A man starts walking north at 2 feet per second from a point P. A minute later a woman starts walking south at 1 foot per second from a point 800 feet due east of P. At what rate are the people moving apart 5 minutes after the woman starts walking?

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):…

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 13-foot ladder leans against a wall. The foot of the ladder begins to slide away from the wall at…

A:

Q: A 50 feet ladder is leaning against a wall of a building. Suppose the base of the ladder slides away…

A: Rate of change

Q: A ball is thrown vertically upwards with a velocity of 48 ft/s from the top of a building 35 ft…

A: Given that,

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

A: Given: Two cars start moving from the same point.One travels  south at 16m/h and the other travels…

Q: A fifteen-foot ladder leans against a wall and slides down, with the base of the ladder observed to…

A:

Q: One ship is sailing south at a rate of 5 knots, and another is sailing east at a rate of 10 knats.…

A: Let the time at 2:00 Pm be t  The two ships will form a right angled triangle, with horizontal side…

Q: Two airplanes are flying in the air at the same height: airplane A is flying east at 290 mi h and…

A: Given that:                      Speed of plain A, vA=290 mi/hSpeed of plain B, vB=290 mi/hDistance…

Q: Two cars start moving from the same point. One travels south at 24 mi/h and the other travels west…

A:

Q: A man 6 feet tall walks at a rate of 4 feet per second away from a light that is 15 feet above the…

A: Please see the explanation below

Q: . A man starts walking north at 4 ft/s from a point P. Five minutes later a woman starts walking…

A: We make diagram of the situation .

Q: A man starts walking north at 4 fts from a point . Fiveminutes later a woman starts walking south…

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: It is height and distance problem.

Q: A ladder 10 ft long rests against a vertical wall. If the bottom of the ladder slides away from the…

A: It is given that,

Q: kite 100 ft. above the ground moves horizontally at the speed of 8ft/sec. At what rate is the angle…

A:

Q: A ladder 13 feet long is leaning against the wall. If the base of the ladder is pushed toward 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…

A:

Q: A light is on the top of a 12 ft tall pole and a 5 ft 6 inches tall person is walking away from the…

A:

Q: A man 6 feet tall walks at a rate of 5 feet per second away from a light that is 15 feet above the…

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:

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 certain clock has an hour hand of length 4 in and a minute hand of length 5 in. In inches per…

A: Using law of cosines the distance between tips when the hands are at angle of θ is:…

Q: A runner starts at the beginning of a runners' path and runs at a constant rate of 5 mi/hr. Fifteen…

A: First, we need to calculate the relative speed which is, the difference between the speed of the…

Q: A man 6 feet tall walks at a rate of 7 feet per second away from a light that is 15 feet above the…

A: The given data is: A man 6 feet tall walks at a rate of 7 feet per second away from a light that is…

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 light is on the top of a 12 ft tall pole and a 5 ft 6 in tall person is waking away from the pole…

A: Given that:Height of the poll is 12 ft and height of the person is 5 ft 6 in or 5.5 ft.Let x and y…

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

A:

Q: and passes directly over a tracking telescope on the ground. When the angle of elevation is ?/4,…

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

Q: The fixed sides of an isosceles triangle are of length 6 cm. (See the figure.) If the sides slide…

A: Given: The fixed sides of an isosceles triangle are of length 6 cm and the sides slide outward at a…

Q: Two cars start moving from the same point. One travelssouth at 60 mih and the other travels west at…

A:

Q: A rubber ball is made to fall from a height of 70 feet and is observed to rebound 3/4 of the…

A: The sum, S, of the infinite geometric series, a+ar+ar2+ar3+⋯ is defined as S=a1-r. Here a is the…

Q: A man 6 feet tall walks at a rate of 7 feet per second away from a light that is 15 feet above the…

A: Let OA= height of light      CD= height of man      BC= length of shadow…

Q: a. How fast is the top of the ladder sliding down the wall when the base of the ladder is 12 feet…

A: It is given that the length of ladder is 13 foot which acts as the hypotenuse of the right angled…

Q: A man 6 ft tall walks at a rate of 5 ft/sec away from a lamppost that is 16 ft high. At what rate is…

A: Given: Height of the man, h=6 ft Height of the post, H=15 ft Walking rate, dxdt=5 ft/sec

Q: A ship leaves port at 2:00 PM and travels S30°E at the rate of 50 km/hr. Another ship leaves the…

A: Given that a ship leaves a port at 2:00 PM and travels S30degree East at the rate of 50km/hour and…

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 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: An observer who is 3km from a launchpad watches a rocket that is rising vertically. At a certain…

A: Rate of change

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 trough is 12 ft long and its ends have the shape of isosceles triangles that are 2 ft across at…

A: Let the volume of the water in the trough at time be V. The rate of change of V is,

Q: A kite is 30 ft. high and is moving horizontally at a rate of 10 ft./min. At what rate is the string…

A: Calculate the rate in the following way:-

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

A:

Q: Consider the given isosceles triangle of base 10 inches and side lengths x inches. If is increasing…

A:

Q: A balloon ascending at the rate of 12 ft/sec is at a height 80 ft above the ground when a package is…

A: Sol:-v0=12 ft/secHeight = h = 80 ftThen, y-y0=v0t-12gt2

Q: Ship A is 15 miles east of P and moving west at 20 mi/hr; ship B is 60 miles south of P and moving…

A: Given data: The speed of  A is dxdt=-20 mph. The speed of  B is dydt=15 mph. Position of A is xA=15…

Q: A ball is thrown vertically upwards with a velocity of 48 ft/s from the top of a building 35 ft…

A: topic-equations