A man is coming down an incline of angle 30^@. When he walks with speed 2(sqrt(3)) m s^-1 he has to keep his umbrella vertical to protect himself from rain. The actual speed of rain is 5 ms^-1. At angle with vertical should he keep his umbrella when he is at rest so that he does not getb drenched ? .

A man is coming down an incline of angle 30^@. When he walks with spee

1.	A man is coming down an incline of angle 30^@. When he walks with speed 2(sqrt(3)) m s^-1 he has to keep his umbrella vertical to protect himself from rain. The actual speed of rain is 5 ms^-1. At angle with vertical should he keep his umbrella when he is at rest so that he does not getb drenched ? .
Answer» SOLUTION :Velocity of rain w.r.t man `vec v_(r,m) = X hat j = vec v_r - vec v_m` `vec v_m = 2 sqrt(3) [COS 30 hat i + sin 30 hat j]` =`3 hat I + sqrt(3) hat j` `vec v_r = -3 hat i + (x - sqrt(3)) hat j` `5 = sqrt(3^2 + (x - sqrt(3))^2)` `16 = (x - sqrt(3))2 rArr 4 + sqrt(3) = x` `vec v_r = - 3 hat i + 4 hat j` `tan theta = (3)/(4) rArr theta = 37^@`.