Asked by Nathan
A street light is at the top of a 17 ft tall pole. A woman 6 ft tall walks away from the pole with a speed of 6 ft/sec. How fast is the tip of her shadow moving when she is 50 ft from the base of the pole.
Answers
Answered by
Reiny
Let her distance from the pole be x ft
let the length of her shadow at that moment be y ft
by ratio:
17/(x+y) = 6/y
17y = 6x+6y
11y = 6x
11 dy/dt = 6 dx/dt
dy/dt = 6(6)/11 = 36/11 ft/s
The tip of her shadow is moving at
dy/dt + dx/dt
= 36/11 + 6
= 102/11 or appr 9.27 ft/s
notice that this is independent of where she is, that is the 50 ft did not even enter the picture.
let the length of her shadow at that moment be y ft
by ratio:
17/(x+y) = 6/y
17y = 6x+6y
11y = 6x
11 dy/dt = 6 dx/dt
dy/dt = 6(6)/11 = 36/11 ft/s
The tip of her shadow is moving at
dy/dt + dx/dt
= 36/11 + 6
= 102/11 or appr 9.27 ft/s
notice that this is independent of where she is, that is the 50 ft did not even enter the picture.
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