Related rates Definition and 371 Threads

Even problem, very please! A baseball diamond is a square with side 90 ft. A batter hits the ball and runs toward first base with a speed of 24 ft/s. a) At what rate is his distance from second base decreasing when he is halfway to the first base? b) At what rate is his distance from third...

[SOLVED] Related Rates Homework Statement Two aircraft are in the vicinity of a control center. Both are at the same altitude. Plane 1 is 36 nautical miles from the center and approaching it at a rate of 410 knots. Plane 2 is 41 nautical miles from the center and approaching it at a rate of...

Homework Statement How fast is the area of a square increasing when the side is 3 meters in length and growing at a rate of 0.8meter/minute? Homework Equations SA=LW L=3 dL/dt=0.8 The Attempt at a Solution I have no clue how to start this and I'm bad at word problems.

Homework Statement A rectangular swimming pool 16m x 10m is being filled at a rate of .8m^3/min. How fast is height of the water rising? Homework Equations V = LWH The Attempt at a Solution H = V/LW (dh/dt) = LW(dv/dt) (dh/dt) = (10)(16)(.8) This question looks so easy...

[SOLVED] Spherical Balloon - Related Rates Problem Homework Statement A spherical balloon is inflated so that its radius increases at a rate of 1 cm/min. How fast is the volume increasing when: a) the diameter is 2000 cm b) the surface area is 324 pi cm^2 ---> I have solved this already...

A sailor in a boat 10 km off a straight coastline wants to reach a point 20km along the coast in the shortest possible time. Toward what point on the shore should he head if he can row at 4 km/h and run at 12 km/h? i believe this involves optomizeation as well ralated rates but i am unsure as...

Need help! Related rates! Homework Statement I am stuck somewhere on a related rates problem, i think that i am missing something rather obvious, but i cannot figure out so far. -A street light is mounted at the top of the 15 ft-tall pole. A man 6 ft tall walks away from the pole with a...

Hey guys can anyone please help find the answer for A, I just can't figure out what they want. I mean I was still able to figure out the answer to B, but I just kept getting the answer to A wrong and I only have one try left. Please help...

Homework Statement A boat is pulled into a dock by means of a winch 12 ft. above the deck of a boat. (A) the winch pulls in rope at a rate of 4 ft/sec. What is the speed of the boat when there is 13ft of rope out. What happens to the speed of the boat as it gets closer to the dock? (B)The boat...

A cylinder is placed in oven where both the height and base radius expand at 0.1 mm/min. When the height is 250 mm and the radius of the base 30 mm, the volume is expanding at ...mm3 /min. (Answer to nearest whole number) r=30, h=250, dr/dh=0.1, dh/dt=0.1 dV/dt = (pi)r^2(dh/dt) +...

Water is leaking out of a cylindrical tank , with circular base radius 0.8 m at the rate of 0.2 m3/min. The water level is falling at ...? ..m/min. What is the question mark? (Hint: the radius does not change) V=(pi)r^2h, dV/dt = 0.2, r = 0.8 ? Can anyone give me a hand in getting this one...

Related Rates Help please! Homework Statement Two cars start moving from teh same point. One travels south at 60 mi/h and the other travels west at 25 mi/h. At what rate is the distance between the cars increasing two hours later?" Homework Equations So far I have the equation...

[SOLVED] Simple Related Rates Homework Statement A baseball diamond is a square 90 ft on a side. A runner travels from home plate to first base at 20 ft/sec. How fast is the runner's distance changing when the runner is half way to first base? Homework Equations a^2+b^2=c^2 The...

Homework Statement You are riding a Ferris wheel 120 feet in diameter. It makes one complete revolution every minute. How fast are you falling when you are halfway to the bottom? Homework Equations None The Attempt at a Solution I really am not sure where to start. I'm actually not even...

Homework Statement "A man pours water into a conical glass (with radius 9cm and height 6cm) at a rate of 8cm^3. At what rate is the height of the water changing per second when the height of the glass is 2/3rd's full of water? NOTE: The answer is supposedly 2/9(pi) cm/sec. I am supposed...

1. Homework Statement A child weighs 34 Kg is seated on a seesaw. While a child who weighs 40 kg is situated on the opposite end of the seesaw. The function B(x)= 34x / 40 gives the distance that the 40 kg child must sit from the center of the seesaw when the 34 kg child sits x meters from the...

Homework Statement A child weighs 34 Kg is seated on a seesaw. While a child who weighs 40 kg is situated on tghe opposite end of the seesaw. The functio B(x)= 34x / 40 gives the distance that the 40 kg child must sit from the center of the seesaw when the 34 kg child sits x meters from the...

A runner sprints around a circular track of radis 100m at a constant speed of 7m/s. The runner's friend is standing at a distance 200m from the center of the track. How fast is the distance between the friends changing when the distance between them is 200m...

Related Rates - Is my set-up correct? A water trough is 10ft long and its ends are isosceles triangles that are 3ft across the top and have height 1ft. If \frac{dV}{dt}=12\frac{\mbox{ft}^{3}}{\mbox{min}}, how fast is the water level rising when the water is 6 inches deep? V=\frac{1}{2}(b_1 +...

[SOLVED] Related Rates - Sort of confused Homework Statement There are two buildings. One 20' high and other 40' high with a 60' distance between them. A person walking between them creates a theta with the buildings (see pic) PICTURE...

A plane flying with a constant speed of 4 km/min passes over a ground radar station at an altitude of 14 km and climbs at an angle of 40 degrees. At what rate, in km/min is the distance from the plane to the radar station increasing 3 minutes later? The only equation I am using is the...

Homework Statement A boy is standing 50 ft. from the end of a swimming pool when he sees a girl 25 ft. along the end. He can swim 3 ft/s and run 5 ft/s. If he runs x feet, set up an equation for time consumed. Homework Equations There is a visual aid: A rectangle with length...

Homework Statement A man 6 ft tall wlaks at a rate of 5ft/s away from a light that is 15ft above the ground. when he is 10 ft from the base of the light, 1) at what rate is the tip of his shadow moving? 2) at what rate is the length of his shadow changing? The answers are 1) -50/7...

Homework Statement A rocket is 1/2 miles in the air going 40mi/h a bystander is standing 1 mile away from where the rocket took off straight up. What is the rate of change of the angle that the bystander makes with the rocket. Homework Equations The Attempt at a Solution I set...

Related Rates! help please! A and B are walking on straight paths that meet at right angles. A approaches at 2m/sec; B moves away from the intersection at 1m/sec. At what rate is the angle \vartheta changing when A is 10m from the intersection and B is 20m from the intersection. Ans in degrees...

Question A street light is mounted at the top of a 15 foot tall pole. A man 6 ft tall walks away from the pole with a speed of 6 ft/s along a straight path. How fast is the tip of his shadow moving when he is 40 ft from the pole? Attempt Well actually, I've drawn it out and stuff, but I was...

Homework Statement A flagpole 40 ft high stands on level ground. A flag is attached to a 120 ft rope passing through a pulley at the top of the flagpole. The other end of the rope is tied to a car at ground level. If the car is driving directly away from the flagpole at 3ft/sec, how fast is...

Homework Statement The length of the hypotenuse of a right triangle is 10 cm. One of the acute angles is decreasing at a rate of 5 degrees/s. how fast is the area decreasing when this angle is 30 degrees?Homework Equations The Attempt at a Solution I got the a and b using the cos and sin of...

Need help guys, not understanding this at all. Can anyone help me out? Two sides of a triangle and their included angle are changing with respect to time. The angle increases at the rate of 1 radian/sec, one side increases at the rate of 3ft/sec, and the other side decreases at the rate of...

Homework Statement A rectangle is expanding so that its length is always twice its width. The perimeter of the rectangle is increasing at a rate of 6cm/min. Find the rate of increase of the area of the renctangle when the perimeter is 40 cm. Homework Equations The Attempt at a Solution p = 6x...

Here is the solution to one of my problems: When inserting dV/dt to differentiate the equation as a function of time, why doesn't the book use the power rule on r^2 and multiply the entire equation by 2? I thought when dr/dt was put into the equation you had to differentiate?

I was pondering a question today. If you have a cube with a sphere inside of it, and the sphere is growing at 2 m/s. The cube itself is expanding at 1 m/s. If the cube is 5 x 5 x 5, and the sphere has a radius of 2. Is it possible to calculate when the sphere and the cube will be expanding...

Homework Statement "On a certain clock the minute had is 4in long, and the hour hand is 3in long. How fast is the distance between the tips of the hands changing at 9 o'clock?" Homework Equations - a^{2} + b^{2} = c^{2} - Law of Cosines? The Attempt at a Solution Ok i drew a clock...

Let x & y be differentiable functions of t and let s = sqrt(x^2+y^2) be the distance between the points (x,0) and (0,y) in the xy-plane. How is ds/dt related to dx/dt if y is constant? So I attempted to implicitly take the derivatives of the changing rates. ds/dt= 1/(2sqrt(x^2+y^2)) times 2x...

Related rates, roflcopter! Homework Statement A helicopter takes off from a landing pad at 10:48am and travels eastward at a speed of 120km/h. A second helicopter traveling south at 150km/h is planning to land at 10:59am, How fast is the distance between them chaging at 10:50am and is...

Homework Statement A light shines from the top of a pole 50 ft high. A ball is dropped from the same height at a point 30 ft away. (see thumbnail). How fast is the shadow of the ball moving along the ground .5 seconds later assuming ball falls a distance of s=16t^2 Homework...

Homework Statement #19 Homework Equations Implicit Differentiation The Attempt at a Solution I have a diagram and I am using the info given to establish some relationships. I guess my main concern is whether I have established a correct relationship between r and y as to eliminate one of...

The volume of a cap, of depth h cm, cut from a sphere of radius a cm (a>h) is given by V = {\textstyle{1 \over 3}}\pi h^2 (3a - h) . A bowl is in the shape of a cap of depth a/2 cm cut from a spherical shell of radius a cm. Water is being poured into the bowl at a constant rate of \frac{{\pi...

Consider the graph of y=x2. A point is moving along the x-axis in such a way, that its speed is proportional to its distance from the origin. At the same time, a point is moving along the curve of the graph, which always has the same x-value as the point moving along the x-axis. At what rate is...

1) (Related Rates) One end of a rope 20 meters long is attached to a box resting on the floor. The other end is passed over a pulley directly above the box, 5 meters above the floor, and attached to the back of a truck at a point 1 meters above the ground. The truck then drives in a straight...

I have this problem, and I have attepmted a classical approach without much success. A man 5 ft tall runs at a rate of 8ft/sec towards a source of light that arises vertically at a point A. The height of the light source H, is given by the formula h(t)=t^3 +1, in feet, where time t is...

Homework Statement The first problem is a related rates question: A swimming pool if 5m wide and 25m long, 1m deep at the shallow end and 4.5 deep at the deepest point. A cross section is shown in the figure below. The pool is being filled at a rate 0.5m^3/hr. Use calculus techniques to...

Homework Statement The side of a cube increases at 1 cm / s. How fast is the diagonal of the cube changing when the side is 1 cm? Homework Equations Involves: a^2+b^2=c^2 Implicit Differentiation Derivation The Attempt at a Solution I'm attempting to find the diagonal of the cube...

Homework Statement Water is draining from a conical tank with height 12 feet and diameter 8 feet into a cylindrical tank that has a base with area 400 \pi square feet. The depth, h, in feet, of the water in the conical tank is changing at the rate of (h-12) feet per minute. A) Write an...

Homework Statement This last related rates HW problem is givin me trouble for some odd reason. A plane flying with a constant speed of 4 km/min passes over a ground radar station at an altitude of 11 km and climbs at an angle of 25 degrees. At what rate, in km/min is the distance from the plane...

Homework Statement 2. Coffee is draining from a conical filter into a cylindrical coffee pot at the rate of 10 in3/min. a) How fast is the level in the pot rising? ____________ b) How fast is the level in the cone falling when the level in the cone is 5 in.? _________ Homework...

Homework Statement A particle is moving along the curve y=\sqrt{x}. As the particle passes through the point (4,2), its x-coordinate increases at a rate of 3 cm/s. How fast is the distance from the particle to the origin changing at this instant? Homework Equations The Attempt at a Solution I...

the altitude of a triangle is increasing at a rate of 1 cm/min while the area of the triangle is increasing at a rate of 2 cm^2/min. at what rate is the base of the triangle changing when the altitude is 10 cm and the area is 100 cm^2. do i use the pythagorin theorem for this

2 cars start moving from the same point. one travels south at 60 mi/h and the other travelks west at 25 mi/h. at what rate is the distance between the cars increasing 2 hourse later. What do i do. I need help some serious help with this one.

Homework Statement A stone dropped into a still pond sends out a circular ripple whose radius increases at a constant rate of 3 ft/s. How rapidly is the area enclosed by the ripple increasing at the end of 10 s?Homework Equations How do I even set up implicit differentiation? The Attempt at a...