HC Verma: Concepts of Physics - Volume 1 Chapter-3 Rest and Motion Kinematics Page 48-49: Q14 Solution: Rain is falling vertically. A man running on the road keeps his …

Part 1: The Man Standing Still (Vertical Rain)

Rain is falling vertically downward due to gravity.
For a stationary man, the rain has no horizontal component of velocity.
The rain falls straight down onto his head and shoulders.
To protect himself, he holds the umbrella vertically (straight up), directly over his head.

✅ Standing man → Umbrella vertical (correct).

Part 2: The Running Man (Rain appears to come at an angle)

The running man moves horizontally (say, forward) with speed vₘ.
From his own frame of reference, the rain appears to have:
A vertical component = downward speed of rain (vᵣ).
A horizontal component = backward (because he is moving forward, the rain seems to come from the front, towards him).
So the relative velocity of rain with respect to the man is the vector sum of downward and backward components.
This resultant velocity is inclined (tilted) towards him.
To keep the rain from hitting him, he must tilt his umbrella in the direction from which the rain appears to come—i.e., he tilts it forward (into the rain).

✅ Running man → Umbrella tilted (correct).

Part 3: Why does a standing man hold his umbrella vertical for vertical sun-rays?

Sunlight (rays) travels in straight lines at the speed of light (~3 × 10⁸ m/s).
Even if the man is running, his speed (~10 m/s) is negligible compared to the speed of light.
The relative velocity of light with respect to the running man is essentially vertical—the horizontal component introduced by his motion is so tiny (about 1 part in 10⁷) that it is completely imperceptible.
For all practical purposes, the sun-rays appear to come from exactly the same vertical direction for both the standing and running man.
So both hold their umbrellas vertically to block the vertical sun-rays.

Step 4: The Core Physics Reason (The Key Difference)

Aspect	Rain	Sunlight
Speed of particles/rays	~10 m/s (slow)	~3 × 10⁸ m/s (extremely fast)
Man's speed	~10 m/s	~10 m/s
Ratio (man's speed / particle speed)	~1 (comparable)	~10⁻⁷ (negligible)
Effect on apparent direction	Large (rain appears slanted)	Negligible (light appears vertical)
Umbrella orientation	Tilted for running man	Vertical for both

Step 5: The Principle of Relativity

For slow-moving objects like rain, the observer's motion significantly changes the apparent direction of the falling particles.
For very fast-moving objects like light, the observer's motion produces an immeasurably small change in the apparent direction (a phenomenon called aberration of light—but it is so tiny that it is ignored in daily life).

Final Answer

For rain: A running man tilts his umbrella because his horizontal motion makes the rain appear to fall at an angle relative to him. A standing man keeps it vertical because rain falls straight down in his frame.

For sun-rays: Both men keep their umbrellas vertical because light travels so fast (~3 × 10⁸ m/s) that the man's running speed (~10 m/s) creates an imperceptible change in the apparent direction of the sun-rays. For all practical purposes, the sun-rays appear vertical to both observers.

The key takeaway: The apparent direction of a moving object depends on the relative velocity between the observer and the object. For slow-moving rain, the effect is large. For fast-moving light, the effect is negligible.

QPage 48-49: Q14: HC Verma: Concepts of Physics - Volume 1 Chapter-3 Rest and Motion Kinematics Page 48-49: Q14 Solution: Rain is falling vertically. A man running on the road keeps his …

Step-by-Step Verified Solution

Part 1: The Man Standing Still (Vertical Rain)

Part 2: The Running Man (Rain appears to come at an angle)

Part 3: Why does a standing man hold his umbrella vertical for vertical sun-rays?

Step 4: The Core Physics Reason (The Key Difference)

Step 5: The Principle of Relativity

Final Answer

All Questions in this Chapter

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