Engineering Board Exam Reviewer · Related Rates (Time Rates) · medium
A man 6 ft tall walks away from a lamp post 18 ft high at a rate of 5 ft/s. Find the rate at which his shadow is lengthening.
- 2.5 ft/s
- 5 ft/s
- 1.67 ft/s
- 3.33 ft/s
Answer
A. 2.5 ft/s
Solution
Let x = distance from the post, s = shadow length. By similar triangles, 18/x+s=6/s s=x/2. So ds/dt= 12dx/dt= 12(5)=2.5 ft/s.
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