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 7 ft/s along
a straight path. How fast is the tip of his shadow moving when he is 30 ft from the pole?
2 answers:
Answer:
Since only his speed affects how fast his shadow moves, then we calculate for the speed which is 11.67ft/s
Step-by-step explanation:
Assuming similar triangle
(y-x)/y = 6/15
15(y-x) = 6y
15y - 15x = 6y
(15 -6)y = 15x
9y = 15x
y = (5/3)x
By differentiating both sides with respect to time t
dy/dt = 5/3 (dx/dt)
But (dx/dt) is 7 ft/s
Therefore dy/dt = 5/3 * 7 = 35/3 = 11.67ft/s
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