Question

1. A swimmer can swim with velocity of
10 kmh-w.rt. the water flowing in a river with veloc-
ity of 5 kmh. In what direction should he swim to
reach the point on the other bank just opposite to
his starting point 7 (in What is the time taken by him
to cross the river if it is 100 m wide ?​

Answer 1

Answer:

Given that the velocity of water flowing in a river, Vr = 5 km/h

Velocity of swimmer, Vs = 10 km/h

 

The swimmer will cross straight to reach the point(C) on other bank just opposite to his starting point(O), if the resultant velocity of river flow and swimmer acts perpendicular to the direction of river flow. i.e. along OC.

It will be so only if the swimmer moves making an angle α with upstream i.e. along OB.

i)

Here θ+α = 90°

θ = 90°-α

 

In ΔOBC, sin θ=sin (90°-α) = cos α

Angle CBO =  α, Hence we can write that:

cos α =BC/OB

cos α =5/10

α =cos-1 (1/2)

α = 60° upstream.

So the swimmer should swim 60º upstream.

 

Let v be the resultant velocity of the swimmer i.e. along OC

ii)

 Time taken by the swimmer to cross the river of width 100 m

t = 100 m / v

t = 0.1 km / 8.6 km/h

t =0.0116 hr

t =0.696 minutes