A boat is being pulled into a dock by means of a winch 12 feet above the deck of the boat (see figure). The winch pulls in rope at a rate of 4 feet per second. How fast is the boat approaching the dock when there is 13 feet of rope out?

Q: 3. A light is hung 15 ft above a straight horizontal path. If a man 2 ft tall is walking away from…

A:

Q: A kite is flying at a height of 40 ft. A boy is flying it so that it is moving horizontally at a…

A: Given: Kite is moving horizontally at a rate of 3 ft per sec. To determine: The rate at which the…

Q: A swimming pool is 20 ft wide, 40 ft long, 3 ft deep at the shallow end, and 9 ft deep at its…

A: Refer to the figure shown below: [Note that we have to consider the depth of 5 ft to solve the…

Q: A kite is 40 ft. high with 50 ft. of cord out. If the kite moves horizontally at 5 mi. per hr.…

A: Draw the position of kite as shown below.

Q: The current in a typical Mississippi River shipping route flows at a rate of 4 mph. In order for a…

A: Let the speed of barge in still water be x miles per hour. Given the speed of river is 4 miles per…

Q: A street light is fastened to the top of a 15-ft-high pole. If a 5-ft-tall women walks away from the…

A: In the figure,  AB=15 ft DE=5 ft BD=yDC=xdydt=3 ft/sec

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 ladder 13 feet long is leaning against a house. The base of the ladder is pulled away from a wall…

A: Let,      x: The distance of the base of the ladder from the wall      y: The height of the ladder…

Q: A weight is attached to one end of a 33-foot rope which passes over a pulley 18 feet above the…

A: The above problem statement can be pictorially represented as:

Q: A light is hung 15 ft above a straight horizontal path. if a man 6 ft tall is walking away from the…

A: Solution :x=distance from lights=length of shadowlet,height of light,D=15 ftheight of…

Q: A girl flies a kite at a height of 300 ft, the wind carrying the kite horizontally away fromher at a…

A:

Q: A boat is being pulled with a rope towards a dock that is 10 ft above the water, as shown in the…

A: Let the distance of the boat= x ft y=length of the rope.  So,  given that dy/dt= 1.5 ft/min We have…

Q: A street light is mounted at the top of a 15-ft-tall pole. A man 6 ft tall walks away from the pole…

A: In the figure, x is the distance of pole from the man at the ground level. s is the length of the…

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

A:

Q: A man 6 ft tall walks along a level sidewalk away from a lamppost. On the post is a street light 18…

A:

Q: A kite 50 ft above the ground is moving horizontally at a rate of 4 ft/s. At what rate is the string…

A: We will be using the trigonometric ratios relating the sides of the triangle formed by strings and…

Q: A weight W is attached to a rope 50 ft long which passes over a pulley at P, 20 ft above the ground.…

A: Given: - A weight W is attached to a rope 50 ft, long which passes over a pulley at P, 20 ftabove…

Q: A person stands at the end of a pier 8 ft above the water and pulls in a rope attached to a buoy. If…

A:

Q: A street light is mounted at the top of a 15-ft-tall pole. A man 6 ft tall walks away from the pole…

A: Given  Height of the man =6ft  A street light is mounted at the top of a 15-ft-tall pole Let the…

Q: A street light is mounted at the top of a 15-ft-tall pole. A man 6 ft tall walks away from the pole…

A:

Q: 8. A street light hangs 24 ft. above the sidewalk. If a man 6 ft. tall walks away from the light at…

A: We can find the required as answer as below.

Q: A light is hung 15ft above a straight horizontal path. If a man 2 ft tall is walking away from the…

A:

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 street light is mounted at the top of a 15-ft-tall pole. A man 6 ft tall walks away from the pole…

A: Please refer the attached image for complete solution. THANK YOU !

Q: A light hangs 15ft above a horizontal path and a man 6ft tall is walking away at 5 ft/sec. i) How…

A: Given problem:- A light hangs 15ft above a horizontal path and a man 6ft tall is walking away at 5…

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 street light is mounted at the top of a 15-ft-tall pole. A man 6 feet tall walks away from the…

A:

Q: A girl flies a kite at a height of 300 ft, the wind carrying the kite horizontally away from her at…

A: Given A girl flies a kite at a height of 300 ft, the wind carrying the kite horizontally away from…

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 sketch the situation roughly  Let us assume x=the distance of the boat from the dock y=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 kite is flying at a fixed height of 30 ft. If 50 feet of stringis out alreadyfrom the spool, what…

A: Given: A kite is flying at a fixed height of 30 ft. If 50 feet of string is out already from the…

Q: A 50 ft ladder is placed against a wall, as shown below. The base of the ladder is slipping away…

A: Let the horizontal distance of the ladder is = x ft Vertical distance = y ft So, Given that:…

Q: A street light is mounted at the top of a 15-ft-tall pole. A man 6 ft tall walks away from the pole…

A: A streetlight is mounted at the top of a 15-ft-tall pole. A man 6 ft tall walks away from the pole…

Q: A ladder 20 feet long is leaning against an embankment inclined 60 degrees to the horizontal. if the…

A: The ladder is leaning against an embankment inclined 60 degrees to the horizontal has length 20…

Q: A boat that arrives at a dock 20 ft above water level is being pulled in by a fisherman using a rope…

A: To find: The speed of the boat approaching the dock when the total length of rope out is 50 feet.…

Q: A street light is mounted at the top of a 15-ft-tall pole. A man 6 feet tall walks away from the…

A: Diagram of the given question will be as following x is the distance of the man from pole y is the…

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: 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 kite at a height of 60 ft is moving horizontally at a rate of 5 ft/sec away from the boy who flies…

A: Let boy is at the point A, and when 100 ft cord is released the kite is at the point C, which is…

Q: 2. A ladder 13 ft long rests against a vertical wall. If the bottom of the ladder slides away from…

A:

Q: A car braked with a constant deceleration of 8 ft/s2, producing skid marks measuring 100 ft before…

A: constant deceleration of 8 ft/s2  skid marks measuring 100 ft

Q: A street light is mounted at the top of a 15-ft-tall pole. A man 6 ft tall walks away from the pole…

A:

Q: A 6-ft man walks away from a 16-ft high lamp post at the rate of 4 ft/s.  How fast does the tip of…

A: Given that, A 6-ft man walks away from a 16-ft high lamp post at the rate of 4 ft/s.

Q: A kite is flying at a fixed height of 30 ft. If 50 feet of string is out already from the spool,…

A: With the given details, we can draw a triangle . Here,  h is the vertical height at which kite is…

Q: A car braked with a constant deceleration of 16 ft/s2, producing skid marks measuring 50 ft before…

A:

Q: A ladder 20 ft long is leaning against an embankment inclined 60° to the horizontal. If the bottom…

A: Let x= distance of ladder from the embankment, y= vertical height. Given: dxdt=-1 ft/sec To find:…

Q: A hot air balloon is tethered at an angle of elevation of a/6. The rope holding the balloon is being…

A: Given Data: The angle of elevation is: α=π6 The rate at which the rope is being brought is: dxdt=-4…

Q: A street light is mounted at the top of a 15-ft-tall pole. A man 6 ft tall walks away from the pole…

A:

Q: The base x of the right triangle in the figure increases at a rate of 6 cm/s, while the height remai

A: In this question we will use basic of calculus i.e application of differentiation. We will first…