I cannot for the life of me figure out this problem:
Find the acceleration of the specified object. (Hint: Recall that if a variable is changing at a constant rate, its acceleration is zero.)
A boat is pulled into a dock by means of a winch 20 feet above the deck of the boat (see figure). The winch pulls in rope at a rate of 2 feet per second. Find the acceleration of the boat when there is a total of 25 feet of rope out. (Round your answer to three decimal places.)
So how I've been going about it is
s(hypotenuse)=25 feet
y=20 feet (constant)
(ds/dt)=2 ft/sec
I found x using the pythagorean theorem which makes x=15 feet
So next I found the derivative of the pythagorean theorem using implicit differentiation>>> x^2+20^2=s^2 which becomes 2x(dx/dt)=2s(ds/dt)
Then I substituted in everything>>> 2(15)(dx/dt)=2(25)(2) which becomes (dx/dt)=100/30 or 3.33 ft/sec^2 which is incorrect but I have no idea why?? Help anybody? I have one more shot at the right answer and I just don't know what I'm doing wrong.
Find the acceleration of the specified object. (Hint: Recall that if a variable is changing at a constant rate, its acceleration is zero.)
A boat is pulled into a dock by means of a winch 20 feet above the deck of the boat (see figure). The winch pulls in rope at a rate of 2 feet per second. Find the acceleration of the boat when there is a total of 25 feet of rope out. (Round your answer to three decimal places.)
So how I've been going about it is
s(hypotenuse)=25 feet
y=20 feet (constant)
(ds/dt)=2 ft/sec
I found x using the pythagorean theorem which makes x=15 feet
So next I found the derivative of the pythagorean theorem using implicit differentiation>>> x^2+20^2=s^2 which becomes 2x(dx/dt)=2s(ds/dt)
Then I substituted in everything>>> 2(15)(dx/dt)=2(25)(2) which becomes (dx/dt)=100/30 or 3.33 ft/sec^2 which is incorrect but I have no idea why?? Help anybody? I have one more shot at the right answer and I just don't know what I'm doing wrong.