Rain drops are falling down ward vertically at 4 kmph. For a person,moving forward at 3 kmph feels the rain at

Options

A. 7 kmph
B. 1 kmph
C. 5 kmph
D. 25 kmph

Answer

To find the speed at which the rain appears to fall for a person moving forward, we can break the problem down into steps:

### Step 1: Understand the velocities involved
- The rain is falling vertically downward at a speed of 4 km/h.
- The person is moving horizontally forward at a speed of 3 km/h.

### Step 2: Represent the velocities as vectors
- Let \( V_R \) be the velocity of the rain, which is \( 4 \, \text{km/h} \) downward.
- Let \( V_M \) be the velocity of the man, which is \( 3 \, \text{km/h} \) forward.

### Step 3: Determine the relative velocity of the rain with respect to the man
- The relative velocity of the rain with respect to the man can be calculated using vector subtraction:
\[ V_{RM} = V_R - V_M \]
- Since the rain is falling vertically and the person is moving horizontally, we can visualize this as a right triangle where:
- One side (vertical) represents the velocity of the rain (\( 4 \, \text{km/h} \)).
- The other side (horizontal) represents the velocity of the man (\( 3 \, \text{km/h} \)).

### Step 4: Apply the Pythagorean theorem
- To find the resultant velocity \( V_{RM} \), we can use the Pythagorean theorem:
\[ V_{RM} = \sqrt{(V_R)^2 + (V_M)^2} \]
\[ V_{RM} = \sqrt{(4 \, \text{km/h})^2 + (3 \, \text{km/h})^2} \]
\[ V_{RM} = \sqrt{16 + 9} = \sqrt{25} = 5 \, \text{km/h} \]

### Step 5: Conclusion
- The speed at which the rain appears to fall for the person moving forward is \( 5 \, \text{km/h} \).