A boat is pulled into a dock by a rope attached to the bow of the boat and passi

cistG 2021-10-15 Answered
A boat is pulled into a dock by a rope attached to the bow of the boat and passing through a pulley on the dock that is 1 m higher than the bow of the boat. If the rope is pulled in at a rate of 1 m/s, how fast is the boat approaching the dock when it is 8 m from the dock?
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Luvottoq
Answered 2021-10-16 Author has 95 answers
The distance of boat from dock be x, then using pythagaros theorem we have
x2+1=y2
Where y is the length of the rope
Differentiate throughout with respect to t.
2xdxdt=2ydydt
We have to find dxdt, and dydt is given as 1ms1
x is 8 m at the given instant and y=65
Therefore we have
8dxdt=65
Result: Rate of decrease of distance between boat and dock is 6581ms1
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