A car is driving northwest at v mph across a sloping plain whose height, in feet above sea level, at a point n miles north and e miles east of a city is given by h(n,e)=1500+75n+50e. (a) at what rate is the height above sea level changing with respect to distance in the direction the car is driving?
Answers
Given:
[tex]h(n,e) = 1500 + 75n + 50e[/tex]
Define
[tex]\hat{r} = unit \, vector \, along \, \vec{v} \\ \hat{i} = unit \, vector \, east \\ \hat{j} = unit \, vector \, north \\ \nabla \equiv \hat{i} \frac{\partial}{\partial e} + \hat{j} \frac{\partial}{\partial n} [/tex]
[tex]\hat{r} = \frac{1}{ \sqrt{2} } (-\hat{i}+\hat{j} )[/tex]
Then the rate of change of h with respect to the vector v is
[tex]\nabla h . \hat{r} = \frac{1}{\sqrt{2}}(50\hat{i} + 75\hat{j}).(-\hat{i}+\hat{j}) = \frac{1}{\sqrt{2}} (-50+75) =17.68[/tex]
Answer: 17.7 ft per mile
Related Questions
A baseball team is practicing throwing balls vertically upward to test their throwing arms. A player manages to throw a ball that reaches a maximum altitude of 10 m above the launch point, before falling back down. The acceleration due to gravity is 9.80 m/s 2 . (a) With what initial speed was the ball thrown? (b) How long did it take for the ball to reach its maximum altitude?
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The speed of an aircraft is sometimes expressed as a mach number: mach 1 means that the speed is equal to the speed of sound. if you wish to determine the speed of an aircraft going mach 2.2, for example, in meters per second or miles per hour, what additional information do you need?
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Refrigerant 134a enters an insulated diffuser as a saturated vapor at 80°f with a velocity of 1453.4 ft/s. at the exit, the temperature is 280°f and the velocity is negligible. the diffuser operates at steady state and potential energy effects can be neglected. determine the exit pressure in lbf/in2 .
Answers
The exit pressure from the diffuser can be found by applying the energy balance, which involves the conversion of the aerodynamic velocity of the refrigerant on entry into an internal energy form. The specific enthalpies at the inlet and outlet aid in the calculation.
Explanation:In this question, we're dealing with a thermodynamics problem involving the diffuser of an HVAC system that uses Refrigerant 134a. In the beginning, the refrigerant enters as a saturated vapor with a certain temperature(80ºf) and velocity(1453.4 ft/s) and exits at different temperatures (280ºf) and negligible velocity. With the assumption of the system operating at a steady state and neglecting potential energy effects, we need to find the exit pressure of the diffuser.
This problem involves the application of the first law for the steady-flow process and Bernoulli's equation. The first law of thermodynamics for a steady-flow process can be written as:
ΔKE + ΔPE + Q = ΔH + W
Since it's given that potential energy effects can be neglected, we have only kinetic energy and enthalpy to consider. Bernoulli's equation can be used to express the principle of energy conservation in terms of fluid flow. At the inlet, the kinetic energy is quite significant, but negligible in the outlet, all of that kinetic energy is converted into internal energy (thermal form). So we can set up the energy balance based on these assumptions:
0.5 * (inlet velocity)^2 = (hout - hin)
where hout and hin are the specific enthalpies at the outlet and inlet respectively. We can find the values for these quantities in the thermodynamic table for Refrigerant 134a based on the given temperatures.
Once we solve this equation for hout, we can use another lookup in the table to find the pressure corresponding to the outlet temperature (280ºf) and the found enthalpy.
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"where are the majority of transform faults located?"
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HELP MEH a beachgoer leaves a pair of sandals on the shore while she swims, when she puts the sandals on again , the bottom of her feet will feel hot because____.
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Answer:
Explained
Explanation:
People visit beaches generally on sunny days. When we leave are sandals on the shore while we swim. The from the sum warm the Sole of the sandals because sandals are generally leather and leather are good absorbers of heat. And once we wear them back after swimming. The heat through conduction is passed on to our feet and our feet feel warm.
What would be the final temperature of the system if all the heat lost by the copper block were absorbed by the water in the calorimeter?
Answers
To find the final temperature of the system, we need to calculate the energy lost by the copper block and the energy gained by the water. Equating these values will allow us to solve for the final temperature.
Explanation:In order to find the final temperature of the system when all the heat lost by the copper block is absorbed by the water in the calorimeter, we need to consider the principles of heat transfer and calorimetry.
First, we need to calculate the energy lost by the copper block using the equation q = m * c * ΔT, where q represents the heat lost, m is the mass of the copper block, c is the specific heat capacity of copper, and ΔT is the change in temperature of the copper block.Next, we assume that all the heat lost by the copper block is absorbed by the water in the calorimeter. We can calculate the energy gained by the water using the same equation as before, but this time using the mass and specific heat capacity of water.Finally, we equate the energy lost by the copper block to the energy gained by the water, and solve for the final temperature of the system.By applying these steps, we can determine the final temperature of the system when all the heat lost by the copper block is absorbed by the water in the calorimeter.
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The final temperature of the system can be calculated using the principle of heat transfer and the concept of specific heat capacity. It assumes that the heat lost by the copper block is entirely absorbed by the water in the calorimeter. By setting up equations for heat change in both copper and water and equating them, we can solve for the final temperature.
Explanation:The final temperature of the system can be calculated using the concept of heat transfer, based on the assumption that the heat lost by the copper block is completely absorbed by the water in the calorimeter. This can be expressed mathematically as:
qmetal = -qwater
We use the formula for calculating heat change which is Q = mcΔT. Here, Q represents heat, m is mass, c indicates the specific heat capacity, and ΔT is the change in temperature (final temperature - initial temperature).
By setting up two situations (one for the copper and one for the water), we can assign known values of specific heat capacity (0.390 J/g°C for copper and approximately 4.18 J/g°C for water) and equate the two equations since the heat lost by the copper block equals the heat gained by the water. This allows us to solve for the final temperature of the system, which is the same for both the copper and the water.
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The molecules that make up a plastic two-liter bottle A) are in constant, rapid, random motion. B) have a volume of more than two liters if melted. C) expand to take the shape of wherever the bottle is placed. D) are closer together than the molecules of soda that they contain.
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hope this helps
The molecules that make up a plastic two-liter bottle are closer together than the molecules of soda that they contain.
What is solid?One of the four common states of matter is solid. Solids have tightly bonded molecules that can only vibrate. This means that solids have a fixed shape that only modifies under the application of force. This contrasts with the random movement of gases and liquids, known as flow.
Melting is the process by which a solid turns into a liquid. When liquids are frozen, they solidify. Dry ice is one of the few materials that can transform directly from a solid to a gas. Sublimation is the term used for this.
Numerous types of forces can exist between the atoms in a solid. For instance, ionic sodium and chlorine are bound together by ionic bonds to form the crystal structure of sodium chloride (common salt).
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A bored kid, 30 meters from a building throws a ball at an angle of 50 degrees with a velocity of 20m/s at the building wall. at what height above the throwing line will the ball hit the wall?
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Roberto was testing how light interacted with a material he had just developed. The initial speed of light was 3.0 × 108 m/s. The final speed of light after it changed direction was 1.7 × 108 m/s. What type of interaction took place?
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The answer to the question would be Refraction.
as we know the two possible answers are refraction and reflection. The questions shows a decrease in speed thus being refraction as a ray in a reflection would not lose its speed. Hope this helps!
Analyzing the question, we can classify the effect of refraction as the speed is reduced when entering the middle.
What is the concept of refraction?Refraction of light is a phenomenon that occurs in electromagnetic waves that are transmitted through some translucent or transparent medium. When light penetrates refractive media, that is, those capable of refracting light, its speed decreases.
the type of interaction that happend is refraction as the speed is reduced when entering the middle.
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A weightlifter is attempting a biceps curl with a 200 n barbell. the moment arm of the barbell about the elbow joint is 40 cm. the moment arm of the elbow flexor muscles is 4 cm. how much force must be produced by these muscles to hold the 200 n barbell in static equilibrium?
Answers
Final answer:
The biceps muscles need to produce a force of 2000 N to hold the 200 N barbell in static equilibrium.
Explanation:
To hold the 200 N barbell in static equilibrium, the biceps muscles need to produce a force equal to the weight of the barbell. The moment arm of the barbell about the elbow joint is 40 cm, so the torque exerted by the barbell is calculated as:
Torque = Force x Moment Arm
Torque = 200 N x 40 cm = 8000 N·cm
The moment arm of the elbow flexor muscles is 4 cm. To maintain static equilibrium, the torque exerted by the biceps muscles must be equal and opposite to the torque exerted by the barbell:
Torque biceps = Torque barbell
Force biceps x Moment Arm biceps = Force barbell x Moment Arm barbell
Force biceps x 4 cm = 200 N x 40 cm
Force biceps = (200 N x 40 cm) / 4 cm
Force biceps = 2000 N
The mixture you separated was mixture oof iron filings, sand, and salt. Based on your understanding of matter, is this mixture a homogeneous mixture or heterogeneous mixture? How do you know? A. Heterogeneous mixture-the parts are not uniformly mixed. B. Homogeneous mixture-the parts are uniform mixed C. Heterogenous mixture-the parts are uniformly mixed d. Homogenous mixture-the parts are not uniformly mixed
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Answer: Heterogeneous mixture
A mixture forms when different elements are put together and yet they are distinct. it means there is no change in the properties of individual components of a mixture. A mixture can be of two kinds: Homogeneous and Heterogeneous mixture. A homogeneous mixture is the one which has uniformity in its every part. For example: salt mixed in water is a homogeneous mixture. A heterogeneous mixture has visibly distinct components. The mixture was of iron fillings, sand and salt is a homogeneous mixture as the component parts are not uniformly mixed.
Mike is conducting an experiment in which he places several different types of soil in a funnel and then pours one liter of water through each. He is careful to pack equal volumes of the soil samples tightly in the funnel and to make sure that only water makes it out of the bottom. He then records the amount of time it takes for half of the water to pass through the soil and out the bottom of the funnel. He records his data in the table below.
Soil Sample Time (seconds)
Soil W 181
Soil X 27
Soil Y 119
Soil Z 50
Which soil sample is the least permeable?
A.
Soil W
B.
Soil Z
C.
Soil Y
D.
Soil X
Answers
Permeability is a measure of how fast a liquid can pass through a layer of solid. In this case, the lesser the time, the more permeable the solid is. Or the other way around, the bigger the time, the less permeable the solid is. Therefore the answer in this problem is:
A. Soil W
Answer:
soil W
Explanation:
Permeability is a measure of how easily water flows through soil. A soil that is made up of large, jagged rocks is likely to be more permeable than a soil that is made up of compact clay. One way to test a soil's permeability is to pour water through it. More permeable soil will allow water to pass through it rapidly, while less permeable soil will block more of the water.
The temperature of a system must increase when heat energy is added.
Please select the best answer from the choices provided
T
F
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a quantity of gas in a cylinder received 1600j of hear from a hot plate at the same time 800j of work are done on the gas what is the change in the internal energy?
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The nearest star to our sun is proxima centauri, at a distance of 4.3 light-years from the sun. a light-year is the distance that light travels in one year (365 days). part a how far away, in km, is proxima centauri from the sun?
Answers
Final answer:
The distance from the Sun to Proxima Centauri is approximately 40 trillion kilometers.
Explanation:
The distance from the Sun to Proxima Centauri is approximately 40 trillion kilometers.
To compute the separation from Proxima Centauri to the Sun in kilometers, we want to change the separation from light-years over completely to kilometers.
In the first place, we should switch 4.3 light-years over completely to kilometers.
The speed of light is around 299,792 kilometers each second.
To change light-years over completely to kilometers, we can utilize the accompanying recipe:
Distance in kilometers = Distance in light-years × Speed of light × Number of seconds in a year
Number of seconds in a year = 365 days × 24 hours × an hour × 60 seconds
Presently, we should connect the qualities:
Distance in kilometers = 4.3 light-years × 299,792 kilometers each second × (365 days × 24 hours × an hour × 60 seconds)
Computing the worth gives us:
Distance in kilometers ≈ 40,080,595,680 kilometers
Subsequently, Proxima Centauri is roughly 40,080,595,680 kilometers from the Sun.
The desert and tundra are alike because they both have
A) extreme daily temperature changes.
B) large seasonal variation.
C) limited available water.
D) sandy soils.
Answers
if im wrong plz let me know
Your answer is A.
G 1470-kilogram truck moving with a speed of 24.0 m/s runs into the rear end of a 1110-kilogram stationary car. if the collision is completely inelastic, how much kinetic energy is lost in the collision?
Answers
Kinetic energy = Potential energy
(1/2)mV^2 = mgh
where
m = mass of the car
V = velocity of the car = 15 m/s (given)
g = acceleration due to gravity = 9.8 m/sec^2 (constant)
h = vertical distance travelled by car = d(sin 19)
d = distance travelled by the car along the incline
Substituting values,
(1/2)(m)(529) = m(9.8)h
and since "m" appears on both sides of the equation, it will simply cancel out, hence the above becomes
(1/2)(529) = 9.8h
h = 225/19.6 = 26,98 m
Let
d = distance that the car will coast up the hill before coming down
h/d = sin 19
and therefore,
d = h/sin 19
and substituting values,
d = 26,98/sin 19
d = 82,870 m --- after coasting up the hill for this distance, the car will start to roll down.
A balloon at an amusement park has 1,500 g of gas. By what amount will the mass of the balloon decrease if all the gas inside it escapes?
- 750 g
- 1,500 g
-2,000 g
- 3,000 g
SOMEONE PLEASE HELP ME IT WILL BE SOOOO APPRECAITED!
Answers
Let m = the mass of the balloon material (g).
At state 1, the total mass of the balloon is the mass of the balloon material and the mass of gas.
The total mass in state 1 is
m₁ =(m + 1500) g
At state 2, 1500 g of gas has escaped. Only the mass of the balloon material remains.
The total mass in state 2 is
m₂ = m g.
The decrease in mass of the balloon is
m₁ - m₂ = (m + 1500) - m = 1500 g
Answer: 1,500 g
Answer:
Answer 1,500 g
because if it has 1,500 g and it loses ALL of the gas...
then it will lose 1,500 g
Hope this Helps!
A hypothetical spherical planet consists entirely of iron. what is the period of a satellite that orbits this planet just above its surface?
Answers
the same gravity force F=m*w^2*r is the centripetal force for the orbiting satellite, where angular speed w=2pi/T, T is period;
thus F=F; G*M*m/ r^2 = m*w^2*r; or;
G*(ρ* (4/3)*pi*r^3)/ r^2 = (2pi/T)^2*r; or;
G*ρ/3 = pi/T^2, hence T= √(3pi/(G*ρ)) =
= √(3pi/(6.6742E-11 *7860)) =4238.62s = 70h 38’;
The orbital period of a satellite orbiting just above the surface of a hypothetical iron planet is approximately 84.5 minutes. This calculation uses Kepler's third law and the known density of iron. The result is derived after integrating the gravitational constant and mass into the formula.
Orbital Period of a Satellite Around an Iron Planet
To determine the period of a satellite orbiting just above the surface of a hypothetical spherical planet made entirely of iron, we can use Kepler's third law in conjunction with some known information about iron and orbital mechanics.
The formula we use here is:
T = 2π √(r³ / GM)
where:
T is the orbital period.r is the radius of the planet.G is the gravitational constant, 6.67430 × 10-11 m³ kg-1 [tex]s^{-2[/tex].M is the mass of the planet.First, we need to calculate the radius of the iron planet. Iron has a density of about 7874 kg/m³. If we assume the planet has a volume V, the mass M can be related to the density ρ and radius r by:
V = 4/3 π r³
M = V × ρ or M = (4/3) π r³ ρ
Next, we substitute this mass into the orbital period formula:
T = 2π √[r³ / G (4/3 π r³ ρ)]
Simplifying, we get:
T = 2π √[3/(4πG ρ)]
Plugging in the values:
ρ = 7874 kg/m³
T = 2π √[3/(4π × 6.67430 × 10-11 m³ kg-1 s-2 × 7874 kg/m³)]
After performing the calculation:
T ≈ 5069.9 seconds ≈ 84.5 minutes
Thus, the orbital period of a satellite just above the surface of an iron planet is approximately 84.5 minutes.
A lightbulb has a resistance of 285 ω when operating with a potential difference of 110 v across it. what is the current in the lightbulb?
Answers
Current = voltage / resistance
= 110 v / 285 Ω
= 0.386 Ampere (rounded)
What minimum speed is required for the ball to clear the 0.90-m-high net about 15.0 m from the server if the ball is "launched" from a height of h = 2.70 m ?
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Suppose the ring rotates once every 3.80 s . if a rider's mass is 59.0 kg , with how much force does the ring push on her at the top of the ride?
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Which statement(s) correctly compare the masses of protons, neutrons, and electrons? Check all that apply.
Protons and neutrons have similar mass.
Protons and electrons have similar mass.
Neutrons and electrons have similar mass.
Protons are smaller than a neutron or an electron.
Neutrons are smaller than a proton or an electron.
Electrons are smaller than a proton or a neutron.
Answers
Protons and electrons have similar mass. FALSE
Neutrons and electrons have similar mass. FALSE
Protons are smaller than a neutron or an electron. FALSE
Neutrons are smaller than a proton or an electron. FALSE
Electrons are smaller than a proton or a neutron. TRUE
Answer:
these 2 are correct-
Protons and neutrons have similar mass.
Electrons are smaller than a proton or a neutron.
Explanation:
hope this helps! got it right on edge :)
which element is a shiny element that conducts heat and electricity