B