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

Rain drops are falling downward vertically at 4 kmph. For a person moving forward at 3 kmph, they will feel the rain falling at an angle with a speed of 5 kmph.

When rain falls vertically at 4 kmph and a person walks forward at 3 kmph, the rain appears to fall at an angle and feels like it is coming at a speed of 5 kmph towards the person. This happens because of the relative motion between the person and the falling rain.

To understand this in detail, we must use the concept of relative velocity in physics. Relative velocity means the speed and direction with which one object appears to move when compared to another object.

Let’s break it down step by step:

1. Speed of Rain: The rain is falling vertically downward at a speed of 4 kmph.
2. Speed of Person: The person is walking forward horizontally at a speed of 3 kmph.

Since the rain is coming down vertically and the person is moving horizontally, these two directions are at a 90° angle (perpendicular to each other).

Using Pythagoras Theorem to Calculate Relative Speed

To find how the rain appears to the person, we calculate the resultant velocity using the Pythagoras theorem.

The formula to calculate the resultant velocity is:

Relative Speed = √(Vertical Speed² + Horizontal Speed²)

Substituting the values:

Relative Speed = √(4² + 3²)
               = √(16 + 9)
               = √25
               = 5 kmph