## mathslover Group Title A 2m wide car is moving uniformly with a speed of 8m/s along the edge of a straight horizontal road. A pedestriun starts to cross a road with a speed "v" when the car is 12 m away from him. The minimum value of v for the pedestrian to cross the road safety is ? one year ago one year ago

1. ash2326 Group Title

There can be two cases, either the man crosses the road before the car reach him or he crosses it after the car has crossed

2. mathslover Group Title

well if we take the man to reach more safely there is that is the first case

3. ash2326 Group Title

see the diagram|dw:1361020408653:dw| Time taken for car to reach the man, $12 m\div 8 m/s= 1.5 seconds$ In this time the man should cover the 2 meter distance, fairly simple now Can you find v?

4. DLS Group Title

|dw:1361020539994:dw| @ash2326 just trying..i dont think there will be 2 cases,he should move making an angle theta with the axis not straight..

5. mathslover Group Title

yeah @DLS has a point\

6. ash2326 Group Title

But we need to find the minimum V for that, he has to walk straight

7. mathslover Group Title

the man will make an angle theta first we have to find the componenets ( x and y ) and then solve for theta

8. ash2326 Group Title

|dw:1361020702285:dw| We aren't given D, we can't find angle without it

9. mathslover Group Title

|dw:1361020857966:dw|

10. DLS Group Title

$v=\frac{d}{t}$ $BC=2cosec \theta$ $t_{bus}=t_{boy}$ $\frac{4+2\cot \theta}{8}=\frac{8}{v}=2\sin \theta+\cos \theta$ $v=\frac{8}{2\sin \theta+\cos \theta}$ for v to be minimummmmmmmmmmm $\frac{dv}{d \theta}=0$ $\frac{d8(2 \sin \theta+\cos \theta)^-1}{d \theta}=0$

11. DLS Group Title

sorry i took the distance 4m correct that value..

12. DLS Group Title

|dw:1361020933104:dw|

13. DLS Group Title

if my solution is close enough

14. mathslover Group Title

how r those angles : 2 cot theta and 2 cosec theta ?

15. DLS Group Title

$\LARGE \frac{12+2\cot \theta}{8}=\frac{8}{v}=\frac{6+\cot \theta}{4}$

16. DLS Group Title

final thing

17. ash2326 Group Title

How do you have 8/v? man isn't travelling 8 meters

18. DLS Group Title

@ash2326 I equated the times.. Tbus=Tboy

19. DLS Group Title

V=s/t

20. ash2326 Group Title

I know that but man has to travel $\sqrt{2^2+(2\cot \theta)^2}$ so it should be $\frac{\sqrt{2^2+(2\cot \theta)^2}}{v}$

21. ash2326 Group Title

|dw:1361021378137:dw|

22. DLS Group Title

yeah i got ur query,hold on

23. DLS Group Title

i took that 12+2cot theta that is the total distance he has to travel i guess distance is scalar :o so why are u adding it vectorally? im getting confused too :S

24. ash2326 Group Title

I solved this, there is no global minima for v. We need to revisit the problem

25. mathslover Group Title

26. DLS Group Title

sure

27. ash2326 Group Title

@DLS the man is travelling with an angle, his speed is v I just found the hypotenuse distance

28. DLS Group Title

i thought that was 2 cosec theta :O

29. ash2326 Group Title

Yes, if you solve the square root, you will get 2 cosec theta

30. DLS Group Title

:D

31. ash2326 Group Title

I'm not convinced about the car travelling an extra distance 2 cot theta

32. ash2326 Group Title

@mathslover do you have answer for this?

33. DLS Group Title

offline~

34. DLS Group Title

Just do the whole thing for him :P From the beginning :D

35. mathslover Group Title

yep --- 4/3 --- ans..

36. Mashy Group Title

bahhhh!!!!..

37. Mashy Group Title

doing all that other crap!! :P.. good thing you put up the answer!!

38. mathslover Group Title

@Mashy you cn put up your soln... I posted it becz ash wnted to check the ans... Please post your soln

39. Mashy Group Title

4/3 is the simple method.. of going straight :O..

40. DLBlast Group Title

before i can start i need to know the in physics what is the start point for all formula is = to ? or 0.00 or what the name of all start point plz? start point =

41. ash2326 Group Title

@mathslover Use my first post, I had told you for minimum it has to be straight

42. mathslover Group Title

DLS can you tell me how you got 2 cot theta there ?

43. DLS Group Title

hold on

44. mathslover Group Title

|dw:1361184323999:dw| ok :)

45. DLS Group Title

isnt the sol clear? they are taking for it to be going straight

46. mathslover Group Title

But I am trying to do for the angle theta... please tell how you got 2 cot theta there

47. mathslover Group Title

??

48. DLS Group Title

wait I got confused :P sec

49. DLS Group Title

|dw:1361185375230:dw| AC=2 cot theta

50. DLS Group Title

$\LARGE \cot \theta=\frac{1}{\tan \theta}$

51. DLS Group Title

idk why i got confused !

52. DLS Group Title

$\LARGE \cot \theta=\frac{AC}{2}$

53. mathslover Group Title

OH got it thanks a lot

54. DLS Group Title

:P