math
posted by jonh .
A man pulls a rope over a simple pulley attached to the bow of a rowboat. The manâ€™s hands are 8 feet above the water and the bow of the boat is 1 foot above the water. How fast must the man pull the rope to tow the boat in at 3 feet per second when it is 25 feet from the dock? How fast must he pull the rope to tow the boat at that same speed when it is 10 feet from the dock? If he pulls the rope at 3 feet per second when the boat is 18 feet from the dock, how fast is the boat moving?

Your situation can be described by a rightangled triangle, where the base is along the water.
let the boat be x ft from the dock, let the length of rope from the man to the boat be y ft
then y^2 = x^2 + 7^2
2y dy/dt = 2x dx/dt
y dy/dt = x dx/dt
case #1, dx/dt = 3 ft/sec, x = 25
y^2 = 25^2 + 7^ = 674 , > y = √674
√674 dy/dt = 25(3)
dy/dt = 75/√674 = appr 2.89 ft/sec
case 2, when x = 10, dx/dt = 3
y^2 = 100+49 = 149 , > y = √149
√149 dy/dt = 10(3)
dy/dt = 2.46 ft/s
case3 , when x = 28 , dy/dt = 3
y^2 = 784+49 = 833 , > y = √833
√833(3 = 28 dx/dt
dx/dt = √833(3)/28 = 3.09 ft/s
Respond to this Question
Similar Questions

calculus
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 … 
Calculus
A boat is pulled into a dock by a rope attached to the bow of the boat an passing through the pulley on the deck that is 1m high than the bow of the boat ,if the rope is pulled im at the rate of 0.8m/s how fast does the boat approach … 
Calculus
A boat is pulled into a dock by a rope attached to the bow of the boat an passing through the pulley on the deck that is 1m high than the bow of the boat ,if the rope is pulled im at the rate of 0.8m/s how fast does the boat approach … 
Calculus
A boat is pulled into a dock by a rope attached to the bow of the boat an passing through the pulley on the deck that is 1m high than the bow of the boat ,if the rope is pulled im at the rate of 0.8m/s how fast does the boat approach … 
calculus
a man on a dock is pulling in a boat by means of a rope attached to the bow of the boat 1ft above the water level and passing through a simple pulley located on a dock 8ft above the water level. if he pulls in the rope at a rate of … 
calculus
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 … 
Calculus
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 … 
Calculus
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 1m/s,how fast is the boat approaching … 
calc 1
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 … 
Calculus
A man on a wharf is pulling in a boat by means of a rope attached to the bow of the boat 1 meter above water level and passing through a simple pulley located on the dock 8 meters above water level. If he pulls in the rope at the rate …