Answer:
Step-by-step explanation:
Given that:
The height of the dock (h) = 6
Let represent d to be the distance between the boat and the dock
Let the length of the rope between the boat and the drum be denoted by (l)
Then, the rate of change for the length of the rope be:
dl/dt = -5 ft/s
Using Pythagoras rule to determine the relationship between these values, we have:
[tex]l^2 = h^2 +d^2[/tex]
[tex]l^2 = 6^2 + d^2[/tex]
[tex]l^2 = 36 + d^2[/tex]
We relate to: [tex]2l * \dfrac{dl}{dt} = 2d* \dfrac{dd}{dt}[/tex]
From the question;
l = 34,
So to find [tex]\dfrac{dd}{dt}[/tex], we get;
[tex]d = \sqrt{l^2 - 36}[/tex]
[tex]d = \sqrt{34^2 - 36}[/tex]
[tex]d = \sqrt{1156- 36}[/tex]
[tex]d = \sqrt{1120}[/tex]
d = 33.46
So, we have:
[tex]\dfrac{dd}{dt}= \dfrac{l}{d} \times \dfrac{dl}{dt}[/tex]
[tex]\dfrac{dd}{dt}= \dfrac{34}{33.46} \times - 5[/tex]
[tex]\dfrac{dd}{dt}= 1.016 \times - 5[/tex]
[tex]\dfrac{dd}{dt}=-5.08 \ ft/sec[/tex]
