Question

Fig. shows a stream flowing with a constant speed of 4 kmhr^-1 from left to right. Points P and Q are directly opposite one another on the river banks. Two swimmers are at point P each swimming with same speed of 5 kmhr^-1. Both start together from point P. Swimmer 1 swims in such a direction as to reach end Q. Swimmer 2 swims in a direction at right angles to direction of flow of river and then walks back from R to Q with a speed v in such a manner that both swimmers reach point Q simultaneously. v is

(1) 4.5 kmhr^-1

(2) 3 kmhr^-1

(3) \(\sqrt{41}\,kmhr^{-1}\)

(4) 6 kmhr^-1

Answer 1

(4) 6 kmhr^-1

Let swimmer 1 swim in a direction to left of point Q in such a manner that his resultant velocity is along PQ. This is shown in Fig. (a). The resultant speed v₁ of swimmer 1 is

Let ω be width of stream in kilometer. 

t₁ = Time taken by swimmer 1 to move from P to Q

For swimmer 2; the velocity vectors are as shown in Fig. (b). Let t₂ be the total time taken by swimmer 2 to reach Q. Obviously

Given, t₁ = t₂ ; therefore