A street light is at the top of a 12 ft tall pole. A woman 6 ft tall walks away from the pole with a speed of 5 ft/sec along a straight path. How fast is the tip of her shadow moving when she is 45 ft from the base of the pole?
1 Answer
May 3, 2016
10 ft/sec. The speed is a constant, like the speed of the lady.
Explanation:
In t sec the lady would be at a distance of (speed)(time) = (5 ft/sec)(t sec) = 5t ft.
As the height of the pole is double the height of the lady, from similar triangles, the tip of the shadow would be at a distance x = 2 (5t) ft = 10t.
The distance equation is x = 10t ft.
So, the speed is x' = 10 ft/sec.
The speed is a constant, like the speed of the lady.
