I have the following related rates I am helping a student on, however, another tutor got $.9923$ and I get $1.007$.
Here is my attempt and someone please just point out the silly mistake I might be making:
Let $a$ be the height above the water of dock which is $1$, let $b$ be horizontal distance between boat and dock which at our instance is $8$, this makes the hypotenuse $c$ being the rope which at this instant is $\sqrt{65}$. Then we have a right triangle
$$a^2+b^2=c^2$$
differentiating with respect to $t$
$$aa'+bb'=cc'$$ But $a'=0$ as height does not change. Then I plug in $c'=-1, b=8, c=\sqrt{65}, a'=0$ and $b'=1.007$, but I am unsure wether it's correct or not. Thanks in advance.
Best Answer
Your method looks correct to me (I did not check the numbers). The other tutor's answer cannot be correct since the boat must be approaching the dock at a faster rate than the rope is.