Related rates Definition and 371 Threads

  1. QuarkCharmer

    Related Rates, Boats Moving Around

    Homework Statement Stewart Calculus 6E, 3.8 #14 At noon, ship A is 150km west of ship B. Ship A is sailing east at 35km/h, and ship B is sailing north at 25km/h. How fast is the distance between the ships changing at 4pm? Homework Equations Distance Formula I think. The Attempt at a...
  2. N

    Calculating the Rate of Water Height Increase in a Filling Swimming Pool

    Ok, I've been trying to figure this problem out of an old textbook for a couple days but seem to get nowhere. "A swimming pool with a rectangular surface 18 meters long and 12 meters wide is being filled at the rate of .80m^3/min. At one end it is 1.0 m deep and at another it is 2.5 m deep...
  3. C

    What is the related rates problem for a ladder leaning against a wall?

    Homework Statement A ladder of 25 feet long is leaning against the wall of a house. The base of the ladder is pulled away at 2 ft per second. (a) How fast is the top of the ladder moving down the wall when the base is seven feet from the wall? (b) Consider the triangle formed by the...
  4. M

    Calculating Related Rates of a Metal Cube

    Homework Statement Dear All, I am having problems understanding how to deal with related rates. The problem is the following: A solid 400gm metal cube of size length 10cm expands uniformly when heated. If the length of its side expand at 0.5cm(hr), find the rate at which, after 5...
  5. M

    Basic Related Rates: Rate of change of length of shadow

    Homework Statement A 6-ft man walks away from a 15-ft lamppost at a speed of 3 ft/s. Find the rate at which his shadow is increasing in length. Homework Equations Pythagorean Theorem, Theorem of Similar Triangles (ratios of corresponding sides are equal) The Attempt at a Solution...
  6. C

    Related rates yeast cells problem

    Homework Statement The number of yeast cells in a laboratory culture increases rapidly at first but levels off eventually. The population is modeled by the function below n=f(t)=\frac{a}{1+be^{-t}} where t is measured in hours. at time t=0 the population is 20 cells and is increasing...
  7. A

    Related Rates air in a balloon

    Homework Statement Air is being pumped into a spherical balloon so that its volume increases at a rate of 70 cm3/s. How fast is the surface area of the balloon increasing when its radius is 5 cm3?Homework Equations A ball with radius r has the following volume (V) and surface area (S): V =...
  8. A

    How is the Height of Water in a Container Changing Over Time?

    Homework Statement If there is a container with a radius in feet given by r(z)=10/sqrt(z) and it is being filled at a constant rate of 22pi ft^3/min. find a function that gives the height of the water as a function of time.The Attempt at a Solution since the radius is a function of the...
  9. S

    Related rates problem involving a piston (simple)

    Homework Statement A piston is seated at the top of a cylindrical chamber with radius 5 cm when it starts moving into the chamber at a constant speed of 3 cm/s. What is the rate of change of the volume of the cylinder when the piston is 2cm from the base of the chamber? Homework...
  10. M

    Understanding Related Rates: In-Depth Explanation and Homework Help

    Homework Statement I am reading about related rates in my calc book but it doesn't really explain it very well. Are there any arcitcals some one can send me that goes indepth about this concept on related rates? Thank you.
  11. M

    Calculating Related Rates: Cone Fluid Flow

    Homework Statement Fluid flows out of a cone at 3 cu ft/min. If the height of the cone is three times the radius how fast is the height of the fluid decreasing when the fluid is 6 inches deep in the middle? The Attempt at a Solution 1. V= ( (pi)(r^2)(h) ) / 3 2. r = h/3 thus... V =...
  12. B

    Trough - Related Rates Problem

    Okay so I have this related rates problem for my AP Calculus Class A trough (Extruded Trapezoid) with a height of 2, Base 1 (bottom) of 2, Base 2 (top) of 6 and a extrusion of 10. (I provided a picture for better understanding) --------------------------------------… A = Area of the top...
  13. M

    Related Rates + HOw to find a variable

    Gravel is being dumped from a conveyor belt at a rate of 30 ft3/min and its coarseness is such that it forms a pile in the shape of a cone whose base diameter and height are always equal. How fast is the height of the pile increasing when the pile is 10 ft high? Known: dV/dt=30 ft^3/min...
  14. M

    Related Rates Problem: Calculating Change in Distance of a Bird and Squirrel

    Related Rates Promlem, Please Help! Homework Statement A bird of prey is perched at the top of a tree that is 40 m high. The bird watches as a delectable Kingston squirrel runs away from the base of the tree at a rate of 2 m/s. What is the rate of change of the distance between the bird...
  15. A

    Related Rates: Solving Radar Station Angle Change Problem

    Homework Statement At a certain moment, a plane passes directly above a radar station at an altitude of 3 miles at a speed of 300 mph. Suppose that the line through the radar station and the plane makes an angle θ with the horizontal. How fast is θ changing 50 min after the plane passes over...
  16. H

    Related rates and the volume of spheres

    Homework Statement The volume of a spherical balloon is increasing at a rate of 4m^3/min. How fast is the surface area increasing when the radius is three meters? Homework Equations V=4/3piR^3 A=4piR^2 The Attempt at a Solution V=s.a.*R/3 dv/dt=d(s.a.R/3)/dt...
  17. G

    Related Rates of a Triangle with Fixed Side Lengths

    Homework Statement Two sides of a triangle of fixed length measure 12m and 15m. The angle between these two sides increases at a rate of 2 degrees per minute. When the angle between these two sides is 60 degrees, at what rate is the third side increasing? Homework Equations That's the...
  18. C

    Related Rates - Differential Equations

    Homework Statement A ladder, of length 13m, is leaning against a wall. The base of the ladder begins to slide, frictionless, away from the wall; by the time the base is horizontally 12m away from the wall it is moving at a rate of 2ms-1 a)How fast is the top of the ladder sliding down the...
  19. A

    How do we calculate the rate of water level increase in a sloped swimming pool?

    URGENT - related rates pool problem Homework Statement A swimming pool with a rectangular surface 18 m long and 12m wide is being filled at the rate of 0.8 cubic metres/min. At one end the pool is 1m deep and at the other end it is 2.5m deep, with a constant slope between the ends. How fast...
  20. F

    Solving Related Rates Problem: Find dz/dt Given Coordinates and Derivative

    Homework Statement [PLAIN]http://img638.imageshack.us/img638/2218/questionscreenshot.jpg The attempt at a solution Step 1. Draw a triangle. Solve for third side (Pythagorean theorem), which I called z. z^2 = x^2 + y^2 Coordinates are given (4, 6). We know x = 4, y = 6...
  21. D

    Related Rates - Cylindrical Pools

    Homework Statement 2 Cylindrical pools are filled simultaneously at the same rate, 1m3/min. The smaller pool has radius 5m and the water level rises at a rate of 0.5m/min. The larger pool has a radius 8m. How fast is the water level rising in the larger pool? Homework Equations V =...
  22. D

    Related rates with circular motion

    Homework Statement I was really struggling with a Calculus problem but I think I have the right answer, this is more just checking with someone than anything. When given a Ferris Wheel has a radius of 10 m, and that it takes 2 minutes for one rotation, find how fast it is moving from the...
  23. D

    Related Rates Problem Help - Understand Concepts & Look for Clues

    When trying to solve a related rates problem, sometimes you need to relate variables. Can anyone help me with the conceptual reasoning or at least what to look for in these problems?
  24. P

    This related rates problem is killing me, help please?

    Homework Statement A pool is 20 ft wide, 40 ft long, 3 ft deep at the shallow end, and 9 ft deep at its deepest point. If the pool is shaped as shown (I attached a picture), and is being filled at a rate of 8 ft^3/min, how fast is the water level rising when the depth at the deepest point is...
  25. S

    Transient Tank Filling Problem (Related Rates?)

    Homework Statement "Consider the tank and water supply system as shown in the figure below. The diameter of the supply pipe, D1 = 20 mm, and the average velocity leaving the supply pipe is V1 = 0.595 m/s. A shut-off valve is located at z = 0.1 m, and the exit pipe, D2 = 10 mm. The tank...
  26. B

    Related Rates Ship Distance Problem

    Please answer this, it's so hard. Problem: At 12 noon, ship A travels due west at 100 knotsshiop B. After 4hours, ship B leaves the same port on the direction N30'W at 80 knots. How fast is the distance between two ships changing at 8PM in the same day? Reply please.I can't solve it...
  27. D

    Related Rates, Volume of liquid change

    Water is emptied from a spherical tank of radius 24 ft. The water in the tank is 8 ft deep and its level is decreasing at the rate of 2 ft/ min. At this time, what is the rate of change of the radius at the top of the water?
  28. B

    Related Rates: Kite String Angle Change

    Homework Statement A kite 100 ft above the ground moves horizontally at a speed of 8 ft!s. At what rate is the angle between the string and the horizontal decreasing when 200 ft of string has been let out? Homework Equations tan \o = x/y The Attempt at a Solution After...
  29. B

    How to Solve Related Rates Problems: Calculating Egg's Shadow Speed"

    One night, a toddler is dropping eggs from a windowof a building which is 20 feet above ground. A neighbor, hearing the commotion, looks through her window which is 15 feet from the toddler's window, on the same wall of the building, and at the same height. She shines a flashlight from her...
  30. O

    Swimming Pool Volume and Related Rates

    Homework Statement A swimming pool is 20 feet wide, 40 feet long, 3 feet deep at the shallow end and 9 feet deep at its deepest point. If the pool is being filled at a rate of 0.8 feet^3/min, how fast is the water level rising when the depth at the deepest point is 5 feet? Homework Equations...
  31. N

    A related rates problem (shouldn't be complicated)

    Homework Statement An inverted conical container has a diameter of 42 in and a depth of 15 in. If water is flowing out of the vertex at a rate of 35 \pi in^3 / sec, how fast is the depth of the water dropping when the height is 5 in? Homework Equations v= (1/3) \pi r^2 * h The...
  32. U

    Related rates change in distance between two boats?

    Homework Statement Two boats leave a dock at the same tie. One goes south at 30 km/h and the other goes southwest at 40 km/h. What is the rate of change of the distance between the 2 boats, 30 minutes after they leave? I know how to do these questions when it's a right triangle...but since...
  33. H

    Finding the Rate of Water Input in a Leaking Conical Tank

    Homework Statement Water is leaking out an inverted conical tank at the rate of 50L/min. The tank has a diameter of 10m at the top and is 6m deep. if the water is rising at the rate of 4cm/min when the greatest depth is 3m, find the rate at which the water is being poured into the tank...
  34. R

    Related Rates Problem: Calculating Sand Leak Rate from Conical Pile Height

    Hi, I've tried this too many ways and i can't seem to figure it out. the question is: As sand leaks out of a hole in a container, it forms a conical pile whose altitude is always the same as its radius. If the height of the pile is increasing at a rate of 6in/min, find the rate at which the...
  35. R

    Visualizing a Cone with Constant Altitude and Variable Radius

    Hi, I've tried this too many ways and i can't seem to figure it out. the question is: As sand leaks out of a hole in a container, it forms a conical pile whose altitude is always the same as its radius. If the height of the pile is increasing at a rate of 6in/min, find the rate at which the...
  36. C

    Related Rates of Change Question

    Homework Statement A spherical tank with an interior diameter of 2m is being filled with water at a rate of 10 liters per second. Determine what rate the height of the water is increasing at when the tank is half full. Homework Equations V=\frac{2\pi r^3}{3}-\pi r^2d+\frac{\pi d^3}{3}...
  37. S

    Related Rates of Planes: Calculating Distance Change at Noon

    Homework Statement At ten am, a plane traveling east at 100km/hr is 500 km west of a jet traveling south at 200km/hr. At what rate is the distance between them changing at noon? Homework Equations The Attempt at a Solution 2aa' + 2bb' = 2cc' 2(300)(-100) + 2(400)(200) = (1000)c'...
  38. S

    How Fast Does the Water Level Change in a Conical Tank?

    Homework Statement Water si emptying out of a tank at a rate of 4 cubic metres/min. The tank is shaped like an inverted circular cone with a diameter of 8 m at the top. The sides of the cone make a 30 degree with the vertical. Determine the exact value of the rate of change of the water level...
  39. S

    Related rates question, shadow

    Homework Statement A man 6m tall walks away from a light 10m above the ground. If his shadow lengthens at a rate of 2m/s, how fast is he walking? Homework Equations The Attempt at a Solution I have nothing.
  40. S

    Related rates question conical reservoir

    Homework Statement A conical reservoir is 50m deep and 200m across the top. Water is being pumped in at a rate of 7000m^3/min, and at the same time, water is being drained out at a rate of 9000 m^3/min. What is the change in diameter when the height of the water in the reservoir is 20m...
  41. H

    Isosceles Triangle related rates problem

    Homework Statement A trough is 9 ft long and its ends have the shape of isosceles triangles that are 5 ft across at the top and have a height of 1 ft. If the trough is being filled with water at a rate of 14 ft3/min, how fast is the water level rising when the water is 8 inches deep...
  42. stripes

    Solving for Rate of Change of Depth in Swimming Pool

    Homework Statement A swimming pool is 5 m wide, 10 m long, 1 m deep at the shallow end, and 3 m deep at its deepest point. A cross-section is shown in the figure. If the poole is being filled at a rate of 0.1 m^3 per minute, how fast is the water level rising when the depth at the deepest...
  43. J

    What is the relationship between lighthouse location and beam rotation speed?

    Homework Statement A lighthouse is located off shore one mile from the nearest point P, on a straight coastline. The light makes 4 revolutions per minute. How fast is the beam of light moving along the shoreline when it is 2 miles from point P? Homework Equations The Attempt at a...
  44. K

    When calculus fails Related rates question

    Hi I was just curious as to why calculus does not seem to work in the situation of area calculation. I came across this doing some HW and noticed that the booked worked out a seemingly similar question in two separate ways First was predicitng the chance in the length of the hypotenuse...
  45. M

    Related Rates and acceleration

    I have a question about a related rates, i already solved it, but i would like someone to confirm it to me . * The relation between distance s and velocity v is given by v=\frac{150s}{3+s}. Find the acceleration in terms of s. As you can see my final answer is a in terms of v and s, not s only...
  46. L

    What is the Related Rate of a Growing Stalk's Shadow?

    Homework Statement A magic stalk starts growing at a spot 10 metres from a 4 metre lamppost. The stalk grows 1 metre per hour. Find the rate at which the length 's' of the stalk's shadow is increasing at the instant when the height h of the stalk is 3 metres. The Attempt at a Solution...
  47. E

    Related Rates Involving a Cone

    Homework Statement Water is being drained from a container which has the shape of an inverted right circular cone. The container has a radius of 5.00 inches at the top and a height of 7.00 inches. At the instant when the water in the container is 4.00 inches deep, the surface level is...
  48. Salazar

    Swimming Pools and Related Rates along with Implicit Differentiation

    Homework Statement A swimming pool is 40 feet long, 20 feet wide, 4 feet deep at the shallow end, and 9 feet deep at the deep end. Water is being pumped into the pool at 10 cubic feet per minute. a. When the water is 3 feet deep at the shallow end, at what rate is the water level rising? b...
  49. Salazar

    Air Traffic Controller and Related Rates along with Implicit Differentiation

    Homework Statement "An air traffic controller spots two planes at the same altitude converging on a point as they fly at right angles to each other. One plane is 120 miles from the point and is moving at 400 miles per hour. The other plane is 160 miles from the point and has a speed of...
Back
Top