# A man and his shadow

1. Jan 15, 2007

### Gyroscope

1. The problem statement, all variables and given/known data
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.

2. Relevant equations

3. 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.

Last edited by a moderator: Jan 15, 2007
2. Jan 15, 2007

### Dorothy Weglend

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

3. Jan 15, 2007

### 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?

4. Jan 15, 2007

### Dorothy Weglend

Hi Gyroscope,

Yes, sorry. I think your solution is correct.

Dorothy

5. Jan 15, 2007

### Gyroscope

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

6. Jan 15, 2007

### Gyroscope

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