A man standing on a wharf is hauling in a rope attached to a boat, at the rate of 4 ft/sec. if his hands are 9 ft. above the point of attachment, what is the rate at which the boat is approaching the wharf when it is 12 ft away?

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Answer 1 · 2018-01-22T17:30:07

#sf(-5" ft/s")#

MFDocs

We are told:

#sf((dr)/dt=-4color(white)(x)"ft/s")#

We need to find #sf((d(d))/dt)#

Pythagoras gives us the value of r at that particular instant:

#sf(r^2=h^2+d^2)#

#sf(r^2=9^2+12^2)#

#sf(r^2=81+144)#

#sf(r=15 color(white)(x)ft)#

We know that:

#sf(r^2=81+d^2)#

Differentiating implicitely with respect to t:

#sf(2r.(dr)/dt=2d.(d(d))/dt)#

Putting in the numbers#rArr#

#sf(2xx15xx-4=2xx12.(d(d))/dt)#

#sf(-120/24=(d(d))/dt)#

#sf((d(d))/dt=-5color(white)(x)"ft/s")#