Question

A swimmer wishes to cross a 500 m river flowing at 5 km/h . his speed with respect to water is 3 km/h (a) if he heads in the direction making an angle say thita with the flow find the time he takes to cross the river (b) find the shortest possibletime to cross the river

Answer 1

 a) vertical component to opposite side is  3sinθ 
Distance = 0.5 km
velocity = 3 sinθ  
Time = Distance/Velocity
= 0.5/3 sin⁡θ
= 10/sinθ min. 

b) vertical component to opposite side = 3 km/hr 
Time = Distance/Velocity
= 0.5/3
= 0.16 hr 
converting into min: 0.16 hr = 60 x 16 = 9.6 or 10 minute.

Answer 2

Explanation:

given s = 500m

Vr = 5 km/h

Speed wrt to water v = 3 km/h

(a). time he takes to cross the river = s/sin@

=500×18/3×5sim@ = 360s/sin@

the man heads in a direction making angle @ with flow. so thats why vertical component is vsin@

(b) for shortest time @=90°