## beth12345 3 years ago A boy and girl both swim at 3.0m/s. They jumpinto a river 1.0km across, with a current of 2.0m/s (E). She swims straight across relative to the shore. How long (in minutes) does each take to cross the river

1. shubham

You are given the velocity of boy and girl w.r.t the ground and velocity of current w.r.t ground. Velocity of girl w.r.t ground, V(g,G) = 3 m/s Velocity of current = V (c,G) = 2 m/s Now, velocity of girl w.r.t current = V(g,G) + V(c,G) [ vector sum!! ] Hope you may try to solve it now...

2. beth12345

is it 5m per second

3. shubham

No... I said the vector sum, as the direction of speeds are different you can't just add both the velocities..

4. beth12345

oh would I use a squared +b squared = c squared

5. shubham

Exactly....

6. beth12345

i got 3.6

7. shubham

But, think.. For calculating time she required to cross the river if she propells herself perpendicular to the shore, would in anyway be affected by velocity of current.

8. shubham

Think why time depends on both components...

9. beth12345

uhm, I don`t understand

10. beth12345

|dw:1331693378113:dw| this is all I understand so far...

11. shubham

Right. See, She propells herself perpendicular to the bank at 3 m/s and at the same time she is getting pushed sideways at 2 m/s. So, her resultant velocity will be directed at an angle b/w the two.

12. shubham

|dw:1331693676065:dw|

13. shubham

Now, see 3m/s contributes to her getting across the bank. Time she requires = 1000 m / 3 m/s = 333.33 sec.

14. beth12345

and then it makes an angle triangle like this |dw:1331693918116:dw| ?

15. beth12345

and then it is 5.6 minutesÉ

16. beth12345

minutes*

17. shubham

RIght, you may shift vectors in a plane, without changing the directions and magnitude.

18. shubham

Yes...

19. beth12345

oh i think i get it, does the 2m per s affect it?

20. shubham

No, it doesn't effect the time, but other parameters like where she would land on the other bank does.

21. beth12345

ok, is it the same for the boy then?

22. shubham

Yes, Gender doesn't effect the time as well.. lol..

23. beth12345

oh right! haha well thanks for helping :)