A van is 5km due north of a bus at 2:00PM. If the van is traveling northward at the rate of 60 kph and the bus is traveling westward at the rate of 75 kph, how fast will the two be separating at 5:00PM?

Q: f. A truck travelling southwards at 40 kph and a car traveling eastward at a rate of 60 kph are…

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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: An airplane is flying west at 500 ft/sec at a constant altitude of 4000 ft and a searchlight on the…

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Q: The length of a rectange is increasing at a rate of 8 cm/s and its width is increasing at a rate of…

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Q: A rocket, rising vertically, is tracked by a radar station that is on the ground 5 mi from the…

A: Given that: Rate of increase of distance from radar station = 2000 mi/hDistance between radar…

Q: At noon, ship A is 160 km north of ship B. Ship A is sailing south at 40km/h and ship B is sailing…

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Q: An airliner passes over an airport at noon traveling 520 mi/hr due east. At 1:00 p.m., another…

A: Given: An airliner passes over an airport at noon traveling 520 mi/hr due east. At 1:00 p.m.,…

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: An airliner passes over an airport at noon traveling 510 mi / hr due east. At 1:00 p.m., another…

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Q: Two cars start moving from the same point. One travels south at 60 km/h and the other travels west…

A: follow next step

Q: A truck travelling southwards at 40kph and a car traveling eastward at a rate of 60kph ar headed for…

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Q: A 13-foot ladder is placed against a wall. If the top of the ladder is sliding down the wall at 3…

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Q: A van is 5 km due north of a pus at 2:00 PM. if the van is traveling northward at the rate of 60 kph…

A: The rate at which the distance between bus and van is changing is solved below

Q: An auto A is moving at 20 ft/s and accelerating at 5 ft/s2 to overtake an auto B which is 384 ft…

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Q: Two cars start moving from the same point. One travels south at 32 mi/h and the other travels west…

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Q: A truck is 300 kilometers due east of a car and is traveling west at a constant speed of 30km/hr.…

A: (a) Let the initial position of the car be at the origin. Take the x-axis from west to east and the…

Q: At noon Person A is 15 km east of person b. person A is walking west at 3km/h, and person b is…

A: initially A and B apart 15 km apart that  person A moves towards west at rate (da/dt) = 3 km/hr…

Q: At noon, ship A is 170 km west of ship B. Ship A is sailing east at 40 km/h and ship B is sailing…

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Q: Two cars start moving from the same point. One travels south at 48 mi/h and the other travels west…

A: Given the data :

Q: An automobile uses gasoline at a rate of 12 kilometres per litre and has a 65 litre tank. How far…

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Q: An airplane flying on a straight flight path will be exactly above a radar tracking station, which…

A: Given: Perpendicular distance between station and plane is 5,000 km To find rate of distance of…

Q: A 3-m long steel pipe has its upper end leaning against a vertical wall and the  lower end on a…

A: Given that: Length of steel pipe=3mLower end moves away from the wall at a speed = 2cm/s

Q: A ladder 10 feet long is leaning against a wall, with the foot of the ladder 8 feet away from the…

A: To determine the rate at which the ladder is sliding.

Q: Two buses are driving along parallel freeways that are 20 mi apart, one heading east and the other…

A: In right angle triangle , B2  + P2 = H2   ( Using Pythagoras Theorem ) Where B is base , P is…

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 lighthouse is located on a small island 4km away from the nearest point P on a straight shoreline,…

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Q: Two railroad tracks are perpendicular to each other. At 12:00 P.M there is a train at each track…

A: Given: Two railroad tracks are perpendicular to each other. At 12:00 P.M, two trains at each track…

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: We sketch the situation roughly  Let us assume x=the distance of the boat from the dock y=the…

Q: A girl starting at 11 A.M., travels east at 4 km/hr while a boy, starting at noon from the same…

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Q: Two airplanes are flying in the air at the same height. Airplane A is flying east at 494 mi/h and…

A: Point A represents position of airplane A. Point B represents position of airplane B.Point C…

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

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Q: The sides of the square are increasing at a rate of 3 cm per second . When the sides are 5cm long ,…

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

A: From the given information, draw a picture.

Q: Two railroad tracts are perpendicular with each other. At 12:00PM, there is a train on each track…

A:

Q: Two cars start moving from the same point. One travels south at 84 mi/h and the other travels west…

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Q: At noon,ship a is 130 km west of ship b.Ship a is sailing east at 25 km/h and ship b is sailing…

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

Q: an ice cube is shrinking uniformly at a rate of 8 cubic inches per hour. when the cube has a volume…

A: We are given the rate of change of volume of ice cube is shrinking uniformly at a rate of 8 cubic…

Q: Two cars start moving from the same point. One travels south at 64 mi/h and the other travels west…

A:

Q: A tubular metal 3.9 meters long leans against a vertical wall and the other foot of the metal is on…

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Q: A 20-ft ladder is leaning against a wall, and the top of the ladder is sliding down the wall at a…

A: We have been given a 20ft ladder which is leaning against a wall and is sliding down the wall AD.…

Q: Car A is traveling west at 50 mih and car B is traveling north at60 mih. Both are headed for the…

A: Since, we have been given that Car A is travelling west at 50 mi/hand Car B is travelling north at…

Q: At noon, ship A is 180 km west of ship B. Ship A is sailing east at 40 km/h and ship B is sailing…

A: Consider the following:

Q: A and B start toward each other at the same time from points 150 miles apart. If A went at the rate…

A:

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 80 foot ladder leaning against a wall is being pushed so that the bottom of the ladder is sliding…

A: Here dydt=6feet/secondx=48 feety=64feet

Q: A 22-foot ladder is leaning against a building. If the bottom of the ladder is sliding along the…

A: Leader is leaning against wall at AC=22 ft. Distance of the ladder from the wall is x=15 ft. Let the…

Q: A car starting at 12:00 noon travels west at a speed of 30 kph. Another car starting from the same…

A: Given: A car starting at 12:00 noon travels west at a speed of 30 kph. Another car starting from the…

Q: 2. Ship A is 15 miles east of O and moving west at 20 mi/hr, ship B is 60 miles south of O and…

A: Given : Ship A is moving west at 20 mph and ship B is moving north at 15 mph