Rain is falling vertically with a speed of ` 10 sqrt 3 ms^(-1)`. A woman rides a bicycle with a speed of ` 10 ms^(-1)` in east to west direction. What is the derection in which she shold hold her umbrella to protect from rain ?

Explanation

To solve the problem, we need to analyze the motion of the rain and the woman on the bicycle. Let's break down the solution step by step.

### Step 1: Understand the velocities involved
- The rain is falling vertically downwards with a speed of \( v_r = 10\sqrt{3} \, \text{m/s} \).
- The woman is riding a bicycle with a speed of \( v_w = 10 \, \text{m/s} \) from east to west.

### Step 2: Set up the coordinate system
- Let's consider the downward direction (where the rain is falling) as the negative y-direction.
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