Answer:
<em>-1.031 m/s or </em>
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
= <em>-1.031 m/s</em>