We can use the Pythagorean theorem to find the length of the rope:
sqrt((14)^2 + (7)^2) = sqrt(245) = 7sqrt(5)
Let x be the distance between the boat and the dock. Then we have:
x^2 + (7)^2 = (7sqrt(5))^2
x^2 = 196
x = 14
Taking the derivative of both sides of the equation above, we get:
2x(dx/dt) = 0
dx/dt = 0 (when x = 14)
So when the point of attachment is 14 ft from the dock, the boat is not approaching or moving away from the dock. Therefore, the boat's speed is 0 ft/sec.
Give your answer accurate to 3 decimal places.
A man on a dock is pulling in a boat by means of a rope attached to the bow of the boat at a point that is 1 ft above water
level. The rope goes from the bow of the boat to a pulley located at the edge of the dock 7 ft above water level. If he pulls
in the rope at a rate of 2 ft/sec, how fast (in feet per second) is the boat approaching the dock when the point of
attachment is 14 ft from the dock?
1 answer