Related rates question?

Question

A boat is pulled into a dock by a rope attached to the bow of the boat and passing through a pulley on the dock that is 1m higher than the bow of the boat. If the roap is pulled in a rate of 1 m/s, how fast is the boat approaching the dock when it is 8 m from the dock?

It is a triangle related rates question.

Answer 1

it depends on the boat.  i have a 92ft steel hull boat with a 30ft beam and it would not be approaching the dock at all because the rope would not be able to pull it anywhere.  the boat weighs about 130 tons

Answer 2

The answer is 7.937 m/s

The rule for a right angle triangle is (all join in!):-

The square on the hypotenuse is equal to the sum of the squares on the other two sides.

So the rope from the boat is 8m long (the hypotenuse), the (vertical) y axis of the triangle is 1m. Square each length and the hypotenuse is 64 and the y axis is 1. According to the rule above, to find the (horizontal) x axis we have to take 1 from 64 which equals 63. The square root (opposite of square) of 63 is 7.937.

So (pull on the rope) reduce the hypotenuse by 1m/s and you reduce the (horizontal) x axis by 7.937m/s which is the speed at which the boat approaches the dock.

Hope this helps Bigpathome.