what is the magnification of a virtual image if the image is 10.0 cm....

Energy/power is not gained or lost going through a (ideal) transformer.

So the transformer in this problem really doesn't matter.  If the lamp is using energy at the rate of 60 watts, then the whole contraption is getting 60 watts of power from the wall outlet.

Power = (voltage) x (current)

60 watts = (120 v) x (current)

Current = (60 watts) / (120 v)

Current = 0.5 Ampere

Answer:

A

Explanation:

The energy of an electromagnetic wave is directly proportional to its frequency, according to the equation:

E = hf

where

h is the Planck constant

f is the frequency

The frequency of a wave is the number of complete cycles per unit of time: in the figures shown, we see that the more we go towards the right, the higher the frequency is (because the wavelength becomes shorter, so the waves makes more complete cycles per second). This means that the more the box is on the right, the higher the frequency: the figure with the box located more on the right is A, so this is also the figure that represents the range of frequencies with most energy.

Answer:

B

Explanation:

The problem you would encounter is measuring the height of two different people, a tall one and a short one, and getting the same answer for both of them.

No matter WHAT we're hearing out of the White House these days, you CAN'T bend and stretch your standard measuring devices, or any other 'facts', to make them fit the thing that you're measuring.  This does not work.  You're always entitled to your own opinions, but you're not entitled to your own facts.

An elastic measuring tape should not be used to measure distance because its stretchability can lead to inaccurate and unreliable measurements.

You cannot use an elastic measuring tape to measure distance accurately because it can stretch, which would result in an unreliable measurement. The problem you may face if you use an elastic measuring tape is that the stretching of the tape will lead to incorrect measurements, especially if the distances being measured require precise and firm measurement tools. Measuring tapes are typically flexible but maintain their length without stretching to ensure that measurements are consistent. For accurate measurement of length or distance, you should select a measuring tool that is suited to the size you are trying to measure, ranging from a ruler for small items to a yardstick or a non-elastic measuring tape for larger distances.

Answer:

John Glenn

Explanation:

Answer:

John Glenn was the first American to orbit the Earth. The first human in space was the Soviet cosmonaut Yuri Gagarin. 

Explanation:

Hope this helps. Feel free to let me know if you need any more help :)

Yes they are all correct

You can check your answers at

https://eesc.columbia.edu/courses/ees/climate/lectures/gen_circ/index.html

Answer:

5 seconds

Explanation:

The straight line distance between (0, 0) and the antelope's position (x, y) at time t can be found using distance formula:

d² = x² + y²

d² = (-39 + 40t)² + (228 + 30t)²

d² = 1521 - 3120t + 1600t² + 51984 + 13680t + 900t²

d² = 53505 + 10560t + 2500t²

The cheetah can run a total distance of:

105 * 7 = 735

The time t at this distance is:

735² = 53505 + 10560t + 2500t²

540225 = 53505 + 10560t + 2500t²

0 = -486720 + 10560t + 2500t²

0 = -24336 + 528t + 125t²

t = 12, -16.224

t can't be negative, so t = 12.

Therefore, the cheetah can wait 5 seconds before it has to start running.

Answer:

Wait time = 5 s

Explanation:

As we know that the position vector of the antelope is given as

[tex]x = -39 + 40 t[/tex]

[tex]y = 228 + 30 t[/tex]

so here at any instant of time its distance from origin is given as

[tex]d^2 = x^2 + y^2[/tex]

so we have

[tex]d^2 = (-39 + 40t)^2 + (228 + 30t)^2[/tex]

[tex]d^2 = 53505 + 2500 t^2 + 10560 t[/tex]

now when cheetah catch the antelope then distance of cheetah and antelope from origin must be same

so distance covered by cheetah in 7 s is given as

[tex]d = 105 \times 7[/tex]

[tex]d = 735 ft[/tex]

now from the above two equation

[tex]735^2 = 53505 + 2500 t^2 + 10560t[/tex]

by solving above equation we got

t = 12 s

so Cheetah must have to waith for

[tex]\Delta t = 12 - 7 = 5 s[/tex]

The acceleration of the object is defined as the rate of change of velocity divided by change in time. Acceleration is the vector quantity.

Acceleration of the object is obtained by a change in velocity. Velocity defines the how speed the object travels in a particular direction. Velocity is also defined as the rate of change of displacement per unit time.

Acceleration depends on the velocity. Acceleration, (a) = Δv/Δt, where Δv changes in velocity and Δt is a change in time. When velocity changes with time gives acceleration. Velocity is the vector quantity and hence, acceleration is also a vector quantity. The SI unit of velocity is m/s².

If the velocity increases with time, it is acceleration and if the velocity decreases with time, it is called deceleration. Hence, the change in velocity divided by the change in time gives, acceleration.

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Acceleration is defined as the change in velocity divided by the time period over which the change occurs, and it is measured in meters per second squared (m/s²).

Acceleration is defined as the change in velocity divided by the period of time during which the change occurs. In mathematical terms, average acceleration (a) can be expressed as: a = Δv / Δt

where Δv is the change in velocity and Δt is the change in time. The SI units for velocity are meters per second (m/s), and for time, they are seconds (s).

Therefore, the SI unit for acceleration is meters per second squared (m/s²). For example, if a car's velocity changes from 10 m/s to 20 m/s over 5 seconds, the average acceleration is (20 m/s - 10 m/s) / 5 s = 2 m/s².

Complete Question :  Acceleration is defined as the change in velocity divided by:

Final Velocity

Distance

Time

Speed

Answer:

Sirius

Explanation:

Sirius is known s the most brightest star in the sky the second brightest star is Canopus

Answer:

The brightness of each bulb would remain the same even though the total resistance of the circuit would decrease.

Explanation:

Brightness of the bulb is given as

[tex]P= \frac{V^2}{R}[/tex]

since all bulbs are connected in parallel so here voltage across each bulb will remain same and resistance of each bulb is "R"

So here power across each bulb will remain the same always.

So there will be no effect on the power or brightness of bulb.

Now we also know that equivalent resistance is given as

[tex]\frac{1}{R_{eq}} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3}............[/tex]

[tex]R_{eq} = \frac{R}{n}[/tex]

so here equivalent resistance will decrease on adding more resistance in parallel.

so correct answer will be

The brightness of each bulb would remain the same even though the total resistance of the circuit would decrease.

Answer: C ON EDGE

Explanation:

Answer:

When it's closest to the sun.

Explanation:

The force of gravity acting on a planet is equal to its mass times its centripetal acceleration.

Fg = m v^2 / r

The force of gravity is defined by Newton's law of universal gravitation as:

Fg = mMG / r^2

Therefore:

mMG / r^2 = m v^2 / r

MG / r = v^2

v increases as r decreases.  So the planet is moving fastest when it's closest to the sun, also known as the perihelion.

The force of gravity acting on a planet is equal to its mass times its centripetal acceleration.

Fg = m v² / r

The force of gravity is defined by Newton's law of universal gravitation as:

Fg = mMG / r²

Therefore:

mMG / r² = m v² / r

MG / r = v²

v increases as r decreases.  So the planet is moving fastest when it's closest to the sun, also known as the perihelion.

perihelion

The fastest a planet moves is at perihelion (closest) and the slowest is at aphelion (farthest). Law 3. The square of the total time period (T) of the orbit is proportional to the cube of the average distance of the planet to the Sun (R)

The Earth is closest to the Sun, at its perihelion, about two weeks after the December solstice and farthest from the Sun, or at its aphelion, about two weeks after the June solstice. Earth is farthest from the Sun when it is summer in the Northern Hemisphere.

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Answer:

True

Explanation:

The masses of the objects and how much distance there is between them

Radio waves are a type of electromagnetic radiation with wavelengths between 10 m to 10,000 m. In the electromagnetic spectrum this wavelength is longer than infrared light and therefore, it goes beyond the visible spectrum.  

This type of electromagnetic waves is very well reflected in the ionosphere, the layer of the atmosphere through which they travel directly or using repeaters.  

In addition, they are very useful to transport information, being important in telecommunications. They are used not only for conventional radio transmissions but also in mobile telephony and TV.  

It should be noted that since radio signals have large wavelengths, they can be diffracted around certain obstacles, such as hills and mountain ranges, preventing the signal from reaching its destination.  

Therefore, the correct option is C.

We have that The speed of the disturbance V is

[tex]V=872.9m/s[/tex]

From the Question we are told that

Density  [tex]\rho=1300 kg/m3[/tex]

Diameter [tex]d=3.0\mu m[/tex]

Tension [tex]T=7.0mn[/tex]

Generally the equation for the  length mass density is mathematically given as

[tex]\pho_{lm}=p \pir^2[/tex]

[tex]\pho_{lm}=1300* \pi (3 *10^{\frac{-6}{2}})^2[/tex]

[tex]\pho_{lm}=9.187*10{-9Kg/m}[/tex]

Therefore

The speed of the disturbance V is

[tex]V=\sqrt{(T/\pho_{lm})}[/tex]

[tex]V= \sqrt{(\frac{7 *10^{-3}}{(9.187 *10^{-9}}))}[/tex]

[tex]V=872.9m/s[/tex]

In conclusion

The speed of the disturbance V is

[tex]V=872.9m/s[/tex]

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The disturbance traveling along the radial thread of the web will reach the spider first, as the speed of sound is significantly slower.

The speed of sound in a material depends on its properties. In the case of a spider's silk thread, sound travels at a much lower speed compared to the disturbance along the thread. Therefore, the disturbance traveling along the radial thread of the web will reach the spider first.

Thus, the disturbance traveling along the radial thread of the web will reach the spider first. The speed at which sound travels is significantly slower than the speed at which disturbances travel along a stretched string or thread. In this case, the radial thread of the web acts like a tensioned string, and the disturbance caused by the impact of the fly will propagate along it faster than the sound of the impact.

Answer:

B) 8.0 m

Explanation:

First of all, we can find the frequency of the wave, which is equal to the number of waves that pass a given point per second. Therefore:

[tex]f=\frac{N}{t}=\frac{5.0}{4.0 s}=1.25 Hz[/tex]

which means 1.25 waves/second.

Then we can find the wavelength of the water waves, which is given by:

[tex]\lambda=\frac{v}{f}[/tex]

where

v = 10.0 m/s is the speed of the wave

f = 1.25 Hz is the wave frequency

Substituting, we find

[tex]\lambda=\frac{10.0 m/s}{1.25 Hz}=8.0 m[/tex]

Answer: SBb

On 1930 the astronomer Edwin Hubble classified the galaxies based on their visual appearance into elliptical, spiral and irregular, being the first two classes the most frequent.  

So, according to this classification, the Milky Way is a barred spiral galaxy (SBb in Hubble's notation system) because it has a central bar-shaped structure of bright stars that spans from one side of the galaxy to the other. In addition, its spiral arms seem to emerge from the end of this "bar".

Scientifics considered this, after measuring the the disk and central bulge region of the galaxy, and the conclusion is the Milky Way fulfills these conditions, because is a galaxy that orbits on its same axis and with this rotation its arms are twisted in opposite directions around the mentioned axis.

Therefore the correct answer is option C.

Answer:

[tex]38.6^{\circ}[/tex]

Explanation:

In order to find the resultant of the two vectors, we need to find the components of each vector along the x- and y- axis.

For the horizontal vector, we have:

x-component: [tex]A_x = 15[/tex]

y-component: [tex]A_y = 0[/tex]

For the vectors of 18 units:

x-component: [tex]B_x = 18 cos 70^{\circ}=6.16[/tex]

y-component: [tex]B_y = 18 sin 70^{\circ}=16.91[/tex]

So the components of the resultant vector are

[tex]R_x=A_x + B_x = 15 +6.16 = 21.16[/tex]

[tex]R_y=A_y + B_y = 0 +16.91 = 16.91[/tex]

And so the direction is given by

[tex]\theta = tan^{-1} (\frac{R_y}{R_x})=tan^{-1} (\frac{16.91}{21.16})=38.6^{\circ}[/tex]

Answer:

The surface gravity is inversely proportional to the square of the radius of the planet

Explanation:

The gravity at the surface of a planet is given by:

[tex]g=\frac{GM}{R^2}[/tex]

where

G is the gravitational constant

M is the mass of the planet

R is the radius of the planet

We see from the formula that the surface gravity is inversely proportional to the square of the radius of the planet, R.

At the Earth's surface, the value of the surface gravity is approximately 9.81 m/s^2.

Answer:

During an alpha decay

Explanation:

An alpha particle is a particle consisting of 2 protons and 2 neutrons - basically it is equivalent to a nucleus of helium.

Alpha particles are emitted during alpha decays, which are one of the three types of radioactive decays (the other two being beta decay and gamma decay) in which an unstable nucleus decays emitting an alpha particle:

[tex]X \rightarrow Y + \alpha[/tex]

In the process, the original nucleus X loses 2 protons and 2 neutrons, so:

- its atomic number decreases by 2 units: Z --> Z-2

- its mass number decreases by 4 units: A --> A-4

Answer:

a) Wavelength .

Explanation:

Visible light is comprised of all the seven colors Violet , Indigo , Blue , Green , Yellow and Red .

Color depends up on the wave length of the light .

For example a red ball appears red because it absorbs wavelengths of all the other colors and reflects only wavelengths corresponding to red color.

Color in terms of light is determined by both the wavelength and frequency, with different combinations producing all the colors we humanly perceive.

In the context of light, color is dependent on both the wavelength and frequency of light. This is because the visible spectrum which represents the colors that can be seen by the human eye, is defined by varying wavelengths and frequencies. Shorter wavelengths (and correspondingly higher frequencies) are associated with cooler colors like blue and violet, while longer wavelengths (and correspondingly lower frequencies) are associated with warmer colors like red and orange. Therefore, the answer to this is option c) both frequency and wavelength determine the color of light.

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Answer:

1/2

Explanation:

The energy stored in a capacitor is given by

[tex]U=\frac{1}{2}CV^2[/tex]

where

C is the capacitance

V is the potential difference

Calling [tex]C_1[/tex] the capacitance of capacitor 1 and [tex]V_1[/tex] its potential difference, the energy stored in capacitor 1 is

[tex]U=\frac{1}{2}C_1 V_1^2[/tex]

For capacitor 2, we have:

- The capacitance is half that of capacitor 1: [tex]C_2 = \frac{C_1}{2}[/tex]

- The voltage is twice the voltage of capacitor 1: [tex]V_2 = 2 V_1[/tex]

so the energy stored in capacitor 2 is

[tex]U_2 = \frac{1}{2}C_2 V_2^2 = \frac{1}{2}\frac{C_1}{2}(2V_1)^2 = C_1 V_1^2[/tex]

So the ratio between the two energies is

[tex]\frac{U_1}{U_2}=\frac{\frac{1}{2}C_1 V_1^2}{C_1 V_1^2}=\frac{1}{2}[/tex]

Answer:

d.100 meters

Explanation:

The diameter of the Milky Way Galaxy is approximately 100,000 light years.

Here we are using 1 millimiter (1 mm) to represent 1 light-year (1 ly). So, we can set the following proportion:

[tex]1 mm : 1 ly = x : 100,000 ly[/tex]

and by finding x, we find the diameter of the Milky Way Galaxy in the scale used:

[tex]x=\frac{(1mm )(100,000 ly)}{1 ly}=100,000 mm = 100 m[/tex]

so the correct answer is

d. 100 meters

Final answer:

Using a scale where 1 millimeter represents 1 light-year, the diameter of the Milky Way Galaxy at 100,000 light-years translates to 100,000 millimeters, which is equivalent to 100 meters. The correct answer is (d) 100 meters.

Explanation:

The Milky Way Galaxy has a diameter of approximately 100,000 light-years. To convert light-years to millimeters, we use a scale where 1 millimeter represents 1 light-year. Therefore, the Milky Way Galaxy's diameter would be 100,000 millimeters, which can be converted to meters by dividing by 1,000 (since there are 1,000 millimeters in a meter).

100,000 millimeters / 1,000 = 100 meters. So, the diameter of the Milky Way Galaxy, when represented at a scale of 1 millimeter per light-year, is 100 meters. Hence, the correct answer is (d) 100 meters.

A change in the speed of a wave as it enters a new medium causes refraction, which alters the wave's direction. This is due to the differing densities of the mediums involved, as demonstrated by Huygens's principle and Snell's law.

A change in the speed of a wave as it enters a new medium produces a change in the wave's direction, a process known as refraction. This phenomenon occurs because different media have different properties, such as density, that affect the wave's speed. For example, when light moves from air into water, it slows down and bends towards the normal due to water's higher density. The same principle applies to water waves going from deep to shallow water; they slow down and their wavelength decreases as they enter the shallower water, bending the path of the wave closer to the perpendicular. This bending of the wave is explained by Huygens's principle of wavefronts and can lead to the derivation of Snell's law for calculating the angle of refraction.

Answer: Seismic waves arrive at a seismograph in the order of fastest to slowest:primary waves, secondary waves, surface waves.

Explanation:

P-waves, S-waves, and surface waves arrive at a seismograph in a specific order.

The three types of seismic waves arrive at a seismograph in a specific order. First, P-waves (also known as pressure waves or longitudinal waves) arrive at the seismograph. These waves are compressional and travel faster than the other two types. Next, S-waves (also known as shear waves or transverse waves) arrive. These waves move the ground perpendicular to their path. Finally, surface waves arrive, which are similar to surface waves on water and cause the most damage during an earthquake.

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Answer:

b. amplitude

Explanation:

There are two types of intereference:

- Constructive interference: it occurs when two waves of same frequency meet at a point in phase - this means , the crest of one wave meets with the crest of the other wave. When this occurs, the resultant wave has an amplitude which is equal to the sum of the amplitudes of the two waves.

- Destructive interference: it occurs when two waves of same frequency meet at a point in opposite phase - this means , the crest of one wave meets with the trough of the other wave. When this occurs, the resultant wave has an amplitude which is equal to the difference between the amplitudes of the two waves.

When interference occurs, the other factors of the waves (period, frequency and wavelength) do not change.

In constructive interference, the factor that increases is the amplitude of the resulting wave. The amplitudes of the individual waves combine to produce a wave with greater amplitude, while the period, frequency, and wavelength remain unchanged.

When two waves meet and interfere constructively, the factor that increases is the amplitude of the resulting wave. Constructive interference occurs when waves are in phase and their crests (and troughs) align. The amplitudes of the individual waves add together, resulting in a wave with a greater amplitude. This is shown in various figures such as FIGURE 16.33 and FIGURE 27.11 in your provided references, which illustrate pure constructive interference producing a wave with twice the amplitude, but the same wavelength.

It is important to note that the period, frequency, and wavelength of a wave are not directly affected by interference. The period and frequency are inversely related, so when the period of a wave increases, its frequency decreases. However, this question refers to the effects of interference, not changes in the wave's frequency or period.

The relation between amplitude and frequency of a wave is that they are generally independent of each other; an increase in amplitude does not necessarily cause a change in frequency, and vice versa.

Answer:

-7.5 cm

Explanation:

OK so in the equation they're having you use the variables are:

[tex]d_o = 5.0 cm\\\\f = 15.0 cm\\\\d_i = ?[/tex]

So we simply plug in the variables:

[tex]d_i = \frac{d_of}{d_o-f} \\\\d_i = \frac{5.0 * 15.0}{5.0 - 15.0}\\\\d_i = \frac{75}{-10}\\\\d_i = -7.5 cm[/tex]

Answer:

C. -7.5 cm

Explanation:

got it right, trust

The answer to your question is Sun.

Answer:

The voltage will quadruple

Explanation:

The power dissipated in a circuit is given by

[tex]P=\frac{V^2}{R}[/tex]

where

V is the voltage

R is the resistance

In this problem, the voltage across the circuit is doubled:

V' = 2V

So the new power dissipated is

[tex]P'=\frac{V'^2}{R}=\frac{(2V)^2}{R}=4\frac{V^2}{R}=4 P[/tex]

so, the power dissipated will quadruple.

When the voltage across a circuit of constant resistance is doubled, the current doubles and the power dissipated increases by a factor of four.

To understand what happens when the voltage across a circuit of constant resistance is doubled, we need to refer to Ohm's Law and the formula for electrical power dissipation.

Ohm's Law states that the current  through a resistor is directly proportional to the voltage  across it and inversely proportional to the resistance

I = V / R

Therefore, if the voltage is doubled, the current will also double, assuming the resistance remains constant.

The power dissipated by a resistor can be calculated using the formula:

[tex]P = V^2 / R[/tex]

When the voltage is doubled, the expression for power becomes:

[tex]P = (2V)^2 / R \\= 4V^2 / R[/tex]

This means that doubling the voltage will result in the power being multiplied by a factor of four.

Thus,when the voltage across a circuit of constant resistance is doubled, the current will double, and the power dissipated by the circuit will increase by a factor of four.

A. [tex]4.64\cdot 10^{11}m[/tex]

The orbital speed of the clumps of matter around the black hole is equal to the ratio between the circumference of the orbit and the period of revolution:

[tex]v=\frac{2\pi r}{T}[/tex]

where we have:

[tex]v=30,000 km/s = 3\cdot 10^7 m/s[/tex] is the orbital speed

r is the orbital radius

[tex]T=27 h \cdot 3600 =97,200 s[/tex] is the orbital period

Solving for r, we find the distance of the clumps of matter from the centre of the black hole:

[tex]r=\frac{vT}{2\pi}=\frac{(3\cdot 10^7 m/s)(97200 s)}{2\pi}=4.64\cdot 10^{11}m[/tex]

B. [tex]6.26\cdot 10^{36}kg, 3.13\cdot 10^6 M_s[/tex]

The gravitational force between the black hole and the clumps of matter provides the centripetal force that keeps the matter in circular motion:

[tex]m\frac{v^2}{r}=\frac{GMm}{r^2}[/tex]

where

m is the mass of the clumps of matter

G is the gravitational constant

M is the mass of the black hole

Solving the formula for M, we find the mass of the black hole:

[tex]M=\frac{v^2 r}{G}=\frac{(3\cdot 10^7 m/s)^2(4.64\cdot 10^{11} m)}{6.67\cdot 10^{-11}}=6.26\cdot 10^{36}kg[/tex]

and considering the value of the solar mass

[tex]M_s = 2\cdot 10^{30}kg[/tex]

the mass of the black hole as a multiple of our sun's mass is

[tex]M=\frac{6.26\cdot 10^{36} kg}{2\cdot 10^{30} kg}=3.13\cdot 10^6 M_s[/tex]

C. [tex]9.28\cdot 10^9 m[/tex]

The radius of the event horizon is equal to the Schwarzschild radius of the black hole, which is given by

[tex]R=\frac{2MG}{c^2}[/tex]

where M is the mass of the black hole and c is the speed of light.

Substituting numbers into the formula, we find

[tex]R=\frac{6.26\cdot 10^{36} kg)(6.67\cdot 10^{-11})}{(3\cdot 10^8 m/s)^2}=9.28\cdot 10^9 m[/tex]

To estimate the distance of matter clumps from the black hole center and the mass of the black hole, one must use Kepler's laws and gravitational physics equations. For calculating the black hole's mass and the radius of its event horizon, principles involving gravitational constant, speed of the matter, the speed of light, and calculated mass of the black hole are applied.

To answer these questions, we can use some fundamental principles of orbital mechanics and gravitational physics. Given the clumps' approximate orbit period of 27 hours and their speed of 30,000 km/s, we leverage Kepler's Third Law of Planetary Motion. However, we should note that direct conversion from the available data to an explicit distance is non-trivial without simplifying assumptions.

To calculate the black hole's mass with this information, the equation GM=(v^2)R is used where G is the gravitational constant, M is the mass of the black hole, v is the speed of the matter, and R is the distance from the center of the black hole. Integer solutions of this equation can offer us an educated estimate of the mass of the black hole in the middle of Galaxy Markarian 766, expressed in multiples of our Sun's mass.

For estimating the radius of the event horizon, the Schwarzschild radius formula R=2GM/c^2 is applied, where c stands for the speed of light. This computation will again depend on the accurate estimation of the black hole’s mass.

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1. +72.0 kg m/s

The momentum of an object is given by:

p = mv

where

m is the mass of the object

v is its velocity

Taking "to the right" as positive direction, for Elena we have

m = 60.0 kg is the mass

v = +1.20 m/s is the velocity

So, Elena's momentum is

[tex]p_e=(60.0 kg)(+1.20 m/s)=+72.0 kg m/s[/tex]

2. -162.5 kg m/s

Here Madison is moving in the opposite direction of Elena (to the left), so her velocity is

v = -2.50 m/s

while her mass is

m = 65.0 kg

Therefore, her momentum is

[tex]p_m= (65.0 kg)(-2.50 m/s)=-162.5 kg m/s[/tex]

3. -90.5 kg m/s

The total momentum of Elena and Madison is equal to the algebraic sum of their momenta; taking into account the correct signs, we have:

[tex]p=p_e + p_m = +72.0 kg m/s - 162.5 kg m/s =-90.5 kg m/s[/tex]

4. 0.72 m/s to the left

We can find the final speed of Elena and Madison by using the law of conservation of momentum. In fact, the final momentum must be equal to the initial momentum (before the collision).

The initial momentum is the one calculated at the previous step:

[tex]p_i = -90.5 kg m/s[/tex]

while the final momentum (after the collision) is given by

[tex]p_f = (m_e + m_m) v[/tex]

where

[tex]m_e[/tex] is Elena's mass

[tex]m_m[/tex] is Madison's mass

v is their final velocity

According to the law of conservation of momentum,

[tex]p_i = p_f\\p_i = (m_e + m_m) v[/tex]

So we can find v:

[tex]v=\frac{p_i}{m_e + m_m}=\frac{-90.5 kg m/s}{60.0 kg+65.0 kg}=-0.72 m/s[/tex]

and the direction is to the left, since the sign is negative.

Elena's momentum is 72.0 kg*m/s to the right, Madison's is -162.5 kg*m/s to the left. The total system momentum is -90.5 kg*m/s to the left. After colliding, they move together with a speed of 0.724 m/s to the left.

The subject here is Physics, specifically the conservation of momentum. Momentum is calculated as mass times velocity. The positive and negative signs denote direction (right, left).

Elena's momentum is the product of her mass (60.0 kg) and velocity (1.20 m/s). Hence, momentum = 60.0 kg * 1.20 m/s = 72.0 kg*m/s towards the right (positive).

Madison's momentum is the product of her mass (65.0 kg) and velocity (2.50 m/s). Because she's moving to the left, the velocity is negative. Hence, momentum = 65.0 kg * -2.50 m/s = -162.5 kg*m/s towards the left (negative).

The total momentum of Elena and Madison is the sum of their individual momenta: 72.0 kg*m/s + (-162.5 kg*m/s) = -90.5 kg*m/s to the left.

When they collide and hold onto each other, they move together, so their combined mass is 60.0 kg + 65.0 kg = 125.0 kg. The total system's momentum should still be conserved, so -90.5 kg*m/s = 125.0 kg * velocity. Solving for the speed gives velocity = -90.5 kg*m/s / 125.0 kg = -0.724 m/s. The negative sign indicates they move in the negative direction or to the left.

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