Please help: A boat is pulled into a dock by means of a winch 12 feet above the deck

[kesang]

ind 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 12 feet above the deck of the boat (see figure). The winch pulls in rope at a rate of 3 feet per second. Find the acceleration of the boat when there is a total of 15 feet of rope out. round answer to 3 desimal places

 

[Harry_the_cat]

ind 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 12 feet above the deck of the boat (see figure). The winch pulls in rope at a rate of 3 feet per second. Find the acceleration of the boat when there is a total of 15 feet of rope out. round answer to 3 desimal places

What figure?

 

[HallsofIvy]

ind 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 12 feet above the deck of the boat (see figure). The winch pulls in rope at a rate of 3 feet per second. Find the acceleration of the boat when there is a total of 15 feet of rope out. round answer to 3 desimal places

If there were a figure, I suspect I would see a right triangle with the rope being the hypotenuse, the horizontal line from the boat to the dock and the vertical line from water to top of dock as legs. Taking "c" to be the length of the hypotenuse, "a" the horizontal distance, and "b" the vertical distance, the Pythgorean theorem gives \(\displaystyle a^2+ b^2= c^2\). The speed of the boat is the derivative of with respect to time, t, is da/dt, the rate at which the rope is pulled is dc/dt, and b is a constant. So from \(\displaystyle a^2+ b^2= c^2\) we have \(\displaystyle 2a(da/dt)= 2c (dc/dt)\). The acceleration is the second derivative.