Rain is vertically down with the velocity of 30m/s, a wind blows from north to south direction with 10m/s then at what angle should the umbrella be held and in which direction.

Explanation

The direction of the rain is determined by the vector sum of the rain's vertical velocity and the wind's horizontal velocity.Given:The rain's vertical velocity (downwards) is 30 m/s.The wind's horizontal velocity (from north to south) is 10 m/s.The angle θ the rain makes with the vertical can be found using the formula for the tangent.So, tan(θ) = (horizontal velocity)/(vertical velocity) = Va/Vr = 10/30 = 1/3.Therefore, the angle θ = tan⁻¹(1/3).The umbrella should be held at an angle of tan⁻¹(1/3) from the vertical. Since the wind is blowing from north to south, the umbrella should be held towards the north to protect against the rain.