## anonymous 4 years ago A boat which has speed of 5 km/hr in still water crosses a river of width 1 km along the shortest possible path in 15 minutes. The velocity of the river water in km/hr is : a) 4 b) 3 c) 1 d) 2

1. Mani_Jha

Did you solve this?

2. anonymous

I tried, but didn't get the equation.

3. anonymous

Can u say the equation?

4. Mani_Jha

Let me see what diagram you've drawn first. By the way, if x is the river's speed, the final equation will be: $\sqrt{25-x ^{2}}*15/60=1$

5. anonymous

Can I post tomorrow? I have to go now to a hospital.

6. Mani_Jha

All right! What happened by the way?

7. anonymous

Regular checkup, That's all.

8. anonymous

|dw:1333604852676:dw|

9. anonymous

@Mani_Jha < can u explain now?

10. Mani_Jha

@Aadarsh, the shortest possible path is that straight line marked 1 km. Now if you attempt to move in this line, the flow of the river will deflect you to a longer path. |dw:1333690533060:dw| You attempt to move through AB, but the river deflects you to the path BC, which is longer. Now try to think: What path must you take, so that, even after the deflection, you take the shortest path AB? Understood?

11. Mani_Jha

|dw:1333690831284:dw|

12. anonymous

So should we take AC?

13. anonymous

@Mani_Jha bhai, u der? Please say now what to do.

14. Mani_Jha

Sorry, I should have mentioned AC is the direction of flow of the river. You can't take AC. Whenever you attempt to move in some direction, the flow of the river deflects you by some angle. |dw:1333691551644:dw| See that if you take this path BA, the river flow will deflect you to the path AC, which is exactly what you want, since it's the shortest path. You can apply this technique while swimming in a river too. Do you understand this? I've assumed that you know vectors.

15. Mani_Jha

So, your speed is sqrt(25-x^2). distance is 1 km and time is 15 minutes. Now find x.

16. anonymous

Thanks bhai, got it. x = 3. Thanks a lot.