# Thread: Related Rates: How fast is the tip of this man's shadow moving?

1. ## Related Rates: How fast is the tip of this man's shadow moving?

A street light is mounted at the top of a 5.4m pole. A man 1.8m tall walks away form the light in a straight path at a speed of 1m/s. How fast is the tip of his shadow moving when he is 10m from the pole?

note: visualise the shadow cast by the man as a horizontal line segment; the starting point of the segment is at the man's feet; the endpoint of the segment is what we call the tip of the shadow.

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I'm completely confused.

I'll be absolutely grateful for any help at all, no matter how small.

THANKS

2. Originally Posted by sodamay
A street light is mounted at the top of a 5.4m pole. A man 1.8m tall walks away form the light in a straight path at a speed of 1m/s. How fast is the tip of his shadow moving when he is 10m from the pole?

note: visualise the shadow cast by the man as a horizontal line segment; the starting point of the segment is at the man's feet; the endpoint of the segment is what we call the tip of the shadow.

-----------------

I'm completely confused.

I'll be absolutely grateful for any help at all, no matter how small.

THANKS
Let x be distance from man to pole and s be distance from tip of shadow to man.

x+s/s = 5.4/1.8 = 3
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x=2s
dx/dt = 2 ds/dt
but dr(total)/dt = dx/dt + ds/dt