A street light is mounted at the top of a 15-ft tall pole. A man 6 ft tall walks away from the pole with a speed of 5 ft/s along a straight path. How fast is the tip of his shadow moving when he is 40 ft from the pole?

---- i drew the picture and got the equation 15/6=(x+y)/y

(y=the shadow)

Question

A street light is mounted at the top of a 15-ft tall pole. A man 6 ft tall walks away from the pole with a speed of 5 ft/s along a straight path. How fast is the tip of his shadow moving when he is 40 ft from the pole?

---- i drew the picture and got the equation 15/6=(x+y)/y

(y=the shadow)

anonymous · Answer

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from the picture: tan(alpha)=9/40  so alpha=arctan(9/40)
since triangles are similar other alngle is equal to alpha too. So the distance from the street light base till shadow tip = 15/(9/40) = 66.7 aproximatly.
Now, man is 40 ft away and he got there by mooving with speed of 5 ft/s, it means it took him 8 sec to get there. Shadow in 8 seconds is at 66.7 feet, so it is mooving at (66.7/8) feet/sec