A man walking with 3 m/s feels the rain falling vertically with a speed of 4 m/s. Find the angle which the rainfall makes with the vertical according to a stationary observer.

Options

A. `37^(@)`
B. `53^(@)`
C. `tan^(-1)(3/5)`
D. `tan^(-1)(5/3)`

Explanation

To solve the problem of finding the angle which the rainfall makes with the vertical according to a stationary observer, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Situation**:
- The man is walking with a velocity of \(3 \, \text{m/s}\) horizontally.
- He perceives the rain to be falling vertically at a speed of \(4 \, \text{m/s}\).

2. **Identifying the Components of Rainfall**:
- Since the man perceives the rain as falling vertically, this means that the horizontal component of the rain's velocity must equal the horizontal speed of the man. Thus, the horizontal component of the rain's velocity is \(3 \, \text{m/s}\).
- The vertical component of the rain's velocity is given as \(4 \, \text{m/s}\).

3. **Setting Up the Right Triangle**:
- We can visualize the situation as a right triangle where:
- The horizontal leg (adjacent side) represents the horizontal component of the rain's velocity, which is \(3 \, \text{m/s}\).
- The vertical leg (opposite side) represents the vertical component of the rain's velocity, which is \(4 \, \text{m/s}\).

4. **Calculating the Angle**:
- We can use the tangent function to find the angle \( \theta \) that the resultant velocity of the rain makes with the vertical:
\[ \tan(\theta) = \frac{\text{horizontal component}}{\text{vertical component}} = \frac{3}{4} \]
- To find \( \theta \), we take the arctangent:
\[ \theta = \tan^{-1}\left(\frac{3}{4}\right) \]

5. **Finding the Angle**:
- Using a calculator or trigonometric tables, we find:
\[ \theta \approx 36.87^\circ \text{ (which can be rounded to } 37^\circ\text{)} \]

### Final Answer:
The angle which the rainfall makes with the vertical according to a stationary observer is approximately \(37^\circ\).