Question

In the absence of wind, rain is falling vertically with speed of 4m/s. After some time, wind starts blowing with 3m/s speed in North to south direction. Find the angle with the vertical that a man standing on horizontal ground must hold his umbrella to keep himself dry.

Answer 1

Answer:

tan ⁻1 (3/4)

Explanation:

Given In the absence of wind, rain is falling vertically with a speed of 4 m/s. After some time, wind starts blowing with 3 m/s speed in North to south direction. Find the angle with the vertical that a man standing on horizontal ground must hold his umbrella to keep himself dry.

Let OP = Vr and PQ = Vm be the velocities of rain and man.

Given Vr = 4 m/s vertically downwards from west to East direction.

Vm = 3 m/s from north to south, to protect himself from rain, the relative velocity is Vrm = Vr - Vm, So PQ¹ = - Vm

Now resultant vector is OQ

So tanθ = PQ¹ / OP

           = Vm /Vr

         = 3/4

Now tanθ = 3/4

      θ = tan⁺¹ (3/4)

Answer 2

Answer:

37 degrees

Explanation:

Vr = 3 m/s        (on y axis)

Vm = 4m/s       (on x axis)

Tan theta = y/x

                = 4/3

       theta = 37 degrees