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 8 ft above water level. If he pulls in the rope at a rate of 3 ft/sec, how fast (in feet per second) is the boat approaching the dock when the point of attachment is 12 ft from the dock?

Q: a 17 foot tall ladder is leaning against a vertical wall and its base is on level ground. The top of…

A: We have to find at what rate is the top of the ladder sliding down the wall when it is 8 feet above…

Q: A 13-foot ladder is resting against a wall and the bottom is initially 10 feet away from the wall.…

A: To find- rate at which its top moving up the wall.

Q: A 50 feet ladder is leaning against a wall of a building. Suppose the base of the ladder slides away…

A: Rate of change

Q: A 10​-foot ladder is leaning against a vertical wall​ when Jack begins pulling the foot of the…

A: The given data can be expressed in a right triangle as shown below.

Q: A 12 foot ladder is leaning against a wall. If the top slips down the wall at a rate of 2 ft/s, how…

A: Given: Since the height is decreasing.     To determine:

Q: A person is standing at the end of a pier 12ft above the water and is pulling on a rope attached to…

A: Given,

Q: A ladder 10 ft long leans against a building. If the bottom of the ladder slides away from the…

A: Given A ladder 10 ft long leans against a building. If the bottom of the ladder slides away from the…

Q: A boat is pulled into a dock by a rope attached to the bow of the boat and passing through a pulley…

A: We have  height of pulley =1 m rate of approach =1 m/s We can assume a triangle as Where x as base…

Q: A 25-foot ladder is leaning against a wall and the base begins to fall away from the wall. When the…

A: A 25-foot ladder is leaning against a wall and the base begins to fall away from the wall. When the…

Q: A ladder 20 feet long leans against a house. What is the rate at the top of a ladder that is moving…

A: Given that ,      A ladder 20 feet long leans against a house. We have to calculate the rate at the…

Q: A 5-foot ladder is leaning against a vertical wall. If the bottom of the ladder is being pulled away…

A: To find the rate of change of area of the triangle formed .

Q: A 25-ft ladder is leaning against a wall. If we push the ladder toward the wall at a rate of 1…

A: Given that

Q: A woman is flying a kite on a long string. The kite itself has a 150 ft above the ground of the wind…

A: In the question we have to find the rate of string to let out.

Q: A boat is pulled into a dock by rope attached to it and passing through a pulley on the dock…

A: Calculus

Q: A 10-foot ladder is placed against a vertical wall. Suppose the bottom of the ladder slides away…

A:

Q: A rope is attached to a boat at water level, and a man on the dock is pulling on the d) rope at the…

A: Draw a schematic diagram of given figure.

Q: A 20 foot ladder is resting against the wall. The bottom of the ladder is being pushed towards the…

A:

Q: A ladder 20 ft. long leans against a vertical wall. If the top slides downward at the rate of 2…

A:

Q: A 15-foot ladder is leaning against a mango tree. If the top of the ladder is sliding down the tree…

A: We need to find rate of bottom of ladder moving.

Q: A 10 ft ladder leans against a wall. If the top of the ladder slides down the wall at a rate of 2…

A:

Q: A bucket that weighs 4 lb and a rope of negligible weight are used to draw water from a well that is…

A:

Q: A spherical balloon is inflated so that its volume is increasing at the rate of 2.2 ft^3/min. How…

A:

Q: A boat is pulled toward a dock by means of a rope wound on a drum that is located 3 ft above the bow…

A: a rough sketch of the problem will be as follows:

Q: A boat is pulled into a dock by a rope attached to the bow of the boat and passing through a pulley…

A:

Q: A 10-ft ladder rests against a vertical wall. If the bottom of the ladder slides away from the wall…

A: Solution..

Q: A 14 ft ladder is leaning against a wall. If the top of the ladder slides down the wall at a rate of…

A:

Q: A boat is pulled into a dock by means of a rope attached to a pulley on the dock. The rope is…

A: Given

Q: A 10-ft ladder is leaning against a wall. If the top of the ladder slides down the wall at a rate of…

A: GivenA 10-ft ladder is leaning against wall .{ HereAB is wallAC is ladder }Let the height of the…

Q: A boat is pulled into a dock by means of a rope attached to a pulley on the dock. The rope is…

A: Introduction:Denote the horizontal distance of the front of the boat from the dock as x.Denote the…

Q: A 26 foot ladder is sliding down a vertical wall.  The base of the ladder is sliding away from the…

A:

Q: A 5 meter long ladder is leaning against a wall. If the bottom of the ladder is being pushed towards…

A: Let AB is h=5 m long ladder leaning against the wall AC. Distance between the bottom of the ladder…

Q: A spherical balloon is inflated so that its volume is increasing at the rate of 2.8 ft^3/min. How…

A: Given  dVdt=2.8  ft3/ min and D=1.6 ft

Q: A 13-ft ladder is leaning against a wall. If the top of the ladder slips down the wall at a rate of…

A:

Q: A 13 foot ladder is leaning against a wall. If the top slips down the wall at a rate of 4 ft/s, how…

A: Let x be the distance between wall and bottom of ladder and y be the distance of top of ladder from…

Q: A ladder 20 feet long rests against a vertical wall. If the bottom of the ladder slides away from…

A:

Q: A street light is at the top of a 29 ft pole. A 4 ft tall girl walks along a straight path away from…

A: Draw a diagram that illustrates the given information Let x be the distance to the girl from the…

Q: A boat is pulled into a dock by a rope attached to the bow of the boat and passing through a pulley…

A: Let A= Pulley , B= Boat Given that AC=1  Let, x= distance of the boat from the dock. y=length of the…

Q: A boat is pulled into a dock by a rope attached to the bow of the boat and passing through a pulley…

A: The dock is 1m higher than the bow of the boat. Pulled rate of the rope of 1.4m/s To calculate the…

Q: A 17 ft ladder is leaning against a wall. If the bottom of the ladder is pulled along the ground…

A: x2+y2=172=289Differentiate with respect to 't'2xdxdy+2ydydt=0   xdxdt+ydydt=0

Q: A 13 foot ladder is leaning against a wall. If the top slips down the wall at a rate of 2 ft/s, how…

A: A 13 feet ladder is leaning against the wall. The top slips down the wall at a rate of 2 ft/s. The…

Q: A small balloon is released at a point 150 feet away from an observer who is on level ground. If the…

A: we have to find

Q: a kite 100 ft ft above the ground moves horizontally at a speed of14ft/s. at what rate is the…

A: If you like the solution then please give it a thumbs up..... The Answer is:     Result = - 0.035…

Q: A worker on a scaffolding 85 feet above the ground needs to lift a 115 pound bucket of cement from…

A:

Q: A ladder 20 meters long leans against a wall. If the bottom of the ladder is being pushed towards…

A: Given a ladder 20 meters long leans against a wall. If the bottom of the ladder is being pushed…

Q: A 25-foot ladder is leaning against a house. The base of the ladder is pulled away from the house at…

A: Let x be the base of the ladder dxdt=3 feet/sec ladder = z = 25 feet x=7 feet y=252-72=24 feet

Q: a 10-foot ladder is leaning against a vertical wall when Jack begins pulling the foot of the ladder…

A:

Q: A 27 ft ladder is leaning against a vertical wall when Jack begins pulling the foot of the ladder…

A:

Q: A 25 -foot ladder is leaning against a vertical wall​ when Jack begins pulling the foot of the…

A:

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.