Answer to Question #336365 in Calculus for John

Question

Related Rates: Problem Solving

Direction: Solve each word problem involving a related rates. Make a sketch of your work

if necessary, and then apply differentiation.

A man on a dock is pulling in a boat at a rate of 50 feet per minute by means of a

rope attached to the boat at water level. If the man’s hands are 16 feet above the

water level, how fast is the boat approaching the dock when the amount of rope

released is 20 feet?

PLEASE ANSWER MY QUESTION QUICKLY!!

DEADLINE : 05/03/2022 11 : 00 PM

Answer 1

$a^2+b^2=c^2$

Now implicitly differentiate that relationship

$2ada/dt+2b db/dt=2c dc/dt$

b=16

db/dt = 0 (that height is not changing)

c=20

dc/dt=50

we can find "a" using the pythagorean theorem

$a^2+16^2=20^2$

$a=\sqrt{20^2-16^2}=12$

We can know plug into our differentiated equation and solve it.

$12da/dt=50x20$

$da/dt=83.3 ft/min$