Row Attach
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How fast a boat approaches the dock when it's 8m away with a row attached to its prow? apply derivatives?
A boat is towed to a dock with a row attached to its prow which passes through a pulley in the dock. This pulley is 1m taller than the boat prow, if the row is moved with a speed of 1m/s. How fast the boat approaches the dock when it's 8m away?
the exercise is solved only with derivatives
pulley, prow, and row form a right triangle:
h = height of pulley above prow = 1
s = distance of boat from the dock
r = length of row
r² = s² + h² = s² + 1
2rdr/dt = 2sds/dt
rdr/dt = sds/dt
dr/dt = 1
r = sds/dt
ds/dt = r/s = 8/s
s = √(r²-1) = √63
ds/dt = 8/√63 ≈ 1.00791 m/s
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