Ship A is 70 km west of ship B and is sailing south at the rate of 25 kph. Ship B is sailing north at the rate of 45 kph. How fast is the distance between the two ships changing 2 hours later?

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: 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 510 mi / hr due east. At 1:00 p.m., another…

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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 ship moving 8 mph sails north for 30 minutes then turns east. If a searchlight at the point of…

A:

Q: One speed skater starts across a frozen lake at an average speed of 9 m/s. Ten seconds later, a…

A: Let t= time in second d=distance Also, consider second skater time in second is t .

Q: Car A is traveling west at 50 mi/h and Car B is traveling north at 60 mi/h. Both are headed for the…

A: In first question we find out dz/dt .and in 2nd question first we put dy/dx=0 for extreme values.and…

Q: One car leaves a given point and travel north at 30 mph. Another car leaves 1 hour later, and travel…

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

A:

Q: A spotlight on the ground is shining on a wall 24m away. If a woman 2m tall walks from the spotlight…

A: Here we use the application of derivative

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…

A:

Q: Two people start from the same point. One walks east at 2 km/h and the other walks northeast at 3…

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Q: wo cars start moving from the same point. One travels south at 16 mi/h and the other travels west at…

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Q: Two runners start moving from the same point. One runs north at 8 km/hr and the other runs east at 6…

A: Pythagoras Theorem states that the square of the hypotenuse is equal to the sum of the squares of…

Q: lamppost 6 m high at the rate of 1.3 m/sec. At what rate is the end of the person’s shadow moving…

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Q: How fast is the circumference of a circle changing if the radius is changing at the rate of 3 mm/s?

A: Solution

Q: The length of a rectangle is increasing at the rate of 2 feet per second, while the width is…

A: Let length = x feet and width = y feet  Given that dx/dt= 2 and dy/dt= 1

Q: Two people on bikes are separated by 350 meters. Person A starts riding north at a rate of 2m/sec…

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Q: Two cars are headed for the intersection of the two roads. If Car A is travelling south at 49 km/h…

A:

Q: The length of a rectangle is increasing at a rate of 4cm/s and its width is increasing at a rate of…

A: The length of a rectangle is increasing at a rate, dldt = 4 cm/s The width of a rectangle is…

Q: Two people start from the same point. One walks east at 2km/h and the other walks northeast at 3…

A: Given

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

A:

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

A: Let y be the distance of lighthouse from nearest point on the shoreline and at time t, the beam…

Q: Two cars are headed for the intersection of the two roads. If Car A is travelling south at 45 km/h…

A:

Q: Two automobiles start from a point A at the same time. One travels west at 80 km/hr and the other…

A: Topic:- application of derivatives

Q: A man rows up a stream 4 ½ hours and finds that it requires only 2 ½ hours down the stream. If he…

A: To find: The rate of current. Given: A person rows up a stream 412 hours and 212 hours to down the…

Q: One speed skater starts across a frozen lake at an average speed of 9 m/s. Ten seconds later, a…

A:

Q: Car A is traveling west at 50 mi/h and car B is traveling north at 60 mi/h. Both are headed for the…

A: topic - application of derivatives

Q: C. Two cars start moving from the same point. One travels east at 55mi/h and the other travels south…

A: We use Pythagoras theorem

Q: At what rate is the distance between Jack and Jill changing if Jack is 3 miles from the bakery and…

A: Given:         To determine:

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

A:

Q: A spotlight on the ground is shining on a wall 24m away. If a woman 2m tall walks from the spotlight…

A:

Q: Charley stands 34 meters west of Robert. Robert starts walking north at a speed of 2 m/s, and…

A:

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: Car B starts 30 miles directly east of car A and begins moving west at 90 mph. At the same moment…

A: We construct a triangle as shown below.

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

A:

Q: Two cars are initially 1200 miles apart. At the same time Car A starts driving at 35 mph to the east…

A: Given ,  Two cars are initially 1200 miles apart  At the same time Car A starts driving at 35 mph to…

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

A:

Q: A helicopter flies parallel to the ground at an altitude of 1/2 kilometer and at a speed of 2…

A:

Q: he surface area of a cube is increasing at a rate of 122.2 cm2/s. At what rate is the side length of…

A:

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

A:

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

A:

Q: A man 6 ft. tall is walking towards a building at the rate of 4 ft./sec. If there is a light on the…

A:

Q: A boat takes 2/3 as much time to travel downstream from C to D, as to return, If the rate of the…

A: A boat takes 2/3 as much time to travel downstream from C to D, as to return. If the rate of the…

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

A:

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

A: