Rain is falling vertically with a speed of 20 ms^(-1). A person is running in the rain with a velocity of 5ms^(-1) and a wind is also blowing with a speed of 15 ms^(-1) (both from the west). The angle with the vertical at which the person hold his umbrella so that he may not get drenched is :

Rain is falling vertically with a speed of 20 ms^(-1). A person is run

1.	Rain is falling vertically with a speed of 20 ms^(-1). A person is running in the rain with a velocity of 5ms^(-1) and a wind is also blowing with a speed of 15 ms^(-1) (both from the west). The angle with the vertical at which the person hold his umbrella so that he may not get drenched is :
Answer» Solution :`VEC(V_("Rain")) = vec(V_(R)) = 20(-hat(K))` `vec(V_("Man")) = vec(V_(W)) = 15 hat(i)` Resultant velocity of rain and WIND = `vec(V_(RM)) = -20 hat(K) + 15 hat(i)` Now, Velocity of Rain relative to man = `vec(V_(RM)) - vec(V_(M))` `= (-20 hat(K) + 15 hat(i)) - (5 hat(i))` `= -20 hat(K) + 10 hat(i)` `Tan alpha = (1)/(2) rArr alpha = Tan^(-1)""(1)/(2)`