If position vector r=bt²i + ct³j, where c are positive constants, when does the velocity vector make an angle of 45° with the x and y axes?

Answers

Answer 1

We want to find the value of t such that the velocity vector makes an angle of 45° with both axes.

We found that:

t = (2/3)*(b/c)

The velocity vector makes an angle of 45° with the x and y axes.

We know that the position vector is:

r = r=b*t²i + c*t³j

Remember that the versor "i" corresponds to the x-component, and the versor "j" corresponds to the y-component, then:

r = r=b*t²i + c*t³j  = (b*t², c*t³)

The velocity vector is the vector that we get when we differentiate the position one, remember that if:

f(x) = a*x^n

then

f'(x) = n*a*x^(n - 1)

Using this, we can find that the velocity vector is:

v = (2*b*t,  3*c*t²)

Now we want to know, when does the velocity vector make an angle of 45° with the x and y axes.

Let's think of the vector as the hypotenuse of a triangle rectangle, where the x-component is the adjacent cathetus, and the y-component is the opposite cathetus. (so the angle is measured counterclockwise from the x-axis)

We have the trigonometric equation:

tan(a) = (opposite cathetus)/(adjacent cathetus)

So now we can replace these things with the known ones:

a = 45°

opposite cathetus = y-component = 3*c*t²

adjacent cathetus = x-component = 2*b*t

So we will get:

tan(45°)  =  (3*c*t²)/( 2*b*t)

1 = (3/2)*(c/b)*t

Now we can solve this for the variable, t.

1*(2/3)*(b/c) = t

t = (2/3)*(b/c)

We can conclude that at the time:

t = (2/3)*(b/c)

The velocity vector makes an angle of 45° with the x and y axes.

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Related Questions

NEED ANSWER! WILL BRAINLIST!
• Why are tailings an environmental concern?

A. They are a form of sewage that is found in agricultural runoff.
B. They are the remains from mining and contain harmful chemicals.
C. They are the waste products left over from fracking for natural gas.
D. They are a type of greenhouse gas that can enter the atmosphere.

Answers

B. They are the remains from mining and contain harmful chemicals.

Is it correct ?!???!);$);

Answers

Answer:

None of the above

Explanation:

process of elimination i guess, also delta E measures the amount of change in visual perception of two colors, so it probably wont mean w (work).

then again i may be wrong-

2CH3CHO+O2=> 2CH3COOH

Answers

Answer:

2CH3CHO + O2 → 2CH3COOH

what is meaning of coordination bond?​

Answers

Answer:

Coordinate-bond meaning

A type of covalent bond in which both the shared electrons are contributed by one of the two atoms. ... The definition of a coordinate bond is a chemical bond between two atoms when one of the atoms shares a pair of electrons.

Explanation:

Explanation:

is a covalent bond in the sharing of electron pair equally between two atoms in which each atom contribute an electron.

it is form when atomic orbitals of atoms each containing an unpaired electron overlap to share the pair of electrons.

What's similar about the valence electrons of Carbon and Silicon?

Answers

Answer:

Explanation: Carbon and silicon BOTH come from Group 14 of the Periodic Table , i.e. both formally have the same number of valence electrons, 4 such electrons.........

a sample of glucose contains 1.250x10^21 carbon atoms, how many atoms of hydrogen does it contain?

Answers

Answer:

Hydrogen = 2.5 * 10^21

Explanation:

Chemical Formula Glucose: C₆H₁₂O₆

One of the ways you could do  this is to notice that for every carbon atom there are two Hydrogen atoms. You can state this more formally by using the formula to set up a ratio: 12/6 = hydrogen to Carbon

So if there are 1.250 * 10^21 Carbon atoms in the Glucose sample, then there will be twice as many hydrogen atoms.

H = 2 * 1.25 * 10^21 = 2.5 * 10^21 atoms

You could do this more formally by setting up a proportion.

6 Carbon / 12 Hydrogen = 1.25*10^21 /  x         Cross Multiply

6*x = 12 * 1.25*10^21                                           Combine the right

6x = 1.5 * 10^22                                                  Divide by 6

x = 2.5 * 10^21

What is the empirical formula for C2H4S2?

Answers

Answer:

46

Explanation: ihjk

WILL BRAINLIST! NEED ANSWER!

• Why is it important to recycle metals?

A. to maintain sustainability
B. to create more tailings
C. to make sure ore remains renewable
D. to make it easier to extract ore from the ground

Answers

It’s C

Recycling metal is considered an environmentally friendly practice since it eliminates the demand for raw (ore) metal and conserves valuable natural resources

list 2 sources of waste water

Answers

Answer:

residential and domestic sources.

Explanation:

residential and domestic waist


brainly!!

What are the gas laws? (Include Boyle's law, charles's law, gay lussac's law, an avogadro's law) Could someone please summarize these for me ples? Brainliest answer also yes

Answers

Answer:

Boyle's Law: When the pressure of a gas increases, the volume of the gas will decrease as long as the temperature and amount of gas are constant.

So basically pressure is inversely proportional to Volume, when one increases, the other decreases, vice versa.

Equation: [tex]P_{1} V_{1} = P_{2} V_{2}[/tex]

Charles Law: When the temperature of a gas increases, the volume of a gas will also increase if the pressure and amount of gas are constant.

So basically Temperature and volume are directly proportional.

Equation: [tex]\frac{V_{1}}{T_{1}} = \frac{V_{2} }{T_{2} }[/tex]

Gay Lussac's Law: When the temperature of a gas increases, the pressure of a gas also increases when volume and the amount of gas remain constant.

Basically, Temperature and Pressure are directly proportional.

Equation: [tex]\frac{P_{1}}{T_{1}} = \frac{P_{2} }{T_{2} }[/tex]

Avogadro's Law: The most intuitive gas law. When you increase the amount of gas, the volume will also increase.

Meaning the moles (amount of gas) is directly proportional to volume.

Equation: [tex]\frac{V_{1} }{n_{1} } = \frac{V_{2} }{n_{2} }[/tex] (n stands for moles)

There is a combined gas law and ideal gas law but those are just the gas laws mentioned above but combined together. These should be everything.

Answer:

Boyle Law is when pressure and volume have a reverse relationship when temperature is the same.Charles law is basically when volume and temperature have a relationship when the pressure is the same.Lussac Law is I think just when I pressure and temperature is directly tied together when the volume stays the same.I dont think there is any "avogadro law", there is only pressure volume and temperature.

Please give brainliest thanks :D

What is a scientific law?

Answers

Answer:

Scientific laws or laws of science are statements, based on repeated experiments or observations, that describe or predict a range of natural phenomena. The term law has diverse usage in many cases across all fields of natural science.

Explanation:

I hope this helps

Answer:

Scientific laws or laws of science are statements, based on repeated experiments or observations, that describe or predict a range of natural phenomena. Scientific law differs from scientific theory. The main difference between a law and a theory is that a theory tries to explain the reasoning behind something that occurs in nature, whereas scientific laws are just descriptive accounts of how something occurs in nature.

A student reads that sodium atoms (Na) react with chlorine (Cl2) molecules to form the compound sodium chloride (NaCl). Which model should the student make to satisfy the Law of Conservation of Matter for the formation of sodium chloride, in simplest form?

Answers

Answer:

c

Explanation:

Law of Conservation of Matter for the formation of sodium chloride, in simplest form would be obeyed when 2 moles of sodium react with 1 ,mole of chlorine to form 2 moles of sodium chloride.

What is law of conservation of matter?

According to law of conservation of matter, it is evident that matter is neither created nor destroyed rather it is restored at the end of a chemical reaction .

Law of conservation of matter and energy are related as matter has mass and mass and energy are directly proportional which is indicated by the equation E=mc².Concept of conservation of matter is widely used in field of chemistry, fluid dynamics.

Law needs to be modified in accordance with laws of quantum mechanics under the principle of mass and energy equivalence.This law was proposed by Antoine Lavoisier in the year 1789.

Learn more about law of conservation of matter,here:

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describe the atomic models above in terms of

a. location of nucleus
b.location of electrons

Answers

I will pick b. I am not sure yet

How many decigrams of chromium are in 3.19 x 10^23 atoms of chromium? show work

Answers

mol = 3.19 × 10^23/6.02^23

= 0.529 mol

mass = 0.529 × 52

= 27.508 g

g to decigram

= 27.508 × 10

= 275.08 decigram

A substance has a molar heat of combustion of -810.4 kj/mol. when 0.285 mol of the substance is burned in a calorimeter containing 8.60 kg of water, the increase in water temperature is:

Answers

Answer:

6.42 °C

Explanation:

Q = mcΔT

Q = energy gain/release (J)

m = mass (kg)

c = specific heat capacity (J/°C/kg)

ΔT = change in temperature (°C)

Qs = n(ΔH°c)

Qs = energy gained/released from substance (kJ)

n = moles (mol)

ΔH°c = molar heat of combustion (kJ/mol)

m = 8.60

n = 0.285

ΔH°c = -810.4

c (of water) = 4184

Qs = 0.285(-810.4)

Qs = -230.964 (or -230964 J)

Q = 230964

230964 = (8.60)(4184)ΔT

230964 = 35982.4(ΔT)

ΔT = 6.4188... °C → 6.42 °C

What is the balanced net ionic equation when aqueous solutions of Pb(NO3)2 and KBr are mixed and form a product

Answers

Answer:

KBr+Pb(NO3)2=? is an equation you can use.

Explanation:

ghjguygyughyyhghygyuguyg

Answers

Sir! I would have to tell that this is a educational website/app so please don’t type random letters in the question bar if you don’t need help with nothing.

can y’all please help me answer?

Answers

Answer:

It really depends on the situation. If you have 1000 elk and 2 wolves, they really would play a better role in killing off elk so that the elk population doesn't get over populated and diseased, causing a major population collapse. But if there were only 10 elk and 50 wolves, the wolves would play a very negative role on the population.

Hope this helps!

Explanation:

The law of conservation of matter states that matter can be neither created nor destroyed. Your friend shows you the following chemical equation: CaCO,CaO+CO, He says that because the oxygen atoms are split between two different molecules in the products, the equation does not support the law of conservation of matter. Is your friend right? Explain your answer.​

Answers

Answer:

According to conservation of matter, there should be equal amounts of all elements on both the reactant and product side.

Reactant:

1 Ca

1 C

1 O

Product:

1 Ca

1 C

3 O

Therefore, your friend is right because the law of conservation of matter is not followed in this chemical equation.

Explanation:

The Planet Venus is surrounded by a thick layer of gases. In fact the atmospheric preassure on Venus is over 90 times grater than the atmospheric preassure on Earth. Wcich statements are true about boiling water on Venus? Choose the TWO STATEMENTS that aply.
A. Water will boil at a higher temperature on Venus than on Earth.
B. Water will boil at a lower temperature on Venus than on Earth.
C. The temperature of the water will remain constant as it boils.
D. The temperature will increase as it boils.

Answers

B. water will boil at a lower temperature on Venus than on Earth.
Explanation:
Because temperature and pressure are directly proportional... increase in pressure will increase in the atmospheric temperature.... Venus has higher pressure than earth that also means it has higher atmospheric temperature and as the temperature is already high the water will require lesser heat to boil

non-protein amino acid (A) orithine (B) homocysteine

Answers

Answer:

Homocysteine is though to be a non-protein animo acid. however in vintro studies suggest that Homocysteine is likely to be incorporated by inderict

What is the stock name for chromic ion

Answers

Answer:

Chromium(III)

PubChem CID 27668

Structure Find Similar Structures

Chemical Safety Laboratory Chemical Safety Summary (LCSS) Datasheet

Molecular Formula Cr+3

Synonyms Chromium(III) Chromic ion chromium(3+) CHROMIUM (III) Chromic cation More

I have a problem with solving this type of chemistry problem. Please Help!

Answers

Umm what chemistry problem ? Umm you could send it so that l can help you better .

The specific heat of water is 4.184 J/gºC. How much energy (in
joules) is required to raise the temperature of 18g of H2O from
283K to 293K?

Answers

62.76 Joules
mark brainleist

Consider the energy transfers and transformations that occur when a person rides a bicycle. Describe thi
process by selecting the correct options from the drop-down menus.
Chemical energy is transformed into
energy in the person's muscles.
Kinetic energy is
from the person's legs to the pedals.
Kinetic energy is
thermal energy due to friction when the wheels get warm.
DONE

Answers

Answer:

b,a,b

Explanation:

The energy transfers and transformations that occur are kinetic energy is from the person's legs to the pedals and thermal energy due to friction when the wheels get warm.

What is law of conservation of energy?

The law of conservation of energy states that energy can neither be created nor destroyed but can be converted from one form to another.

The energy transfers and transformations that occur when a person rides a bicycle are:

Kinetic energy is from the person's legs to the pedals Thermal energy due to friction when the wheels get warm

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Which of the following is an example of a scientific model?

The total inches of rainfall during a thunderstorm
A telescope used to study the stars
A computer program that simulates atmospheric conditions
A song about the Grand Canyon

Answers

A computer program that simulates atmosphere conditions :)

Passive prostheses are:
- self-regulated
- easily corroded
- made of nanotubes
- self-powered

Answers

Passive prostheses are self-regulating, as shown in the first answer option.

We can arrive at this answer because:

Passive prostheses are devices used to replace parts of the body that were lost by an incident.These prostheses are very useful to establish balance or the aesthetics of the body, but they have no articulations and no movement mechanism, being static.

This limitation allows passive prostheses not to need external regulation and to be self-regulated by fitting the body parts.

You can find more information about articulations and their effects on the link:

https://brainly.com/question/5847359?referrer=searchResults

Answer:

self-powered.

What volume of 0.100 M AgNO3 is
needed to react completely with
45.0 mL of 0.230 M Na2S?
2AgNO3 + Na2S → Ag2S + 2NaNO3
[?] mL AgNO3

Answers

Answer:

448mL AgNO3

Explanation:

M x V

n = 0.230 x .045 = 0.01

2AgNO3 + Na2S --> Ag2S+2NaNO3

1 mol Ag2S --> 2 moles AgNO3

.01 mol Ag2S --> ? moles AgNO3

.01x2/1=.02 moles AgNO3

Moles to L conversion is multiplying by 22.4L so we do .02 x 22.4=0.448L

Then we convert to mL so we multiply by 1000 (1000 x 0.448)

448mL AgNO3

There you go friend, good luck with chemistry :)

4 Mg & 3 Cu(NO3)2 + Cu(NO3)2 (aq) + Mg(NO3)2 (aq) + Cu (s)

balance?

Answers

Here you go

Mg + 2CuNO3 → Mg(NO3)2 + 2Cu

A sample of CO2 gas at 100 degrees Celsius has a volume of 250 mL at 760 mm Hg. How many moles of CO2 are present

Answers

There are 8.16 × 10-³ moles of CO2 gas at 100°C with a volume of 250 mL at 760 mm Hg.

HOW TO CALCULATE NUMBER OF MOLES:

The number of moles of a sample of gas can be calculated using the following formula:

PV = nRT

Where;

P = pressure of gas (atm)V = volume (L)n = number of moles (mol)R = gas law constant (0.0821 Latm/molK)T = temperature (K)

According to this question;

P = 760mmHg = 1 atmT = 100°C = 100 + 273 = 373KV = 250mL = 0.250Ln = ?

1 × 0.250 = n × 0.0821 × 373

0.250 = 30.62n

n = 0.250 ÷ 30.62

n = 8.16 × 10-³mol

Therefore, there are 8.16 × 10-³ moles of CO2 gas at 100°C with a volume of 250 mL at 760 mm Hg.

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