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 1 m higher than the bow of the boat. If the rope is pulled in at a rate of 1 m/s, how fast is the boat approaching the dock when it is 4 m from the dock

-1.031 m/s or  

Step-by-step explanation:

We take the length of the rope from the dock to the bow of the boat as y.

We take x be the horizontal  distance from the dock to the boat.

We know that the rate of change of the rope length is = -1 m/s

We need to find the rate of change of the horizontal  distance from the dock to the boat =   = ?

for x = 4

Applying Pythagorean Theorem we have

   .... equ 1

solving, where x = 4, we have

Differentiating equ 1 implicitly with respect to t, we have

substituting values of

x = 4

y =

= -1

into the equation, we get

= -1.031 m/s

step-by-step explanation: