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[evilevoevil]

from exercise 25 a q 2 fitzpatrick 3u

A lamp is 6m directly above a straight path. A man 2 m tall walks along the path away from the lightt at a constant speed of 1 m/s. At what speed is the end of the shadow moving along the path? At what speed is the length of his shadow increasing?

thanks in advance

 

[YannY]

from exercise 25 a q 2 fitzpatrick 3u

A lamp is 6m directly above a straight path. A man 2 m tall walks along the path away from the lightt at a constant speed of 1 m/s. At what speed is the end of the shadow moving along the path? At what speed is the length of his shadow increasing?

thanks in advance

First you draw the picture
Then prove the two triangles are similar and what you come to realise is the smaller triangle is 1/3 of the bigger triangle.

Thus the length between the man and the lamp is x and the length of the shadow must be x/2.

Ultimately that means if the man is traveling towards the lamp at 1m/s then the mans shadow is decreasing at a rate of 0.5m/s

They two key points is that you realise the triangles are similar and that the length of the lamp to the end of the shadow is 3 times the length of the shadow.
Hence the length of the lamp to the man is twice the length of the shadow