One particle, of mass m , moves with a speed v in the x-direction, and another particle, of mass 2 m , moves with a speed v/2 in the y-direction. what is the velocity of the center of mass of these two particles?

Answers

Answer 1

Given :

One particle, of mass m , moves with a speed v in the x-direction, and another particle, of mass 2 m , moves with a speed v/2 in the y-direction.

To Find :

The velocity of the center of mass of these two particles.

Solution :

Speed of mass m, [tex]v\ \hat i[/tex].

Speed of mass 2m , [tex]\dfrac{v}{2}\ \hat{j}[/tex] .

Speed of center of mass is given by :

[tex]v_{cm }= \dfrac{m\times( v\ \hat{i}) + 2m \times \dfrac{v}{2}\ \hat{j} }{m + 2m}\\\\v_{cm}=\dfrac{v( \hat{i} + \hat{j})}{3}[/tex]

Hence, this is the required solution.

Answer 2

The velocity of the center of mass of these two particles will be [tex]\rm v_{cm}= \frac{v(\vec i+\vec j)}{3}[/tex]

What is velocity?

The change of displacement with regards to time is defined as speed. Speed is a scalar quantity. It is a time-based component. Its unit is m/sec.

The given data in the problem is

[tex]\rm V_i[/tex] is the speed of mass m

[tex]\rm \frac{v}{2} \hat j[/tex] is the speed of mass 2m

Speed of the center of mass will be;

[tex]\rm v_{cm}=\frac{m \times (v \hat i)+2m \times \frac{v}{2}\hat j }{m+2m} \\\\ \rm v_{cm}= \frac{v(\vec i+\vec j)}{3}[/tex]

Hence the  velocity of the center of mass of these two particles will be [tex]\rm v_{cm}= \frac{v(\vec i+\vec j)}{3}[/tex].

To learn more about the velocity refer to the link;

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Related Questions

Help me

An atomic nucleus suddenly bursts apart (fission) into two pieces. Piece A with mass mA travels to the left with a speed of vA. Piece B with mass mB travels to the right with speed vB. Show the velocity of piece B in terms of mA, mB and VA.

Solution:

Consider that the nucleus is not acted by an external force. Thus, momentum is conserved, so: pBf + pAf = 0

Substituting the expression for momentum results to

mBv (_______) + (_________) mAv (______) = 0

Deriving the expression for the velocity of piece B results to

v(_____) =(mA/m ______)vA

Answers

Answer:

[tex]v_{B} = \frac{m_{A}v_{A}}{m_{B}}[/tex]

Explanation:

We can apply the law of conservation of momentum on the nucleus in its initial and final state of nucleus:

Initial Momentum = Final Momentum

momentum of nucleus before bursting = momentum of piece A + momentum of Piece B

[tex](m_{nucleus})(velocity of nucleus) = m_{A}v_{A} + m_{B}v_{B}\\[/tex]

since, nucleus was initially at rest. Therefore,

velocity of nucleus = 0 m/s

and due to opposite direction of forces:

Vb = - Vb

Therefore,

[tex](m_{nucleus})(0) = m_{A}v_{A} - m_{B}v_{B}\\\\m_{A}v_{A} = m_{B}v_{B}\\\\v_{B} = \frac{m_{A}v_{A}}{m_{B}}[/tex]

Of the pairs of galaxies listed in the answer choices, which is the closest to the Milky Way Galaxy?

Answers

Answer:

Andromeda galaxy

Explanation:

Answer:

Andromida galaxy

Explanation:

In 4 billion years the milky way and the Andromida galaxy will collide with each other

What season is it in your town when it is fall in the Southern Hemisphere

Answers

Answer:

i am in the southern hemisphere

Explanation:

Answer:

its winter ................

how do you believe the brain works to help you learn and grow

Answers

Answer:

I think

Explanation:

the brain grows more when you learn something new, and less when you practice things you already know. i think- lol

The relative age of lower layers of rock is _______ than the
relative age of rocks above them.

Answers

Answer:

the relative age of lower layers of rock is more than the relative age of rocks above them.

Astronomers discover a bright X-ray source in the Milky Way. They see no counterpart in the optical bands, but it has another star orbiting it, and they determine that the X-ray source has a mass of 10 MSun. What is the most likely origin of the X-rays?

a. a black hole
b. a neutron star
c. a white dwarf
d. a gamma-ray burst

Answers

Answer:

a. a black hole

Explanation:

X-ray emission from the central degrees of the Milky Way Bright X-ray emission traces the coherent edge brightened shell-like feature, dubbed the northern chimney, located north of Sgr A* and characterized by a diameter of about 160 pc. On the opposite side, the southern chimney appears as a bright linear feature. Bright X-ray emission is observed at high latitude

A refrigerator draws 4.5 A of current while operating on a 120-V power line. If the refrigerator runs 50% of the time and electric power costs $0.15/kWh, how much does it cost to run this refrigerator for a 30-day month

Answers

Answer:

$ 29.16

Explanation:

The following data were obtained from the question:

Current (I) = 4.5 A

Voltage (V) = 120 V

Time (t) = 30 days

1 KWh = $ 0.15

Cost for 30 days =.?

From the question given above, we were told that the refrigerator runs 50% of the time.

Thus, the time of operation of the refrigerator will be:

Time (t) = 30 × 50% = 30 × 50/100

= 15 days.

Next, we shall convert 15 days to hours. This can be obtained as follow:

1 day = 24 h

15 days = 15 days × 24 h / 1 day

15 days = 360 h

Next, we shall determine the energy consumed in KWh This can be obtained as follow:

Current (I) = 4.5 A

Voltage (V) = 120 V

Time (t) = 360 h

Energy (E) =?

E = ivt

E = 4.5 × 120 × 360

E = 194400 Wh

Next, we shall convert 194400 Wh to KWh. This can be obtained as follow:

1000 Wh = 1 KWh

Therefore,

194400 Wh = 194400 Wh × 1 KWh/ 1000 Wh

194400 Wh = 194.4 KWh

Thus the energy consumed is 194.4 KWh

Finally, we shall determine the cost of energy consumed. This can be obtained as follow:

From the question given above,

1 KWh cost $ 0.15

Therefore, 194.4 KWh will cost = 194.4 KWh × $ 0.15 = $ 29.16

Therefore, the cost of running the refrigerator for 30 days is $ 29.16

What are the results if you fail to turn the Bucky on?

Answers

Answer:

♡ here's your answer ♡

if you fail to turn the bucky on, it might result in your life being dangered since if in one case, your protecting yourself and you don't have it on, you could get killed ☆

- madeline/madi

✧・゚: *✧・゚:・゚✧*:・゚✧・゚

Explanation:

A 200.0 kg sled is being towed horizontally with a force of 25 N for 120 m in 30 seconds. What is the power of the applied force?

Answers

Answer:

.

Explanation:

Based on the information in the passage, What is true of gases

Answers

Answer:

that gases are gases

Explanation:

Answer:

A. Some, but not all gases are harmful to humans.

Explanation:

A 100-turn coil has a radius of 7.50 cm and a resistance of 50.0 W. At what rate must a perpendicular magnetic field change to produce a current of 5.00 A in the coil

Answers

Answer:

dB / dt = -141.47 T / s

Explanation:

For this exercise let's use Faraday's law to calculate the induced electromotive force

          E = - N dФ / dt

the magnetic flux is

         Ф = B. A

in this case the direction of the field and the normal to area are parallel so the scalar product is reduced to the algebraic product

         Ф = B A

  we substitute

        E = - N A dB / dt

the area of ​​the loop is

        A = π r²

we substitute

          E = - N π r² dB / dt

in the exercise indicate that the resistance of the coil is R = 50.0 Ω,

           E = i R

we substitute

           i R = -N π r² dB / dt

           dB / dT = - i R / N π r²

let's calculate

           dB / dt = - 5.00 50.0 / (100 π 0.075²)

           dB / dt = -141.47 T / s

A 0.5 kg ball is thrown horizontally towards a wall with a speed of 10 m/s. The initial velocity is chosen to be the positive x -direction for this question. The ball horizontally rebounds back from the wall with a speed of 10 m/s in the negative x -direction. What is momentum of the ball before it hits the wall, p? What is momentum of the ball after it hits the wall, p,? What is the change in momentum of the ball, delta p? (Give both magnitude and direction for each answer.) Is momentum conserved for the ball?

Answers

Explanation:

Step one:

given dara

mass of ball m=0.kg

initial velocity u= 10 m/s

final velocity v=10m/s

Required

momentum before and after impact

the expression for momentum P

P=mv

before impact

P=mv

P1=0.5*10

P1=5(kg⋅m/s)

after impact

P=mu

P2=0.5*10

P2=5(kg⋅m/s)

change  in momentum is =P1-P2= 5-5=0

yes, momentum is conserved.

neon sign transformer has a 460W AC output with an rms voltage of 15 kV when connected to a normal household outlet. There are 500 turns of wire in the primary coil. How many turns of wire does the secondary coil have

Answers

Answer:

The number of turns in the secondary coil is 62,500 turns.

Explanation:

Given;

power of the transformer, P = 460 W

output voltage, V₂ = 15 kV = 15,000 V

input voltage of normal household outlet, V₁ = 120 V

number of turns in the primary coil, N₁ = 500 turns

number of turns in the secondary coil, N₂ = ?

Apply the following the transformer equation;

[tex]\frac{N_2}{N_1} = \frac{V_2}{V_1}\\\\N_2 = \frac{V_2}{V_1}*N_1\\\\N_2 = \frac{15000}{120}*500\\\\N_2 = 62500 \ turns[/tex]

Therefore, the number of turns in the secondary coil is 62,500 turns.

Assume that the left side of your heart creates a pressure of 118 mm Hg by exerting a force directly on the blood over an effective area of 16.0 cm^2. What force does it exert to accomplish?

Answers

Answer:

251.5 x 10⁻⁴ N  

Explanation:

Pressure = Force / surface area

Force = pressure x area

pressure = 118 mm of Hg

= .118 x 13.6 x 9.8 N / m²

= 15.72 N / m ²

area = 16 x 10⁻⁴ m²

Force = 15.72 x 16 x 10⁻⁴

= 251.5 x 10⁻⁴ N  .

Arocket with an initial velocity of 20 m/s another engine that gives it an acceleration of 4 m/s ^ 2 over 10 secondsHow far did the rocket travel during this time

Answers

Answer:

50m

   

Explanation:

Given parameters:

Initial velocity  = 20m/s

Acceleration  = 4m/s²

Time  = 10s

Unknown:

Distance traveled by the rocket  = ?

Solution:

To solve this problem use the expression below;

   

     v² = u² + 2as

v is the final velocity

u is the initial velocity

a is the acceleration

s is the distance

  final velocity = 0

 Insert the parameters and solve;

  0²  = 20² + 2 x 4 x s

   -400  = 8s

         s  = 50m

   Disregard the negative sign because distance cannot be negative.

A student is planning to make changes to a circuit. Which change will
increase the resistance?
A. Replace the wire with one that is longer.
B. Swap ne positions of the battery and the switch.
C. Replace the wire with one that is shorter.
D. Swap the positions of the lightbulb and the switch.

Answers

Answer:

A)

Explanation:

This is because the longer the wire is, the more resistance there is for the electricity to run through.

The student can increase the resistance by replacing the wire with one that is longer. Thus, option A is correct.

What is Ohm's law?

The voltage across a conductor, according to Ohm's law, is precisely proportional to the current that passes through it.

A wire's resistance is inversely correlated with its cross-sectional area and directly correlated with its length. Most conductors have a resistance to the flow of an electric current through them. As the wire's length increases, the resistance in the wire rises.

However, according to Ohms law V=IR, a wire's length increases its resistance while decreasing its current for a given potential difference (voltage).

Therefore, replacing the wire with a longer one will increase resistance if a student plans to modify a circuit.

Thus, option A is correct.

Learn more about Ohm's law here:

https://brainly.com/question/1479631

#SPJ5

A plane flies from NY to LA at a constant speed of 800 km/hr. How long will it take a plane to fly 4200 km?

Answers

Answer: i don’t know the answer but

Explanation:

Divide the distance by the speed. That gives the travel time.

t = d/v = (4200 km) / (800 km/hr) = ? hrs

If it takes Jeff 3 hours and 33 minutes to drive 500 miles, what is his average velocity over this time?

Answers

Answer:

141  mph

Explanation:

aver. velocity = distance over time

                      =          500 miles          

                         3 hours + (33 min. x  1 hr.  )

                                                           60 min.

                     =   500 miles

                          3.55 hours

                     = 140.845 ≈ 141  miles / hour

In 1926 Babe Ruth hit a home run that was estimated to have landed 180. meters from home plate and to have reached a height of 21.3 meters. What was the initial velocity of the ball?

Answers

Answer:

v = 47.85 m / s ,   θ = 64.7º

Explanation:

This is a missile throwing exercise.

Let's find the speed to reach the maximum height, at this point the vertical speed is zero

        [tex]v_{y}^{2}[/tex] = v_{oy}^{2} - 2 g y

         0 = v_{oy}^{2} - 2gy

        v_{oy} = √2gy

let's calculate

        v_{oy} = √ (2 9.8 21.3)

        v_{oy} = 20.43 m / s

now we can calculate the time it takes to get to this point

      vy = v_{oy} - g t

       t = v_{oy} / g

       t = 20.43 / 9.8

       t = 2.08 s

in projectile launching, the time it takes for the body to rise is the same as the time it takes to go down, so the total launch time is

     [tex]t_{v}[/tex] = 2 t

     t_{v} = 2 2.08 = 4.16 s

let's use the horizontal throw ratio

      x = v₀ₓ t_{v}

      v₀ₓ = x / t_{v}

      v₀ₓ = 180 / 4.16

      v₀ₓ = 43.27 m / s

initial velocity is

      v = √ (v₀ₓ² + v_{oy}^{2})

      v = √ (20.43² + 43.27²)

      v = 47.85 m / s

with an angle of

      tan θ = I go / vox

      θ = tan⁻¹ (43.27 / 20.43)

      θ = 64.7º

in the velocity and acceleration are in the same direction the speed of the object decreases
true or false

Answers

Answer:

False

Explanation:

Im pretty sure the answer is false


What is the average velocity in the time interval 3 to 4
seconds?

Answers

Answer:

0 m/s.

Explanation:

The average velocity from 3 to 4 seconds is 0 m/s.

A 5000 kg meteorite falls toward the earth. What is the magnitude of the earth's acceleration just before impact? The earth's mass is 5.98 × 10^24 kg.

Answers

Answer:

8.193x10^-21m/s²

Explanation:

We have it that the gravitational force that is acting on this object is equal to the earth's gravitational force.

We start by using this formula

Ma = mg

We make a the subject of formula

a = mg/M

m = 5000kg

g = 9.8

M = 5.98x10^24kg

mg = 5000x9.8

= 49000

49000/5.98x10^24

= 8.193x10^-21m/s²

The magnitude of the earth's acceleration is 8.20 × 10^27

The parameters given in the question are;

mass= 5000 kg

g= 9.81

earth's mass= 5.98 × 10∧ 24

The formula is

= mass × acceleration due to gravity/earth's mass

= 5000 × 9.81/ 5.98^24

= 49,050/5.98 × 10^24

= 8.20 × 10^27

Hence the magnitude of the earth's acceleration just before impact is 8.20 × 10^27

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11. A 100-W incandescent light bulb has a cylindrical tungsten filament 30.0 cm long, 0.40 mm in diameter, and with an emissivity of 0.26. (a) What is the temperature of the filament

Answers

Answer:

 T = 556K

Explanation:

For this exercise let's use Stefan's law

        P = σ A e T⁴

where the stafan-Boltzmann constant is 5,670 10⁻⁸ W / m² K⁴.

In this case the area of ​​a circular cylinder is

        A = π r²

the radius is

         r = d / 2 = 0.150 m

        A = π (0,150)²

        A = 7.0685 10⁻² m²

let's clear

         T⁴ = P /σ A e

         T⁴ = 100 / (5.670 10⁻⁸   7.0685 10⁻²  0.26)

         T⁴ = 9.5966 10¹⁰ = 959.66 10⁸

         T = 5.56 102 K

         T = 556K

The temperature of the filament is 366.3 K

Using the equation for radiated power, P

P = σεAT⁴ where σ = Stefan-Boltzmann constant = 5.67 × 10⁻⁸ W/m²K⁴, ε = emissivity = 0.26, A = area of cylindrical tungsten filament = πDh (since it radiates through its sides)where D = diameter of tungsten filament = 0.40 mm = 0.4 × 10⁻³ m and h = length of tungsten filament = 30.0 cm = 0.3 m and T = temperature of tungsten filament.

Since we require the temperature of the filament, making T subject of the formula, we have

T = ⁴√(P/σεA)

T = ⁴√(P/σεπDh)

Since P = 100 W, substituting the values of the variables into the equation, we have

T = ⁴√(P/σεπDh)

T = ⁴√(100 W/5.67 × 10⁻⁸ W/m²K⁴× 0.26 × π× 0.4 × 10⁻³ m × 0.3 m)

T = ⁴√(100 W/0.5558 W/K⁴ × 10⁻⁸)

T = ⁴√179.93 × 10⁸ K⁴)

T = 3.663 × 10² K

T = 366.3 K

So, the temperature of the filament is 366.3 K

Learn more about temperature of a filament here:

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Consider a 75.5-kg man standing on a spring scale in an elevator. Starting from rest, the elevator ascends, attaining its maximum speed of 1.65 m/s in 0.675 s. What does the spring scale register in pounds during these 0.675 s?

Answers

Answer:

208.08 pounds

Explanation:

Given that,

Mass of a man, m = 75.5 kg

Starting from rest, the elevator ascends, attaining its maximum speed of 1.65 m/s in 0.675 s.

We need to find the value of spring scale during these 0.675 s.

As the elevator ascends, net force will be given by :

F = mg + ma

a can be calculated as follows :

[tex]a=\dfrac{1.65-0}{0.675}\\\\a=2.45\ m/s^2[/tex]

So,

F = 75.5[(9.81) + (2.45)]

F = 925.63  N

We know that,

1 N = 0.224 Pounds

It means, 925.63  N = 208.08 pounds

So, the spring scale will register 208.08 pounds.

as a result of photosynthesis is the production of sugar molecules known as what?

Answers

Answer:

Glucose

Explanation:

Answer:

Check in your science textbook

A wagon having a mass of 32 kg is accelerated across a level road at 0.50 m/s2 . What net force acts on the wagon horizontally?

Answers

Answer:

16 N

Explanation:

The force acting on an object given it's mass and acceleration can be found by using the formula

force = mass × acceleration

From the question we have

force = 32 × 0.5

We have the final answer as

16 N

Hope this helps you

4. Name three things that all games, no matter where they are played around the world, have in common.

Answers

Answer:

Key components of games are goals, rules, challenge, and interaction.

Explanation:

Hope I helped.

Answer:

the name of the games are goals, rules, challenges and interaction and mabe there can be more.

Explanation:

I hope this helped your day better this is the correct answer i got it correct on the test.

How fast would a rock fall in a vacuum? Based on this, why would Aristotle say that there could be no such thing as a vacuum?

Answers

Answer:

In real measurements, the acceleration that is measured is always less than the acceleration of gravity, therefore there must be a force that opposes the movement, which is why Aristotle says that vacuum stenos

Explanation:

When a rock starts the vacuum, there are no friction forces that make its movement, therefore, if close to the Earth, the rock has an acceleration equal to the acceleration of gravity.

In real measurements, the acceleration that is measured is always less than the acceleration of gravity, therefore there must be a force that opposes the movement, which is why Aristotle says that vacuum stenos

As you get older your muscles grow.

True
True

False

Answers

Answer:

f

Explanation:

Answer:

yeah but if you get in your 30s you start to lose muscles

cloudy nights are usually warm because​

Answers

Answer:

When you have a cloudy night, the clouds prevent heat from escaping through the atmosphere and into space.

The clouds act like a blanket and trap the heat it, and that is why every time you have a cloudy night, it is always warmer than a clear night.

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Rosa spent $11.52 on 8 candy necklaces for each of her two friends. How much did each necklace cost? 2.16 or 2.8 which is bigger Which of the following situations is the best example of a positive consequence?A.Adams dad made him pay for his own car insurance because he got a third speeding ticket.B.Adriana had to repeat the sixth grade because she decided her homework was not important.C.Maurices coach made him sit on the bench during the track meet because he chose to skip track practice on Wednesday.D.Dillon was able to play on his computer for an extra hour because he watched his brother and sister when his mom went to the store. Which of following is the graph of y = -(x + 1)2-3? all of the following are terminating decimals except__.17/501/82/32/5 Consider a risky portfolio. The end-of-year cash flow derived from the portfolio will be either $150,000 or $290,000 with equal probabilities of 0.5. The alternative risk-free investment in T-bills pays 6% per year. A. If you require a risk premium of 7%, how much will you be willing to pay for the portfolio?B. Suppose the portfolio can be purchased for the amount you found in (a). What will the expected rate of return on the portfolio be? C. Now suppose you require a risk premium of 15%. What is the price you will be willing to pay now? select all that apply which decimals in the list are repeating decimals5/6 4/153/51 3/41/34/1000 Evaluate the expression x/2+5x7 when x=2 . Mr. Ramsey bought 5 pounds of dog food for $10. How much did he pay per pound in dollars?$15.00 per pound$5.00 per pound$50.00 per pound$2.00 per pound What is the relationship between interest rates and aggregate spending?A.when interest rates increase, aggregate spending also increasesB.when interest rates increase, aggregate spending decreasesOC. they do not have any relationODboth the factors are affected favorably by any external factorO E.both the factors are affected adversely by any external factor Convert -145 degrees to radians. Valerie bought a coat at a winter half-price sale. A sales tax of $6.24 was added to the sale price, bringing the cost of the coat to $84.24. Which of the following equations would give the original price ( p ) of the coat? A t-shirt increased in price by 14. After the increase it was priced at 20. What was the original price of the t-shirt? The recipe for beef stew calls for 1/4 teaspoon of pepper for every 3 potatoes. If 9 potatoes are used, how much pepper is needed?Solve the proportion StartFraction one-fourth over 3 EndFraction = StartFraction p over 9 EndFraction to answer the question. Explain your steps: Which inequality relates BC and XY? 80 points and brainliest!!!!Pleaseeeeee Help Meeeee!!!! Find the quotient 4020. Tori is sending a birthday gift to her friend out of state and wants to know how much brown paper she will need tocover the box.8 in10 in.14 inWhich statement is true about the amount of paper Tori will need to cover the entire box?O Covering the entire box is the surface area, which is 664 in.?.O Covering the entire box is the surface area, which is 1,120 in.?O Covering the entire box is the volume, which is 664 in.3.O Covering the entire box is the volume, which is 1,120 in.?. The first 3 terms of n+7 how many moles of water are needed to react with 100. g of al4c3