Engineering Board Exam Reviewer · Related Rates (Time Rates) · medium
A boat is pulled toward a dock by a rope passing through a pulley on the dock 8 ft above the water. If the rope is pulled in at 3 ft/s, how fast is the boat approaching the dock when it is 15 ft from the dock?
- 3.4 ft/s
- 3.0 ft/s
- 2.65 ft/s
- 4.25 ft/s
Answer
A. 3.4 ft/s
Solution
Let x = horizontal distance, L = rope length: x2+64=L2. At x=15, L=17. Differentiating: dx/dt=L/xdL/dt=17/15(-3)=-3.4 ft/s, so the boat approaches at 3.4 ft/s.
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