A street light is at the top of a 11 ft tall pole. A woman 6 ft tall walks away from the pole with a speed of 4 ft/sec along a straight path. How fast is the tip of her shadow moving when she is 30 ft from the base of the pole?
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let x_p be the distance of the person from the pole,
x_s the length of the shadow, &
x = x_p + x_s
we want to find x' when x_p = 30 given x'_p = 4
by similar triangles
6/11 = x_s/x = x_s/(x_p + x_s) =
6(x_p + x_s) = 11x_s
6x_p = 5x_s
x_s = 1.2x_p
x = 2.2x_p
x' = 2.2x'_p = 2.2*4 = 8.8 ft/sec
x_s the length of the shadow, &
x = x_p + x_s
we want to find x' when x_p = 30 given x'_p = 4
by similar triangles
6/11 = x_s/x = x_s/(x_p + x_s) =
6(x_p + x_s) = 11x_s
6x_p = 5x_s
x_s = 1.2x_p
x = 2.2x_p
x' = 2.2x'_p = 2.2*4 = 8.8 ft/sec