the 30kg girl pushes the 20kg boy, and he moves away at a speed of 2.0m/s. if momentum is conserved, what is the girls speed?

Answer:

k = 65.3 N/m

Explanation:

Fs = Fg = mg = (1.0 kg)(-9.8 m/s²) = -9.8 N

x = 15 cm = 0.15m

Fs = -kx  (Hooke's Law)

-k = Fs/x = (-9.8 N)(0.15 m) = -65.3

k = 65.3 N/m

Density of the object is 3333.33 kg/m³.

Density can be defined as the ratio of the mass of a body to its volume.

From Archimedes principle,

Rd = W/U = D/D'

Where Rd = relative density,

W = weight of the object in air,

U = upthrust in water,

D = Density of the object,

D' = Density of water.

W/U = D/D'

Density (D) of the solid can be calculated by the equation,

D = D'(W/U)

As we have,

W = 5.0 N,

U = 5.0 -3.5 = 1.5 N,

D' = 1000 kg/m³

Since U = lost in weight = weight in air - weight in water

D = 1000(5/1.5)

D = 3333.33 kg/m³

Thus the density of the solid object is 3333.33 kg/m³

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The magnetic field for this wave is

[tex]B(x, t)=(9*10^{-8}T )i sin[2\pi (1.5*10^{-8}x-2*10^{14}t )][/tex].

Electromagnetic Wave:

The oscillations between an electric field and a magnetic field produce waves known as electromagnetic waves or EM waves. In other words, magnetic and electric fields oscillate to form electromagnetic (EM) waves.

Given,

         Frequency of the wave;  [tex]f=[/tex] [tex]2*10^{14} Hz[/tex]

         The amplitude of the Electric Field;  [tex]E_{0} = 27 N/C[/tex]

We know that Maxwell's equation is given by,

                                      [tex]\frac{E_{0} }{B_0} =c[/tex]        .....................(1)

Where,

         [tex]E_{0} =[/tex] The amplitude of the electric field

         [tex]B_{0}=[/tex] The amplitude of the magnetic field

            [tex]c=[/tex] The velocity of light = [tex]3*10^{8} N/m^{2}[/tex]

By solving equation (1), we get

                                     [tex]B_{0} =\frac{27}{3*10^{8} }[/tex]

                                      [tex]B_{0}=9*10^{-8}[/tex]

We know that,

         Angular frequency; ω [tex]= 2\pi f[/tex]

The equation of the magnetic field can be given by

                  [tex]B_{0}sin(kx-\omega t) =B_{0}sin(2\pi (\frac{x}{\lambda}-ft ))[/tex]

                  [tex]B_{0}sin(kx-\omega t)=9*10^{-8} sin(2\pi (\frac{x}{\lambda}-2*10^{14} t))[/tex].

Hence,

         The magnetic field for this wave is

                        [tex]B(x, t)=(9*10^{-8}T )i sin[2\pi (1.5*10^{-8}x-2*10^{14}t )][/tex].

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Induction charging is a method used to charge an object without actually touching the object to any other charged object. The process by which an object receives a static charge when placed near a second charged object is known as inductance.

Induction charges another body without came in contact with that body.

During induction, charges move between objects that briefly touch; during conduction, charges move between objects that are rubbed together.

if the charges have the same sign, then the force is repulsive, this means that the forces point away from each other, so in this case the forces have opposite directions.

Charging by conduction refers to the contact of a charged object to a neutral object, which is the opposite of induction.

Charging by induction refers to charging an object without making contact, it could be through an electric field.

Therefore, the induction charging is a method used to charge an object without actually touching the object to any other charged object. The process by which an object receives a static charge when placed near a second charged object is known as inductance.

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The probability mass function is obtained as:

[tex]p(x=x)=12 c_x \quad(0.4)^x(1-0.4)^{1 x-x} ; x=0,1,2 \ldots .12[/tex]

Outcome is,

[tex]n=12 \\ p=0.4[/tex]

Let X be discrete random variable which takes value [tex]$i=1,2 \ldots$[/tex].

Now the probability of mass function at point is is given by:

[tex]p(x=p)=p\left(x_i\right)=F\left(x_i\right)-F\left(x_{(i-1)}\right)[/tex]

By using Bernoulli's random variable:

[tex]P(x=x)=p^x(1-p)^{1-x} x=0,1[/tex]

where as [tex]$x=0 \Rightarrow$[/tex] corresponds to failure

[tex]$x=1 \Rightarrow$[/tex] correspond to Success

p is probability function of Success.

Therefore the total number of Success in ' n ' independent Bernoulli trials is Sum of ' n ' bernoulis random variable which gives binomial distribution.

By using multiplication rule the probability of observing ' x 'Successes in ' n ' independent bernoulli trials it can be written as:

[tex]\underbrace{p \times p \times \ldots \times p}_{x \text { times }} \times(\underbrace{() 1-p) \times(1-p) \times \ldots \times(1-p)}_{n-x \text { times }}[/tex]

The probability mass function :

[tex]p(x=x)=12 c_x \quad(0.4)^x(1-0.4)^{1 x-x} ; x=0,1,2 \ldots .12[/tex]

where as

[tex]n=12 \\ p=0.4[/tex]

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Note:- The question is as follow,

Consider the probability space [tex]$(S, M, P)$[/tex] that models the observed proportion of successes in n independent Bernoulli trials with probability of success equal to p. For example, given n=12 and p=0.4, the outcome [tex]\frac{5}{12}=.41 \overline{6} \:in $(S, M, P)$[/tex] should have the same probability as the outcome of 5 successes in 12 independent Bernoulli trials with probability of success equal to 0.4. Give a formula for the density function f(s) for this probability space in terms of the density [tex]$f_{n, p}$[/tex] of the binomial distribution with size n and probability p. ( points)

The maximum absolute values of the shear and bending moment is 2P and 3Pₐ respectively.

(a) Diagram is shown in image.

From A to B:

+∑Fy = 0: V = -P

+∑M₁ = 0: M = -P

From B to C:

+∑Fy = 0:

-P-P-V = 0

⇒ V = -2P

+∑M₂ = 0:

Pₓ+P(x - a)+M =0

⇒ M = -2Pₓ + Pₐ

(b) The maximum bending moment occurs in a beam, when the shear force at the section is zero or changes the sign because at point of contra fixture the bending moment is zero.

Therefore

= |V|max = 2P

= |M|max = 3Pₐ

Thus, the maximum absolute values of the shear and beading moment is 2P and 3Pₐ.

-- The given question is incomplete, I answer the question in general according to my knowledge and the complete question is

"For the beam and loading shown, (a) draw the shear and bending-moment diagrams, (b) determine the maximum absolute values of the shear and bending moment." --

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In a series resonant LCR circuit, the voltage across R is 100 volts and R= 1Ω with C = 2μF. The resonant frequency ω is 200 rad/s. At resonance, the voltage across L is D) 2.5 × 10⁵ volt.

given that :

V = 100 v

R = 1Ω

ω = 200 rad/s

C = 2μF

ω²  = 1 / LC

(200)² = 1/ L × 2 × 10⁶

L = 12.5 H

current = 100 A

now, at resonance ,

voltage across the L is equals to voltage across C

voltage across L = 100 × ( 1 / 200  × 2 × 10⁶)

voltage across L =  2.5 × 10⁵ volt.

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The speed of the to stick together blobs immediately after colliding will be 2m/s.

Given that:

Mass of first blob = 4kg = m1

Velocity of blob = 8m/s = v1

Mass of second blob = 12kg = m2

Velocity of blob = 0m/s = v2

To find:

Final velocity = Vf

Formula to be use:

(m1*v1) + (m2*V2) = Vf(m1 + m2)

(4*8) + (12*0) = Vf(4+12)

32 + 0 = Vf(16)

32 = Vf(16)

Vf =  2m/s

So the speed of two blobs immediately after colliding = 2m/s

V1: (m1-m2/m1+m2)

u1 + (2m2/m1+m2)

u2 V2: ( 2m1/m1+m2) u1 + (m2-m1/m1+m2) u2 Assume that mass 1 has an initial velocity of u1, a final velocity of v1, a mass 2 beginning velocity of u2, and a mass 2 final velocity of v2.

V1 stands for the volume of stock solution required to create the new solution. M1 = Stock solution concentration. The total volume of the solution is V2.

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If a conductor is in electrostatic equilibrium near an electrical charge i.e. the correct option is, B) The electric field inside the conductor must be zero.

The conductor in electrostatic equilibrium has characteristics such as a zero electric field inside and excess charges that are located on the surface. Therefore, the conductor's internal electric field must be zero.

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The roller coaster is going with 15.34 m/s when it reaches the bottom.

Energy cannot be created or destroyed, according to the law of conservation of energy. However, it is capable of change from one form to another.

According to the question, potential energy of the roller coaster at initial position = mass * acceleration due to gravity* height = mgh

Let the speed of the roller coaster at the bottom = v.

So, kinetic energy at the bottom = 1/2 * mass * speed^2 = 1/2 mv^2

From conservation of energy:

mgh = 1/2mv^2

v= √( 2gh)

= √( 2 × 9.8 × 12) m/s

= 15.34 m/s.

Hence, the speed of it at the bottom is 15.34 m/s.

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(a) The growing rate of shadow when the person is 30 ft from the lamp post is 15/7 ft/m

(b) The moving rate of the tip of the shadow when the person is 30 ft from the lamp post is 50/7 ft/m

Given,

      Height of the man = 6 ft

      Height of the lamp post = 20 ft

                                        [tex]\frac{dx}{dt} =5 ft/m[/tex]

Let,

      The distance between the base of lamp and the man = x

From the geometry,

             [tex]\frac{6}{20} =\frac{y}{x+y}[/tex]

          [tex]6(x+y) = 20y[/tex]

                [tex]3x=7y[/tex]                       .......................(1)

And,

            [tex]6(\frac{dx}{dy} )=14(\frac{dy}{dt} )[/tex]

               [tex]\frac{dy}{dt}=\frac{15}{7}[/tex]

∵              [tex]\frac{dx}{dt} =5 ft/m[/tex]

∴        [tex]\frac{dx}{dt}+\frac{dy}{dt} =5+\frac{15}{7}[/tex][tex]=\frac{50}{7}[/tex]

Hence,

         (a) The growing rate of shadow when the person is 30 ft from the lamp post is 15/7 ft/m

         (b) The moving rate of the tip of the shadow when the person is 30 ft from the lamp post is 50/7 ft/m

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After extinguishing a fire on the first floor of a two-story balloon-framed house, the best action for crews is to immediately open the walls and check for fire in the basement, second floor, and attic.

The vertical struts of the outer wall are continuous from the foundation to the roof with a balloon frame structure. When the roof collapses into a structure, it can provide a watertight cover over a buried fire. Heavy wood is more stable than lightweight structures in fire conditions.

Marion of the building is surrounded by balloons, from the foundation to the eaves line he extends upwards more than two stories. A mansard or mansard roof is his four-sided gambrel-style hipped roof characterized by his two slopes on either side, the lower slope pierced with dormer windows and angled more steeply than the upper.

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This radiator's Heat radiation is 12.8 W.

Provided, the temperature of the radiator θ = 30°C

So, the absolute temperature of the radiator,

T = ( θ + 273 ) K

  = ( 30 +273 ) K

  = 303 K

Also provided, the temperature of the surrounding space, T₀ = 3 K

The emissivity of the white paint, ε = 0.89

The length of one side of the radiator, L = 0.3m and the breadth, B = 0.1m.

Now, the amount of rate of  heat transfer by a system at temperature T to a surrounding space at temperature T₀ is given by the formula,

Q = σεFA(T⁴-T₀⁴).

where A is the area of the system exposed to the surrounding, F is the view factor, σ is the Stefan-Boltzmann constant = 5.67 × 10⁻⁸Wm⁻²K⁻⁴ and σ is the emissivity of the system.

Here, the surface area of the radiator,

A = LB = (0.3m) (0.1m) = 0.03 m²

According to the question, the radiator has a full view factor to the space, i.e. we can say, the view factor in this case is, F = 1.

Substituting all known values into the equation we just mentioned we get,

Q = σεFA(T⁴-T₀⁴)

   = (5.67 × 10⁻⁸Wm⁻²K⁻⁴) (0.89) (1) (0.03 m²) [ (303K)⁴ - (3K )⁴ ]

   = 12.76 W

   ≈ 12.8 W

So, the rate of heat radiation is, Q = 12.8 W

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The final velocity equations for elastic collisions is

[tex]$\begin{aligned}& u_1=\frac{3}{2} v_i \\& u_2=\frac{1}{2} v_i\end{aligned}$$[/tex]

A collision between two bodies in physics is referred to as an elastic collision if their combined kinetic energy stays constant. There is no net conversion of kinetic energy into other forms, such as heat, noise, or potential energy, in an ideal, fully elastic collision.

Lat their final speeds of bouncing back are u_1 and u_2 As the collision is clastic, e=1So,u_1+u_2=v_i+v_i=2 v_i

From momentum conservation, 3 m v_i-4 m v_i=4 m u_2-3 m u_1

[tex]$$\begin{aligned}& \Rightarrow \quad-2 v_i=4 u_2-3 u_1 \\& \Rightarrow 3 u_1-5 u_2=2 v_i-\text { (2) }\end{aligned}$$[/tex]

From (1) and (2),

[tex]$$\begin{aligned}u_1+u_2 & =3 u_1-5 u_2 \\\Rightarrow 2 u_1 & =6 u_2 \Rightarrow u_1=3 u_2\end{aligned}$$[/tex]

From (1),

[tex]$3 u_2+u_2=2 v_i$[/tex]

[tex]$$\text { and } \begin{aligned}\Rightarrow u_2 & =\frac{1}{2} v_i \\u_1 & =3 u_2=\frac{3}{2} v_i .\end{aligned}$$[/tex]

So,

[tex]$$\begin{aligned}& u_1=\frac{3}{2} v_i \\& u_2=\frac{1}{2} v_i\end{aligned}[/tex]

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Answer:

work, power

Explanation:

Work = Fnet x distance

Work is NOT dependent on time

Power = Work ÷ time

The slower the work is done, the higher the power.  The faster the same amount of work is done, the lower the power.  Power, with work constant, is inversely proportional to time.

The hitters final displacement from home plate is 60 m.

The displacement of an object is the change in the position of the object.

The displacement of an object is determined from the shortest distance between the initial position and the final position of an object.

The hitters final displacement from home plate is calculated as follows;

Δx = x₁ - x₂

where;

Δx = x₁ - x₂

Δx = 30 m  - ( - 30 m)

Δx = 30 m + 30 m

Δx =  60 m

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The image height for a converging lens with a 20 cm focal length and a diverging lens with a 38 cm focal length that are 78.0 cm apart is 1.35 cm. 40 cm are in front of the converging lens

And a 2.7 cm tall object is there. An optical lens that converges all light rays travelling through it is known as a converging lens. A converging lens  main function is to concentrate and converge the incoming light rays from an object to create an image. Depending on how close an object is to the lens, the image may be enlarged or unchanged.

h = (-di/do)(-di2/do2)*height

h = (-38/38)(-(-15))/30 (2.7)

h = -1.35 cm

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The complete question is-

a converging lens with a focal length of 20 cm and a diverging lens with a focal length of -38 cm are 78.0 cm apart. a 2.7-cm-tall object is 40 cm in front of the converging lens. Calculate the image height. Express your answer to two significant figures and include the appropriate units.

Playing sport is the activity in which you can be sure that athletes find great utility and is therefore denoted as option C.

This is referred to a person who competes in one or more sports such as soccer, basketball etc that involve physical strength, speed, or endurance etc.

Therefore playing sports by an athlete will lead to an increase in utility as a result of them developing various skills and composure from it in the form of endurance, strength etc and various positions on the field which isn't applicable in reading books or composing music and is therefore the reason why it was chosen as the correct choice in this scenario.

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Answer:

Gamma Ray but read below

Explanation:

All of the types of electromagnetic radiation listed can pass through Earth's atmosphere, although some types are absorbed or blocked more easily than others.

Visible light, infrared radiation, and radio waves are able to pass through the atmosphere relatively easily, while gamma rays are more likely to be absorbed.

This is because gamma rays have a higher energy than the other types of radiation, so they are more easily absorbed by the atoms and molecules in the atmosphere.

Answer:

Gamma Rays

Explanation:

It has the highest possible frequency lowest wavelength and the most energetic charge. Its travels at the speed of light and is highly penerative

No, the activation energy for a forward reaction is not equal to the activation energy for the reverse of the same reaction.

In order for compounds to undergo a chemical reaction, a certain amount of energy is required, known as the activation energy. The unit of measurement for a reaction's activation energy (Ea) is either joules per mole (J/mol), kilojoules per mole (kJ/mol), or kilocalories per mole (kcal/mol). You can think of activation energy as the size of the potential barrier between the minima of the potential energy surface related to the initial and final thermodynamic states, which is also referred to as the energy barrier. If the system temperature is high enough, there should be a sizable number of molecules with translational energies that are equal to or higher than the activation energies.

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The figure shows a block of mass m resting on a 20 degree slope. As the system is at rest For the equilibrium of 2 kg block

What is mass ?

A body's mass is an inherent quality. Prior to the discovery of the atom and particle physics, it was widely considered to be tied to the amount of matter in a physical body.A measurement of how much matter is present in or makes up a physical body. In classical mechanics, an object's mass is crucial to Newton's laws of motion because it influences the force needed to accelerate it and, consequently, how much inertia it has.

[tex]$$\begin{aligned}& T-2 k g \times 9.8 \mathrm{~m} / \mathrm{s}^2=0 \\& T=2 \mathrm{~kg} \times 9.8 \mathrm{~m} / \mathrm{s}^2=19.6 \mathrm{~N}\end{aligned}$$[/tex]

For the equilibrium of second block

[tex]$$\begin{aligned}& T=m g \sin 20^0+f \\& T=m g \sin 20^0+\mu_s R \\& T=m g \sin 20^0+\mu_s m g \cos 20^0 \\& T=m\left(g \sin 20^0+\mu_s g \cos 20^0\right) \\& m=\frac{T}{\left(g \sin 20^0+\mu_s g \cos 20^0\right)} \\& m=\frac{19.6 N}{\left(9.8 \mathrm{~m} / \mathrm{s}^2 \sin 20^0+0.64 \times 9.8 \mathrm{~m} / \mathrm{s}^2 \cos 20^0\right)} \\& m=\frac{19.6 \mathrm{~N}}{9.25 \mathrm{~m} / \mathrm{s}^2}=2.12 \mathrm{~kg}\end{aligned}$$[/tex]

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The linear acceleration of the spool below (mass m, moment of inertia i) if it is rolling without slipping: A spool of mass m and moment of inertia I (around its center) is free to roll without slipping on a table. It has an inner radius of r and an outer radius of R.

In mechanics, acceleration is the charge of the alternate velocity of an item with recognition of time. Accelerations are vector portions. The orientation of an item's acceleration is given by the orientation of the internet pressure acting on that item.

Acceleration, is the price at which speed modifications with time, in terms of each pace and path. A point or an object transferring in an instant line is accelerated if it quickens or slows down. movement on a circle is multiplied although the rate is constant due to the fact the path is always converting.

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Answer:

a) >26.7 N

b)  >13.3 N

Explanation:

a)  Fg = (17 kg)(9.8 m/s²) = 166.6 N

Fnormal = Fg = 166.6 N

Ff = μFn = 0.16(166.6 N) = 26.7 N

Janitor needs to push >26.7 N to overcome the Force of friction (Ff) on a horizontal floor.

b)  You have to determine Fn on the object by figuring out the y-component of Fg.

Fn/Fg = sin30

Fn = sin30(166.6 N) = 83.3 N

Now you can find Ff.

Ff = μFn = 0.16(83.3 N) = 13.3 N

Janitor needs to push >13.3 N down the incline to overcome Ff

Makes sense that he has to push less down an incline.

Understanding an object's structure and function requires observation at a variety of wavelengths.

This is due to the fact that we have just lately been able to view the complete electromagnetic spectrum of the universe.There are objects in our universe that emit a wide variety of radiation having wavelengths either being too short or long for human eyes to see.

Astronomers can learn something distinctive about an item by examining its light at various wavelengths.Astronomers may see "the broad picture" of what's actually happening with that object by examining all available wavelengths and developing models that account for everything those photographs show.

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The lead pollution can be remediated by the appllication of the approppiate reagents.

We know that we need to always consider the threshold concentration of pollution as we are looking at the safety of the environment

Now we are told that the safe concentration of the lead must not be more than 400 ppm. Above that concentration, the effects may be quiet fatal.

There should be spirited attempts to remediate the soil by the use different methods so that the soil can become good again for the growing of crops.

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In cases when the stairway is straight, the width of the landing in the direction of travel must at least match the stair's width and cannot be greater than 1219mm.

The four main axes are north, south, east, and west. A map is a representation or drawing of the entire or a portion of the surface of the earth done to scale and on a flat surface. A spherical shape, however, cannot be totally flattened. Distance, direction, and symbol are the three elements that make up a map.

Most maps have an arrow with the letter "N" on them in the upper right-hand corner. North is indicated by this arrow's orientation. It is referred to as the north line. You can determine which direction is east, west, or south once you know which way is north. The four main axes are North, South, East, and West. ​

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The required wave speed and tension in the string are 15 m/s , 0.036 N respectively.

Speed is characterized as. The pace of progress of position of an item toward any path. Speed is estimated as the proportion of distance to the time in which the distance was covered. Speed is a scalar amount as it has just course and no extent.

(a) The wave speed is given by v=λ/T=ω/k,

where λ is the frequency, T is the period ω is the precise recurrence (2π/T), and k is the rakish wave number(2π/λ).

The displacement  has the structure y=y sin(kx+ωt), so 4k=2.0m

 furthermore, ω=30 rad/s.

Hence v=(30 rad/s)/(2.0m)=15 m/s.

b) Since the wave speed is given by v= τ/μ

, where τ is the pressure in the string and μ is the straight mass thickness of the string, the strain is

τ=μv =(1.6×10 kg/m)(15 m/s) =0.036 N.

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The person exerts negative work on the book by applying a force in the direction opposite to its displacement, causing the total mechanical energy to decrease. Hence, option (D) is correct.

The given problem is based on the concept of mechanical energy. The mechanical energy is the energy of any object by virtue of its position or motion. And mathematically, it is expressed as the sum of kinetic energy and potential energy.

And the work completed is described as,

W = F * d

here,

W is the work done

F is the applied force

d is the displacement

The individual lowers the book in the provided situation at a slow manner. This means some work has been done by applying force in downward direction. This work will be negative, because it is opposite to the displacement. So, work done is negative.

And according to work energy concept,

Work done = Change in kinetic energy

Negative work accounts for negative value of kinetic energy. Which means kinetic energy is decreasing continuously. Additionally, if kinetic energy declines, mechanical energy will eventually follow.

The question is incomplete. The complete question is ' A. the total mechanical energy is unchanged, because there is no change in the book's kinetic energy as it is lowered to the table.

B. the total mechanical energy is unchanged, because no work is done on the earth-book system while the book is lowered.

C. the total mechanical energy decreases, because the person does positive work on the book by exerting a force that opposes the gravitational force.

D. The total mechanical energy decreases, because the person does negative work on the book by exerting a force on the book in the direction opposite to its displacement.'

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the bitewing tab is a heavy paperboard tab or loop fitted around a periapical film or sensor and used to stabilize the receptor during exposure. true

What is stabilize?

to stop changing and fix something, especially to prevent it from getting worse, or to induce something to stop changing and fix it: These drugs reduce blood pressure and calm your heart rate.

the periapical receptor is oriented in the bite loop so that the tab portion extends from the white side (tube side) of the film or sensor.True

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The velocity of the drone that travels a distance of 924 m is 10.5 m/s.

Velocity is defined as a vector measurement of the rate and direction of motion. The S.I unit of velocity is m/s

To calculate the velocity of the drone, we use the formula below.

Formula:

Where:

From the question,

Given:

Substitute these values into equation 1

Hence, the velocity of the drone is 10.5 m/s.

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