- #1
dajugganaut
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Q. A street light is mounted at the top of a 15-ft tall pole. A man 6 ft walks awsay from the pole with a speed of 5ft/s along a straight path.How fast is the tip of his shadow moving when he is 40 ft from the pole?
What I've done so far:
this scenario can be drawn as similar triangles. from similar triangles i got eh equation 15/6 = (x+y)/y, which is also equal to 6x-9y = 0.
i found the derivative of that, which is 6(dx/dt) - 9 (dy/dt) = 0. then, i substituted (dx/dt), which gives dy/dt = (10/3) ft/s. however, the textbook states that the tip of his shadow is moving at (25/3) ft/s.
have i done anything wrong?
What I've done so far:
this scenario can be drawn as similar triangles. from similar triangles i got eh equation 15/6 = (x+y)/y, which is also equal to 6x-9y = 0.
i found the derivative of that, which is 6(dx/dt) - 9 (dy/dt) = 0. then, i substituted (dx/dt), which gives dy/dt = (10/3) ft/s. however, the textbook states that the tip of his shadow is moving at (25/3) ft/s.
have i done anything wrong?