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

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

1.	Rain is falling vertically with a speed of 20ms^(-1). A person is running in the rain with a velocity of 5ms^(-1) and a wind is also blowing with a speed of 15ms^(-1) (both from the west). The angle with the vertical at which the person should 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_(M))=5hat(i)` `vec(V_(wind))=vec(V_(W))=15hat(i)` Resultant velocity of rain and wind = `vec(V_(RM))=-20hat(K)+15hat(i)` Now, Velocity of Rain relative to man= `vec(V_(RM))-vec(V_(M))` `=(-20hat(K)+15hat(i))-(5hat(i))` `=-20hat(K)+10hat(i)` `Tanalpha==(1)/(2)rArr alpha = Tan^(-1)(1)/(2)`