# A man and his shadow

Gyroscope

## Homework Statement

One man, with height h, is inside a room. On the ceiling of the room there is a candle that is at a height H from the floor. The man moves in a straight line with velocity v1, passing below the candle.

a) Determine the velocity of the shadow of his head projected on the floor.

b) What is the relationship between the velocity of the man and the velocity of the shadow of his head when he walks outside below the sun.

## The Attempt at a Solution

a)

$$v_{\rm shadow}=\left \frac{H}{H-h} \right v_1$$

b)

In this case, H >> h, so vshadow=vman.

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I don't think you can use a scalar here. My experience is that a shadow "accelerates". When he is underneath the candle, there will be practically no shadow. When he is farther away, the shadow will be much larger. So it accelerates, so to speak.

Dorothy

Gyroscope
Dorothy, but we are concerned only about the shadow of his head as we can see it as a point. Why do you say it is accelerating?

Hi Gyroscope,

Yes, sorry. I think your solution is correct.

Dorothy

Gyroscope
No problem ... Thanks for replying to my post.

Gyroscope
It is not that I don't trust Dorothy, but I would like a second opinion. I just love second opinions!!!