On a certain day, rain was falling vertically with a speed of 35ms^(-1) . A wind started blowing after sometime with a speed of 12ms^(-1)in east to west direction . In whichdirection should boy waiting at a bus stop hold his umbrella ?

On a certain day, rain was falling vertically with a speed of 35ms^(-1

1.	On a certain day, rain was falling vertically with a speed of 35ms^(-1) . A wind started blowing after sometime with a speed of 12ms^(-1)in east to west direction . In whichdirection should boy waiting at a bus stop hold his umbrella ?
Answer» Solution :In the FIGURE , Velocity of rain, `grad _(r) = vec(OA)= 12 MS^(-1)`(vertically downwards) Velocity of wind . `grad_(w) = vec(OB) = 12 ms^(-1) `,east to west The MAGNITUDE of the resultant velocity is `V = SQRT(V_(R)^(2)+ V_(w)^(2)) = sqrt(35^(2) + 12^(2))` `= 37 ms^(-1)` Let the resultant velocity `vec(V) = (vec(OC))` make an angle `theta`with the vertical , them `TAN theta = (AC)/(OA) = (V_(w))/(V_(R)) = (12)/(35) = 0 . 343` ` :. theta = tgan^(-1) (0.343) = 19^(@)` Hence the boy should hold umbrella bending it towards east making an angle of about `19^(@)`with the vertical .