A child flies a kite at a height of 50 ft, the wind carrying the kite horizontally away from the child at a rate of 26 ft / sec. How fast must the child let out the string when the kite is 130 ft away from the child? The child must let out the string at a rate of ft/ sec when the kite is 130 ft away from the child.

Q: 3. A man 6 ft tall walks along a straight path away from a lamp post 15 ft high at the rate of 2…

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Q: A lamp post 3 m high is 6m from the wall. A man 2 m tall is walking directly from the post toward…

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Q: 4. A boy is flying a kite at a height 150 ft. If the kite moves horizontally away from the boy at…

A: Given query is to find the rate of change of length of string.

Q: A 12 foot ladder is leaning against a wall. If the top slips down the wall at a rate of 4 ft/s, how…

A: A 12 foot ladder is leaning against a wall. If the top slips down the wall at a rate of 4ft/s.

Q: 5. A kite 100 feet above the ground is being blown away from the person holding its string in a…

A: So, here x2+1002=s2...(1) Given dxdt=10 Now, at s=200, from (1):…

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Q: A 10-foot ladder leans against the side of a building. If the top of the ladder begins to slide down…

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Q: An equilateral triangle gutter is 27 ft long, 1 ft wide across the top, and 6 ft deep. If rainwater…

A: Let Vt be the volume of the water at time t. Given that dVdt=12 ft3/min Let h be the height of 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: A balloon is rising at a constant speed of 10 ft/sec. A boy is cycling along a straight road at a…

A: Explanation and solutions is given below....

Q: A kite 160 feet above the ground moves in a direction parallel to the ground at the rate of 5 feet…

A: Let, x= the horizontal distance of the kite y=the length of the string Given that dx/dt=5 ft/sec  We…

Q: A street light is at the top of a 16 foot tall pole. A 6 foot tall woman walks away from the pole…

A: Draw a diagram using the given information A 6 foot tall woman walks away from the pole with a…

Q: A ladder 10 feet long is leaning against the side of a vertical wall. The bottom of the ladder…

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Q: A ladder 25 feet is leaning against a wall. If the foot of the ladder is being pulled away from the…

A: To determine the rate at which the ladder is sliding. Given: Ladder is 25 feet long dx/dt = 14…

Q: A 14 foot ladder is leaning against a wall. If the top slips down the wall at a rate of 4 ft/s, how…

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

A: Calculus

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

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Q: a man 6ft tall walks at rate 5ft/sec away from a lamppost that is 13 ft high. At what rate is the…

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Q: A child flies a kite at a height of 70 ft, the wind carrying the kite horizontally away from the…

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

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Q: A 5-foot-tall person is walking towards a 7-foot-tall lamppost at a uniform rate of 2 feet per…

A: The rate of change of a function at a value is equal to the derivative of the function at that…

Q: A baseball diamond is a square with sides of length 90 ft. A batter hits the ball and runs toward…

A: Given data:     The given sides of the square is: a=90 feet. The speed of the batter towards the…

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

A:

Q: A child flies a kite at a height of 70 ​ft, the wind carrying the kite horizontally away from the…

A:

Q: Two boats leave a port at the same time: one travels west at 20 mi/hr and the other travels south at…

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

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Q: The speed of a moving sidewalk at an airport is 2ft/sec. A person can walk 45ft forward on the…

A: Let his speed on a non-moving sidewalk is = x ft/sec Given the speed of the moving sidewalk = 2…

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: 2. A man walks across a bridge at the rate of 5 ft/s as a boat passes directly beneath him at10…

A: From the given data , Man walks across a bridge in one second AC=5 feet and boat passes in one…

Q: 4. A basketball player is 7 feet tall walking away from a light that is 28 feet above the ground at…

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

A: This problem is based on the application of differentiation.  First we have to write an equation in…

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

A: Given : The pulley is 1 m higher than the bow The rate at which rope is pulled dydt=-1m/s and x=8.…

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 child flies a kite at 90ft. The wind is carrying the kite horizontally away from the child at a…

A:

Q: A street light is at the top of a 20 foot tall pole. A 6 foot tall woman walks away from the pole…

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Q: pushed

A: Given: A ladder 10 meters long is leaning against a wall. If the bottom of the ladder is being…

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A: Let the speed of second plane be x mph Then speed of first plane =(x-25) mph Distance travelled by…

Q: A street light is at the top of a 11.0 ft. tall pole. A man 6.5 ft. tall walks away from the pole…

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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 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: A 15 foot ladder is leaning against a wall. If the top slips down the wall at a rate of 4 ft/s, how…

A:

Q: A 15 foot ladder is leaning against a wall. If the top slips down the wall at a rate of 4 ft/s, how…

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…

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Q: A ladder 13 meters long is leaning against a wall. If the bottom of the ladder is being pushed…

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Q: Ship A is 70 km west of ship B and is sailing south at the rate of 25 kph. Ship B is sailing north…

A: At t = 0 { initial position } , distance between ships.Let the distance between ship A and ship B be…

Q: A tiger is 45 ft directly south of a herd of elephants. The tiger starts to slink towards the…

A: