A Man and His Shadow: Velocity and Relationship with Sunlight

[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.

Homework Equations

The Attempt at a Solution

a)

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

b)

In this case, H >> h, so v_shadow=v_man.

Am I right? Thanks in advance for your replies.

 

[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

 

[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?

 

[Dorothy Weglend]

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!