(adsbygoogle = window.adsbygoogle || []).push({}); Imagine a boat on the water being putted

towards the shore by a winch mounted a height

h above the water. The winch reels in cable

(shortening the hypotenuse) at constant rate

u in m/s . When the boat is a distance d from

the shore, find its speed and acceleration.

This is an example of motion at non-uniform

acceleration.

im letting hypotenuse here = x, so x^2 = d^2 + h^2

Im thinking i want to solve for d' to get the velocity at of d at distance d. okay im going to give it a shot, but bear with me, i have little confidence in this answer and i understand that reading these next steps will probably be a little frightening for those who know how to solve this.

-------------------------------

x^2 = d^2 + h^2

d^2 = x^2 - h^2

2dd' = 2xx' - 2hh'

d' = [2xx' - 2hh']/(2d) <--- this is what i was thinking to explain the speed of d at distance d . my intuition was the to allow x' be u to explain the constant rate of the shortening of the hypotenuse, but im not sure about it. i want to differentiate again to find d'' to explain acceleration, but i need to establish the correct way to do this first step before moving on.

can anyone give me a pointer or two.

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# Homework Help: Rate of change of a right triangle

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