Abel A.
asked • 09/30/23A street light is mounted at the top of an 18-ft-tall pole. A man 6ft tall walks away from the pole with a speed of 8ft/s along a straight path. How fast is the tip of his shadow moving when he is 30ft from the pole? (Hint: Use the Triangle Ratio to find the length of the tip of his shadow first.)
William C. answered • 09/30/23
Experienced Tutor Specializing in Chemistry, Math, and Physics
If D = the distance from the pole and L = the length of the shadow, it can be shown that
L = (1/2)D, which means that
dL/dt = (1/2)dD/dt
Since dD/dt = 8 ft/sec at any distance from the pole
dL/dt = (1/2)(8) = 4 ft/sec at any distance from the pole
From the pole, his shadow is moving at a rate of 8 + 4 = 12 ft/sec.
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William C.
Where L = (1/2)D comes from. The larger triangle and the smaller triangle contained within are similar, so (L +D)/L = 1+ D/L = 18/6 = 3. This means D/L = 2. So L/D = 1/2.09/30/23