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hen the distance of the plane from at the rate of 8,000 km/hr. At w

hen the distance of the plane from at the rate of 8,000 km/hr. At w

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
e An airplane flying on a straight flight path will be exactly above a radar tracking station, which is 5,000 km below the path. When the distance of the plane from the station is 40,000 km, this distance decreases at the rate of 8,000 km/hr. At what rate is the plane flying at that instance? novi f. A truck travelling southwards at 40 kph and a car traveling eastward at a rate of 60 kph are headed for an intersection. At what rate are the vehicles approaching each other when the truck is 1 km from the intersection while the car is 2 km from the intersection? g. Water is being poured at the rate of 5 m³/sec into an inverted conical tank of radius 10 m and altitude 20 m. How fast is the water level rising when the water level is at 8 m? (Note: Here you will be using the concepts of similar triangles in order to rewrite the radius in terms of the height.) itoun bont h. A particle is moving along the curve with equation y = 3-x. At the point (2, 1), it was observed that the x-coordinate is decreasing at a rate of 2 cm/sec. How fast is the y-coordinate changing at that instance?
Transcribed Image Text:e An airplane flying on a straight flight path will be exactly above a radar tracking station, which is 5,000 km below the path. When the distance of the plane from the station is 40,000 km, this distance decreases at the rate of 8,000 km/hr. At what rate is the plane flying at that instance? novi f. A truck travelling southwards at 40 kph and a car traveling eastward at a rate of 60 kph are headed for an intersection. At what rate are the vehicles approaching each other when the truck is 1 km from the intersection while the car is 2 km from the intersection? g. Water is being poured at the rate of 5 m³/sec into an inverted conical tank of radius 10 m and altitude 20 m. How fast is the water level rising when the water level is at 8 m? (Note: Here you will be using the concepts of similar triangles in order to rewrite the radius in terms of the height.) itoun bont h. A particle is moving along the curve with equation y = 3-x. At the point (2, 1), it was observed that the x-coordinate is decreasing at a rate of 2 cm/sec. How fast is the y-coordinate changing at that instance?
i. In a hot-air balloon contest, it was observed that a particular contestant's hot-air balloon rises vertically at a constant speed of 20 m/min. At an observation point 400 m away from the point directly under the hot-air balloon, determine how fast the angle of elevation of the balloon is changing when the time that had elapsed is 10 min. j. A boat that arrives at a dock 20 ft above water level is being pulled in by a fisherman using a rope at the rate of 1.5 ft/sec. How fast is the boat approaching the dock when the total length of rope out is 50 ft? K. Brain weight A grams was modeled to be a function of body weight B grams for a mouse, according to the equation A = 0.015B3. How fast is the brain weight increasing when the mouse's body weight is 200 grams? 1. Sand is being sifted onto a conical pile at the rate of 0.3 ft /sec. It was also observed thát at any instance, the base diameter of the pile is twice that of the height. How fast is the height of the pile increasing when the pile is 2 ft high?
Transcribed Image Text:i. In a hot-air balloon contest, it was observed that a particular contestant's hot-air balloon rises vertically at a constant speed of 20 m/min. At an observation point 400 m away from the point directly under the hot-air balloon, determine how fast the angle of elevation of the balloon is changing when the time that had elapsed is 10 min. j. A boat that arrives at a dock 20 ft above water level is being pulled in by a fisherman using a rope at the rate of 1.5 ft/sec. How fast is the boat approaching the dock when the total length of rope out is 50 ft? K. Brain weight A grams was modeled to be a function of body weight B grams for a mouse, according to the equation A = 0.015B3. How fast is the brain weight increasing when the mouse's body weight is 200 grams? 1. Sand is being sifted onto a conical pile at the rate of 0.3 ft /sec. It was also observed thát at any instance, the base diameter of the pile is twice that of the height. How fast is the height of the pile increasing when the pile is 2 ft high?
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