Glycerin at 30°C has a density of 1,260 kg/m3 and a viscosity of 0.630 Pa s. In a laboratory experiment, some glycerin is forced through a horizontal tube that is 10.0 cm long and 1.00 cm in diameter. The high-pressure end of the tube is held at a gauge pressure of 618 Pa, while the other end is open to the atmosphere. What is the flow rate of the glycerin through the tube?

Answers

Answer 1

Answer:

Explanation:

Rate of flow of liquid through a tube can be expressed by the following expression

V = π P r⁴ / 8ηl

P is pressure difference between end of tube = 618 Pa

r , radius of tube = .5 x 10⁻²

η is viscosity of liquid flowing = .63  

l is length of tube = .10 m

V = 3.14 x 618 x (  .5 x 10⁻² )⁴ / (8 x .63 x .10 )

= 240.64 x 10⁻⁸ m³ /s

mass = 240.64 x 1260 x 10⁻⁸ kg / s

= 3.03 x 10⁻³ kg /s

= 3.03 gram /s .


Related Questions

2) What does the specific heat capacity of a material tell you about how easy it is to heat up
that material

Answers

Answer:

High specific heat -> takes more energy to raise/lower object's temperature

Low specific heat -> takes less energy to raise/lower object's temperature

Explanation:

The specific heat capacity is the amount of heat required to raise the temperature of something per unit of mass.

A high specific heat value for an object means it takes more energy to raise or lower that object's temperature. A low specific heat value for an object means it does not take very much energy to heat or cool that object.

A racecar accelerates from rest at 6.5 m/s2 for 4.1 s. How fast will it be going at the end of that time?

Answers

Answer:

The final velocity of the car is 26.65 m/s.

Explanation:

Given;

acceleration of the racecar, a = 6.5 m/s²

initial velocity of the car, u = 0

time of motion, t = 4.1 s

The final velocity of the car is given by;

v = u + at

where;

v is the final velocity of the car

suvstitute the givens

v = 0 + (6.5)(4.1)

v = 26.65 m/s.

Therefore, the final velocity of the car is 26.65 m/s.

The atomic of nitrogen is 7. The number of electrons a neutral atom has is_, and its atomic mass is approximately_amu.

Answers

The atomic of nitrogen is 7. The number of electrons a neutral atom has (6) and its atomic mass is approximately (1) amu

A plane mirror is placed to the right of an object. The image formed by the mirror will be a
real image that appears to be on the right of the mirror.
real image that appears to be on the left of the mirror.
virtual image that appears to be on the right of the mirror.
virtual image that appears to be on the left of the mirror.




Hamish is studying what happens when he sends a sound wave through different mediums, and he records his data in a table.
A 2-column table with 4 rows titled Hamish's Waves. The first column labeled Wave has entries 1, 2, 3, 4. The second column labeled Information has entries liquid, solid, gas, liquid.

Which statement could made about the data collected in Hamish’s table?
Wave 1 will move the fastest.
Wave 2 will move the slowest.
Wave 3 will move the slowest.
Wave 4 will move the fastest.



What is common between transverse waves and longitudinal waves?
Both include an amplitude, crest, and rarefactions
Both move faster at higher temperatures
Both move slower through densely packed molecules
Both include a wavelength from compression to compression



An angle of refraction is the angle between the refracted ray and the
incident ray.
normal.
medium.
boundary.

Answers

Answer:

A plane mirror is placed to the right of an object. The image formed by the mirror will be a virtual image that appears to be on the left of the mirror.

Explanation:

Real time that appears to be on the right if the mirror

True or False when an object speeds up it gains momentum

Answers

Yes ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ

Answer: True

Explanation:

If the particles were moving with a speed much less than c, the magnitude of the momentum of the second particle would be twice that of the first. However, what is the ratio of the magnitudes of momentum for these relativistic particles?

Answers

Answer:

p₂ / p₁ = 2 (v₁ / v₂)

Explanation:

The moment is a very useful concept, since it is one of the quantities that is conserved during shocks and explosions, for which it had to be redefined to be consistent with special relativity,

         p = m v / √[1+ (v/c)² ]

for the case of speeds much lower than the speed of light this expression is close to

         p = m v

 

In this exercise they indicate that the moment of the second particle is twice the moment of the first, when their velocities are small

        p₂ = 2 p₁

       p₂/p₁ = 2

in consecuense

       m v₂ = 2 m v₁

       v₂ = 2 v₁

consider particles of equal mass.

By the time their speeds increase they enter the relativistic regime

        p₂ = mv₂ /√(1 + v₂² /c²)

        p₁ = m v₁ /√(1 + v₁² / c²)

let's look for the relationship between these two moments

       p₂ / p₁ = mv₂ / mv₁   [√ (1+ v₁² / c²) /√ (1 + v₂² / c²)

       

from the initial statement

      p₂ / p₁ = 2 √(c² + v₁²) / (c² + v₂²)

we take c from the root

      p₂ / p₁ = 2 √ [(1+ v₁²) / (1 + v₂²)]

this is the exact result, to have an approximate shape suppose that the velocities are much greater than 1

      p₂ / p₁ = 2 √ [v₁² / v₂²] = 2 √ [(v₁ / v₂)²]

      p₂ / p₁ = 2 (v₁ / v₂)

we see the value of the moment depends on the speed of the particles

(b) In the USA, drones are not allowed to be flown too high above the ground.

Suggest one possible risk of flying a drone too high above the ground.




Plz complete thank you in advance

Answers

One possible risk is it could effect planes, radars, weather patterns.

The 400-foot altitude limit was put in place for the sake of airspace safety, and there is a risk to country security as well as the privacy of citizens.

What are drones?

Unmanned aerial vehicles (UAVs), sometimes known as drones, are used for a variety of jobs, from routine to extremely dangerous. These robotic-looking planes can be seen practically everywhere, from delivering groceries to your home to rescuing avalanche victims.

The 400-foot altitude restriction was ultimately implemented for airspace safety. Given the breadth of the airspace above 400 feet, the likelihood of a drone colliding with a human aircraft is exceedingly remote, but the consequences might be disastrous.

Any aerial vehicle that uses software to fly autonomously or that may be controlled remotely by a pilot is referred to as a drone. Numerous drones come equipped with cameras to gather visual data and propellers to stabilize flying paths. Drone technology has been incorporated into industries like videography, search and rescue, agriculture, and transportation.

When in uncontrolled (Class G) airspace, your drone must be flown 400 feet above the ground or less.

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he gravitational force between two objects of masses m1m1m_1 and m2m2m_2 that are separated by distance rrr is

Answers

Answer:

[tex]F = \frac{6.67408m_1 m_2}{10^{11}r^2}[/tex]

Explanation:

Given

[tex]Object_1 = m_1[/tex]

[tex]Object_2 = m_2[/tex]

[tex]Distance = r[/tex]

Required

Determine the force of attraction

This is calculated as:

[tex]F = \frac{GMm}{d^2}[/tex]

Where

M = mass of object 1

m = mass of object 2

d = distance

Where G = gravitational constant

[tex]G = 6.67408 * 10^{-11}\ m^3 kg^{-1} s^{-2}[/tex]

Substitute these values in

[tex]F = \frac{GMm}{d^2}[/tex]

[tex]F = \frac{6.67408 * 10^{-11} * m_1 * m_2}{r^2}[/tex]

[tex]F = \frac{6.67408 * m_1 * m_2* 10^{-11}}{r^2}[/tex]

[tex]F = \frac{6.67408m_1 m_2* 10^{-11}}{r^2}[/tex]

[tex]F = \frac{6.67408m_1 m_2}{10^{11}*r^2}[/tex]

[tex]F = \frac{6.67408m_1 m_2}{10^{11}r^2}[/tex]

Power is the rate at which work is done true or false

Answers

Answer:

false

Explanation:

5.
An 80 newton force and a 45 newton force act on an object
as shown below.
80 N
30°
4S N
Which of the following vectors would bets represent an
equilibrant when added to this system?
(1) 24 N to the left (3) 24 N to the right
(2) 114 N to the right (4) 45 N to the left
Tirant Showroiculations

Answers

Answer:

the answer is a time your welcome

Answer:

(1)

Explanation:

What is the similarity between relative dating and radioactive dating? I will mark brainlest. I dont know how btw

Answers

Answer:

relative dating and radioactive dating are two methods in archeaology to determine the age of fossils and rocks

Explanation:

the act of or study of fossils is important for the determination of the kind of organism it represents how the organism lived and how it was preserved on the Earth’s surface over the past 4600000000 years

Answer as soon as possible

Answers

Answer:

the velocity of the acorn

Explanation:

just do in in real life and see

Answer:

it is probably the velocity of the acorn

A 715 kg car stopped at an intersection is rear-ended by a 1490 kg truck moving with a speed of 12.5 m/s. If the car was in neutral and its brakes were off, so that the collision is approximately elastic, find the final speed of both vehicles after the collision.

Answers

Answer:

The final velocity of the car is 16.893 m/s

The final velocity of the truck is 4.393 m/s

Explanation:

Given;

mass of the car, m₁ = 715 kg

mass of the truck, m₂ = 1490 kg

initial velocity of the car, u₁ = 0

initial velocity of the truck, u₂ = 12.5 m/s

let the final velocity of the car, = v₁

let the final velocity of the truck, = v₂

Apply the principle of conservation of linear momentum for elastic collision;

m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂

(715 x 0) + (1490 x 12.5) = 715v₁ + 1490v₂

18625 = 715v₁ + 1490v₂ -----equation (1)

Apply one-directional velocity formula;

u₁ + v₁ = u₂ + v₂

0 + v₁ = 12.5 + v₂

v₁ = 12.5 + v₂

Substitute v₁ into equation (1)

18625 = 715(12.5 + v₂) + 1490v₂

18625 =8937.5 + 715v₂ + 1490v₂

18625 - 8937.5 = 715v₂ + 1490v₂

9687.5 = 2205v₂

v₂ = 9687.5 / 2205

v₂ = 4.393 m/s

solve for v₁

v₁ = 12.5 + v₂

v₁ =  12.5 + 4.393

v₁ = 16.893 m/s

A bug crawls 2.25 m along the base of a wall. Upon reaching a corner, the bugs direction of travel changes from south to west. THe bug that crawls 3.15 m before stopping. What is the magnitude of the bugs displacment?A) 5.40 m.B) 2.72m.C) 3.45 m.D) 3.87 in.E) 4.29 m.

Answers

Answer:

The magnitude of the bugs displacement is 3.87 m

Explanation:

An illustrative diagram for the scenario is given in the attachment below.

In the diagram, the bug's displacement is given by x. The diagram shows a right angle triangle with x as the hypotenuse. We can determine x from the Pythagorean theorem which states that " the square of the hypotenuse equals sum of squares of the other two sides". That is

x² = 2.25² + 3.15²

x² = 5.0625 + 9.9225

x² = 14.985

x = √14.985

x = 3.87 m

Hence, the magnitude of the bugs displacement is 3.87 m.

How should the magnetic field lines be drawn for the magnets shown below?​

Answers

Answer:

Magnetic field lines can be drawn by moving a small compass from point to point around a magnet. At each point, draw a short line in the direction of the compass needle.When opposite poles of two magnets are brought together, the magnetic field lines join together and become denser between the poles.

Explanation:

What type of meter would be connected on both sides of a resistor in a circuit?

Answers

Type of meter would be connected on both sides of a resistor in a circuit is a a voltmeter , which measures potential difference .

What is a voltmeter ?

A voltmeter is an instrument used for measuring the potential difference , or voltage between two points in an electrical circuit .

A voltmeter is always attached in a series combination and an ammeter (which measures current in a circuit ) always attached in parallel combination with the circuit.

Since , in question it is given that a meter would be connected on both sides of a resistor in a circuit that means it must be a series combination

hence , correct answer is B) a voltmeter , which measures potential difference .

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A 3520 kg truck moving north makes an INELASTIC collision with an 1480 kg car moving 13.0 m/s east. After colliding, they have a velocity of 9.80 m/s at 66.9 degrees. What was the initial velocity of the truck? (m/s)

Answers

Answer:

v = 12.8 m/s

Explanation:

Assuming no external forces acting during the collision, total momentum must be conserved.Since momentum is a vector, their components must be conserved too.Choosing a pair of axes coincident with the N-S and W-E directions, naming x to the W-E axis and y to the N-S one, we can write the following algebraic equations:      

       [tex]p_{ox} = p_{fx} (1)[/tex]

       [tex]p_{oy} = p_{fy} (2)[/tex]

Since we know all the information needed to solve (1), assuming a completely inelastic collision, we can focus in (2), writing both sides of the equation as follows:

       [tex]p_{oy} = m_{t} * v_{ot} = 3520 kg* v_{ot} (3)[/tex]

       [tex]p_{fy} = m_{f} * v_{fy} = 5000 kg* 9.8 m/s * sin 66.9 = 45080 kg*m/s (4)[/tex]

Since (4) and  (3) are equal each other, we can solve for vot, as follows:

       [tex]v_{ot} =\frac{45080kg*m/s}{3520kg} = 12.8 m/s (5)[/tex]

A box of books weighing 319 N is shoved across the floor by a force of 485 N exerted downward at an angle of 35 degres below the horizontal.a) If the coeficent of friction between the box and the floor is 0.57, how long does it take to move the box 4 meters, starting from rest?b) If If the coeficent of friction between the box and the floor is 0.75, how long does it take to move the box 4 meters, starting from rest?

Answers

Let w, n, p, and f denote the magnitudes of the 4 forces acting on the box.

• w = weight = 319 N

n = normal force

p = pushing force = 485 N

f = friction = µ n, where µ is the coefficient of static friction

The net force on the box points in the direction that the box moves, which is to the right. In particular, this means the box is vertically in equilibrium. Split up the vectors into their vertical and horizontal components, and apply Newton's second law. (I take up and right to be the positive vertical and horizontal directions, respectively.)

• vertical:

p sin(-35°) + n - w = 0

and solving for n,

- (485 N) sin(35°) + n - 319 N = 0

n ≈ 597 N

• horizontal:

p cos(-35°) - f = m a

where a is the magnitude of the net acceleration on the box. Solve for a. Since f = µ n and m = w / g (where g = 9.80 m/s² is the mag. of the acc. due to gravity) we get

p cos(35°) - µ n = (w / g) a

(485 N) cos(35°) - µ (597 N) = (319 N) / (9.80 m/s²) a

a ≈ (12.2 - 18.3 µ) m/s²

(a) If µ = 0.57, then the net acceleration on the box is

a ≈ (12.2 - 18.3 • 0.57) m/s² ≈ 1.75 m/s²

so that the time t required to move the box 4 m is

4 m = 1/2 a t ²

t ≈ √((8 m) / (1.75 m/s²))

t ≈ 2.14 s

(b) The box does not move.

If µ = 0.75, then

a = (12.2 - 18.3 • 0.75) m/s² ≈ -1.55 m/s²

but a negative acc. here means the applied acc. points *opposite* the direction of movement, thus making the box move backward which doesn't make sense. The coefficient of friction is too large for the given applied force to get the box moving. With µ = 0.75, the frictional force to overcome has mag. f ≈ 448 N. But the given push contributes a horizontal force of (485 N) cos(-35°) ≈ 397 N. This mag. needs to be increased in order to get the box moving.

(a) The time taken to move the box 4 meters is 2.14 s.

(b) The box will decelerate when the coefficient of friction is 0.75 and cannot be moved to 4 meters forward.

The given parameters;

weight of the book, W = 319 Napplied force, F = 485 Nangle of inclination, θ = 35 ⁰

The mass of the books is calculated as;

[tex]m = \frac{W}{g} \\\\m = \frac{319}{9.8} \\\\m = 32.55 \ kg[/tex]

The normal force on the box is calculated as follows;

[tex]F_n = -W - Fsin\theta\\\\F_n = -319 - (485\times sin35)\\\\F_n = -597.18 \ N[/tex]

The frictional force when the coefficient of friction is 0.57;

[tex]F_f = \mu F_n\\\\F_f = 0.57 \times -597.18\\\\F_f = -340.39 \ N[/tex]

The acceleration of the box is calculated as follows;

[tex]F cos \theta - F_f = ma\\\\(485)cos(35) \ - 340.39 = 32.55 a\\\\56.899 = 32.55a\\\\a = \frac{56.899}{32.55} \\\\a = 1.75 \ m/s^2[/tex]

The time taken to move the box 4 meters is calculated as;

[tex]s = v_0t + \frac{1}{2} at^2\\\\s = 0 + \frac{1}{2} at^2\\\\t = \sqrt{\frac{2s}{a} } \\\\t = \sqrt{\frac{2\times 4}{1.75} } \\\\t = 2.14 \ s[/tex]

(b) The frictional force when the coefficient of friction is 0.75;

[tex]F_f = \mu F_n\\\\F_f = 0.75 \times -597.18\\\\F_f = -447.885 \ N[/tex]

The acceleration of the box is calculated as follows;

[tex]F cos \theta - F_f = ma\\\\(485)cos(35) \ -447.885 = 32.55 a\\\\-50.596 = 32.55a\\\\a = \frac{-50.596}{32.55} \\\\a = -1.55\ m/s^2[/tex]

Thus, the box will decelerate when the coefficient of friction is 0.75 and cannot be moved to 4 meters forward.

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a. What frequency is received by a person watching an oncoming ambulance moving at 115 km/h and emitting a steady 753 Hz sound from its siren?
b. What frequency does she receive after the ambulance has passed?

Answers

Answer:

A)828.8Hz

B)869.2Hz

Explanation:

Here is a complete question;

What frequency is received by a person watching an oncoming ambulance moving at 115 km/h and emitting a steady 753 Hz sound from its siren? Speed of sound is 345m/s

b. What frequency does she receive after the ambulance has passed?

Vs= speed of the ambulance

, We convert to m/s for unit consistency

= 115 km/h= 115km× 1000m/1m × 1hr/3600s= 31.94m/s

Dopler effect is when observed frequency of wave changes with respect to the source or when observed moves relative to transmitting medium can be expressed as

f'=[ (v + vo)/(v- vs)]*f

=[ (v )/(v- vs)]*f

The sign vo and vs depends on vthe direction of the velocity

f= frequency of ambulance siren= 753Hz

v= speed of sound in air= 345m/s

Vo= speed of observer= 0

A) we are to determine the f' of ambulance as heard by person as ambulance approaching.

To find the frequency f' observed by the person we use the expresion below

Then substitute the values

f'=[ (v )/(v- vs)]*f

=[ (345)/(345-31.94)]×753

= 828.8Hz

B)What frequency does she receive after the ambulance has passed?

To find the frequency f' observed by the person we use the expresion below

Then substitute the values

f'=[ (v )/(v + vs)]*f

=[ (345)/(345 + 31.94)]×753

= 869.2Hz

=

A plane starts from rest accelerates to 40 m/s in 10 seconds. How far did the plane travel during this time?

Answers

Answer:

200 m

Explanation:

We are given:

Initial velocity of the plane (u) = 0 m/s

Final velocity of the plane (v) = 40 m/s

Time interval (t) = 10 seconds

Displacement of the plane (s) = x m

Solving for x:

Acceleration of the plane

v = u + at                                                     [First equation of motion]

40 = 0 + a(10)                                              [replacing known variables]

a = 4 m/s²                                                    [dividing both sides by 10]

Displacement of the Plane:

s = ut + 1/2 (at²)                                            [Second equation of motion]

s = (0)(10) + 1/2(4)(10)²                                  [replacing known variables]

s = 200 m

Hence, the Plane covers a distance of 200 m in the given time interval

(A star if you answer this question) A school bus is traveling at 11.1 m/s and has a
momentum of 152,625 kgm/s. What is the mass of the bus?

Answers

[tex]\mathfrak{\huge{\pink{\underline{\underline{AnSwEr:-}}}}}[/tex]

Actually Welcome to the Concept of the Kinematics in real world.

So, as given here, we have to find the Mass of the bus from the given momentum, so we get as,

P = m * V

momentum = mass * velocity

here, P= 152625 kgm/s and v= 11.1 m/s

so substituting we get as,

m = 152625 ÷ 11.1 => 13,750 kg

hence,the mass of the bus is 13,750 kg.

When particles get close to the surface, they interact with atoms in
the
(Finish the sentence)

Answers

Is there anything else in the page I think it’s missing a part

Can someone please answer how to convert mass into weight?

Answers

Answer:

To find the weight of something, simply multiply its mass by the value of the local gravitational field, and you get a result in newtons (N). For example, if your mass is 50 kg (about 110 pounds), then your weight is (50) (9.8). The point that must be overwhelmingly emphasized is that weight is a force.

Explanation:

plzzzzzzzzzzzzzzzzzzzzzzzzzz help 20 points

Answers

Answer:

1.23

Explanation:

[tex]{\underline{\pink{\textsf{\textbf{ Answer : }}}}}[/tex]

➩ 1.23 feet

[tex]{\underline{\purple{\textsf{\textbf{Explanation : }}}}}[/tex]

Given :

Simon cuts a pipe that was 4.92 feet long Then he cuts it into four equal pieces.

To find :

What is the length of the each piece.

Solution :

As it is told that it's divided into four equal pieces

Therefore,

We must divide it by 4 to get the length of each piece.

So,

[tex] \sf \to \: \frac{4.92}{4} \\ \sf \to \: 1.23 \: feet \: ans.[/tex]

How much work is done by the gravitational force on the block?

Answers

Answer:

Work = Mass * Gravity * Height and is measured in Joules. Imagine you find a 2 -Kg book on the floor and lift it 0.75 meters and put it on a table. Remember, that “force” is simply a push or a pull. If you lift 100 kg of mass 1-meter, you will have done 980 Joules of work.

Explanation:

What is the force of gravity for a 12 kg turkey?

Please help asap

Answers

Answer: 117.6N

Explanation:

By the second Newton's law, we know that:

F = m*a

F = force

m = mass

a = acceleration

We know that in the surface of the Earth, the gravitational acceleration is g = 9.8m/s^2.

Then we just can input that acceleration in the above equation, and also replace m by 12kg, and find that the force due the gravity is:

F = 12kg*9.8m/s^2 = 117.6N

4. A substance has a density of 0.79 g/cm'. It is soluble in water. List all the possibilities of what it might be How could you determine the actual identity?​

Answers

Answer:

See explanation

Explanation:

Given that the density of the unknown substance is 0.79 g/cm3 and is soluble in water, the possible substances it could be are;

i) t-butanol

ii) ethanol

iii) 2-propanol

iv) acetone

However, the actual identity of the unknown substance can be obtained by carrying out a boiling point test. The four substances listed above have different boiling points. Hence the boiling point of the unknown substance ultimately discloses its identity.

The cardinal, central, and secondary traits are all part of __________ categorized traits. A. Gordon Allport’s B. Robert McCrae’s C. Paul Costa’s D. Hans Eysenck’s

Answers

Answer:

Gordon Allport’s

Explanation:

edge2o2o

The cardinal, central, and secondary traits are all part of Gordon Allport’s categorized traits. The Correct option is A

Who was Gordon Allport ?

Gordon Willard Allport was born on 11 November 1897 and died 9 October 1967. He was an American psychologist. Allport was first psychologists who studied on personality. he has developed theory of personality. which was one of the greatest finding in the study of personality psychology. He was Appointed  as a social science instructor at Harvard University in 1924,

Gordon Allport was  a great trait theorist who categorized personality traits into three categories cardinal, central, and secondary.

Hence option A is Correct.

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A woman standing before a cliff claps her hands, and 2.8s later she hears the echo. How far away is the cliff? The speed of sound in air a ordinary temperature is 343 m/s.

Answers

Answer:

480.2 m

Explanation:

The following data were obtained from the question:

Speed of sound (v) = 343 m/s.

Time (t) = 2.8 s

Distance (x) of the cliff =?

The distance of the cliff from the woman can be obtained as follow:

v = 2x /t

343 = 2x /2.8

Cross multiply

2x = 343 × 2.8

2x = 960.4

Divide both side by the coefficient of x i.e 2

x = 960.4/2

x = 480.2 m

Therefore, the cliff is 480.2 m away from the woman.

The distance should be 480.2 m

The calculation is as follows:

Since A woman standing before a cliff claps her hands, and 2.8s later she hears the echo. And, there is the velocity of 343 m/s

[tex]v = 2x \div t\\\\343 = 2x \div 2.8\\\\2x = 343 \times 2.8[/tex]

2x = 960.4

x = 480.2 m

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The x component of vector A is -25.0m and the y component id +40.0m (a) what is the magnitude of A?(b) What is the angle between the direction of A and the positive direction of x?

Answers

Answer:

θ = 122°

Explanation:

Components of a Vector

A vector in the plane can be defined by its rectangular components:

[tex]\vec A =<x,y>[/tex]

Or also can be given by its polar components:

[tex]\vec A =<r,\theta>[/tex]

Where r is the magnitude of the vector and θ is the angle it forms with the positive direction of x.

The relation between them is:

[tex]r=\sqrt{x^2+y^2}[/tex]

[tex]\displaystyle \theta=\arctan\frac{y}{x}[/tex]

It's given the x-component of vector A is x=-25 m and the y-component is y=40 m

(a)

The magnitude of the vector is:

[tex]r=\sqrt{(-25)^2+40^2}[/tex]

[tex]r=\sqrt{625+1600}[/tex]

[tex]r=\sqrt{2225}[/tex]

[tex]r\approx 47.2\ m[/tex]

(b)

[tex]\displaystyle \theta=\arctan\frac{40}{-25}[/tex]

[tex]\displaystyle \theta=\arctan (-1.6)[/tex]

The calculator gives us the value

θ = -58°

But the real angle lies on the second quadrant since x is negative and y is positive, thus:

θ = -58° + 180° = 122°

θ = 122°

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