a child rocks back and forth on a porch swing with an amplitude of 0.204 m and a period of 2.80 s.assuming the motion is approximately simple harmonic, find the child's maximum speed.

The induced EMF increases to four times its initial value if the rate of change of the magnetic field quadruples.

Faraday's law of electromagnetic induction specifies that an emf (electromotive force) is induced in a closed conductor or coil whenever there is a change in magnetic flux associated with it.

  EMF = − d(ΦB) /dt

  ΦB = BAcosθ

This equation suggests that emf is proportional to the rate at which magnetic flux ΦB is changing with respect to time. As a result, if the rate of change of the magnetic field quadruples, the induced EMF increases to four times its initial value.

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The first dark fringe is located approximately 7.35 mm from the central maximum on the screen.

The location of the first dark fringe can be found using the formula:

y = (mλD) / d

where y is the distance from the central maximum to the first dark fringe, m is the order of the fringe (m = 1 for the first dark fringe), λ is the wavelength of light, D is the distance from the double-slit to the screen, and d is the slit spacing (which is the sum of the slit width and the distance between the centers of the two slits).

The slit width is given as 0.15 mm = 0.00015 m, and the wavelength of light is 450 nm = 0.00045 m. The distance from the double-slit to the screen is 2.3 m.

To find the slit spacing, we need to know the distance between the centers of the two slits. If the double-slit is a single piece with two slits, the distance between the centers of the slits is usually given as the width of the slits plus the distance between them. If this information is not provided, we can assume that the distance between the centers of the slits is approximately equal to the width of each slit. Therefore, we can estimate the slit spacing as:

d ≈ 2 × 0.00015 m = 0.0003 m

Substituting the values into the formula, we get:

[tex]y = (1 × 0.00045 m × 2.3 m) / 0.0003 m[/tex]

y ≈ 7.35 m

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The component vr of velocity vector v along the radial direction from the radar gun to the car is the component of the velocity that is in the direction of the radial line that connects the radar gun to the car.

It can be calculated by taking the dot product of the velocity vector and the unit vector of the radial line.

The unit vector of the radial line is a vector that has a magnitude of one and that is pointing in the direction of the radial line.

The dot product of two vectors is equal to the magnitude of the first vector multiplied by the projection of the second vector on the first vector.

Thus, the component of velocity vr along the radial line is calculated by taking the magnitude of v multiplied by the projection of the unit vector of the radial line on v.

The component vr can be used to determine the speed of the car from the radar gun. The speed of the car is equal to the magnitude of vr divided by the speed of light.

By knowing the speed of the car, the speed limit can be compared to it in order to determine if the car is driving at a legal speed.

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Power is the rate at which work is done. Hence most appropriate option among the four given options is the second option which is "The rate at which work is done".

Power is the rate at which work is done or the rate of energy transfer. It is the amount of energy transferred per unit time. The unit of power is the watt (W), which is defined as one joule per second (J/s).

The definition "the amount of energy transferred per unit time" is incomplete because power can vary over time, and this definition only applies when the energy transfer is constant.

The definition "voltage multiplied by current" gives the electrical power in a circuit, but this definition is specific to electrical power, and power can also be in the form of mechanical, thermal, or other types of energy.

The definition "the amount of energy supplied by a battery per unit time" is a measure of the battery's power output, but it is specific to batteries and does not apply to other sources of power.

Therefore, the most complete and accurate definition of power is "the rate at which work is done."

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The magnitude of the force that Alice is applying to the box is 110 N.

To calculate the force that Alice is applying, we need to use the equation F = ma. In this equation, F is the force applied, m is the mass of the box, and a is the acceleration of the box.

Since Alice is pushing the box at a constant speed of 2.8 m/s, the acceleration is 0, and the equation simplifies to F = 0 x m. Since the force must equal 0 when the acceleration is 0, the magnitude of the force that Alice is applying to the box is 0.

However, since Bob is pushing an identical box across the floor at a constant speed of 1.4 m/s, the acceleration is 0 and the equation simplifies to F = m x a. In this case, a is the acceleration of the box, which is 1.4 m/s.

Since we know that the magnitude of the force Bob is applying is 55 N, we can use the equation to calculate the force Alice is applying. 55 N = m x 1.4 m/s, which simplifies to m = 39.286.

We then substitute m back into the equation F = ma, so F = 39.286 x 1.4 m/s. This simplifies to F = 55.0 N, so the magnitude of the force Alice is applying is 55.0 N.

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The definition of current is a. the amount of charge that flows through a cross-section of wire per unit time.

Current is he flow of electric charge through a conductor or circuit is known as electric current. In other words, an electric current is defined as the movement of charge carriers (electrons) through a conductor. The SI unit of electric current is the ampere, symbolized as A. Electric current is a scalar quantity that can be positive or negative, depending on the direction of movement of the charge carriers.

The following formula gives the current in a wire: I = ΔQ/Δt, where I is the current, ΔQ is the change in charge, and Δt is the change in time. The electric current is the number of electrons passing through a cross-sectional area of a conductor per unit time. Electric current flows from a higher potential to a lower potential, that is, from a positive to a negative charge carrier.

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The current through the bulb is 2.0 amperes. Then the electric charge that passes through Luighbu is 120 Columbs.

Given that the current through a lightbulb is 2.0 amperes. To find the coulombs of electric charge that pass through the light bulb in one minute, we need to know the formula that relates current, time, and electric charge:

Q = It

Where Q is the electric charge (in coulombs), I is the current (in amperes), and t is the time (in seconds).

To convert one minute to seconds, we multiply it by 60. Hence, the time t = 1 minute × 60 seconds/minute = 60 seconds.

So, the electric charge that passes through the light bulb in one minute is given by

Q = It = 2.0 A × 60 s

Q = 120 C

Therefore, the number of coulombs of electric charge that pass through the light bulb in one minute is 120 C.

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(a) The equivalent capacitance of the 4.20 µF and 8.50 µF capacitors when connected in series is approximately 4.2017 µF.

(b) The equivalent capacitance of the 4.20 µF and 8.50 µF capacitors when connected in parallel is 12.70 µF.

When two capacitors are connected in series, the equivalent capacitance is given by the formula,

1/Ceq = 1/C1 + 1/C2

where C1 and C2 are the capacitances of the two capacitors.

Substituting the given values,

1/Ceq = 1/4.20 µF + 1/8.50 µF

1/Ceq = 0.238 µF^-1

Ceq = 1 / (0.238 µF^-1)

Ceq = 4.2017 µF (rounded to four significant figures)

When two capacitors are connected in parallel, the equivalent capacitance is given by the formula,

Ceq = C1 + C2

where C1 and C2 are the capacitances of the two capacitors.

Substituting the given values,

Ceq = 4.20 µF + 8.50 µF

Ceq = 12.70 µF

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To clean grease or carbon tracks from capacitors or coils that are used in magnetos, use a good quality electrical contact cleaner. Electrical contact cleaners can remove any dirt, grease, or carbon tracks that may have accumulated on the coils and capacitors used in magnetos.

A capacitor is a device that stores electric charge. It's a passive electrical component that can store energy in an electric field. Capacitors are widely used in electronic circuits for a variety of purposes, including storing electrical energy, separating DC signals from AC signals, and tuning radio frequencies.

A magneto is an electrical generator that converts mechanical energy into electrical energy. It's a type of alternator that is self-contained and does not require a separate power source. Magnetos are used in internal combustion engines, such as those found in automobiles, motorcycles, and aircraft.

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This principle can be observed in other everyday scenarios, such as jumping on a trampoline or the recoil of a gun after firing.  Newton's Third Law of Motion is a fundamental principle in classical mechanics and explains why the spring will bounce when the weight is released.

The bouncing of the weight when released is explained by Newton's Third Law of Motion, which states that for every action there is an equal and opposite reaction. When the weight is released, the spring exerts an equal and opposite force on the weight, propelling it upwards and causing it to bounce. This is because when the weight is pulled down, it compresses the spring, storing potential energy. When the weight is released, the spring decompresses and the potential energy is released, propelling the weight in the opposite direction.

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The average force required to stop a 900 kg car in 7.0 s if the car is traveling at 90 km/h is -3213 N.

First, we need to convert the speed from km/h to m/s,

90 km/h = 25 m/s (approx)

We can use the equation,

a = (v_f - v_i) / t

where a is the acceleration, v_f is the final velocity (which is zero since the car comes to a stop), v_i is the initial velocity (which is 25 m/s), and t is the time it takes to come to a stop (which is 7.0 s).

Plugging in the values,

a = (0 - 25 m/s) / 7.0 s = -3.57 m/s^2

The negative sign indicates that the acceleration is in the opposite direction to the car's initial velocity.

Now, we can use Newton's second law of motion, which states that force is equal to mass times acceleration,

F = ma

where F is the force required to stop the car, m is the mass of the car (which is 900 kg), and a is the acceleration we calculated earlier.

Plugging in the values,

F = 900 kg x (-3.57 m/s^2) = -3213 N

The negative sign indicates that the force is in the opposite direction to the car's motion.

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Answer:

Explanation:

Durante as aulas, os estudantes da 3ª série deveriam escolher uma entre as três atividades físicas possíveis, sendo elas: natação, futsal e dança. Na turma, 25% escolheram dança, 15% escolheram natação, e os outros 24 estudantes escolheram futsal. Podemos afirmar que, nessa turma, existe um total de:

A) 64 alunos

B) 55 alunos

C) 48 alunos

D) 45 alunos

E) 40 alunos

If a 100-ohm resistor is connected in series with a 300-ohm resistor, Then the equivalent resistance of the circuit is 400 ohm.

Resistance in electrical circuits is a measure of how much a component or material opposes the flow of electric current through it. It is denoted by the symbol R and is measured in units called ohms, represented by the Greek letter omega (Ω).

When resistors are connected in series, their resistances add up to give the total or equivalent resistance of the circuit.

Now, to find the equivalent resistance of a circuit with a 100-ohm resistor and a 300-ohm resistor in series, we simply add their resistances together:

Equivalent resistance = 100 ohm + 300 ohm

Equivalent resistance = 400 ohm

Therefore, the equivalent resistance of the circuit is 400 ohms.

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Quantum mottle, also known as quantum noise, is caused by a lack of photons reaching the image receptor due to insufficient mAs (milliamperage-seconds) in digital radiography. The correct answer is option : a.

This results in a grainy, speckled appearance in the image. Increasing mAs can help to reduce quantum mottle by providing more photons to the image receptor. However, other exposure factors such as kVp and distance also play a role in achieving a diagnostic quality image while minimizing patient dose. Quantum mottle is caused by insufficient mAs in digital radiography, resulting in a grainy, speckled appearance in the image. Correct answer is option: a.

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No, it is not necessary to limit the charge of your device to 60% when gaming. When it comes to gaming, it is recommended to charge your device between 40-90%.

This is because if your device is fully charged, it may reduce the lifespan of your battery and make it more vulnerable to heat-related damage.

As for light tasks such as web browsing and email, it is best to keep your device's charge between 30-60% in order to maximize battery life.

When it comes to gaming, you should make sure your device is not exposed to extremely high temperatures or charged beyond the recommended range.

Overcharging can damage the battery and lead to overheating which can reduce the performance of your device.

It is important to check the power settings of your device to ensure that your device is not wasting too much power. You can do this by going to the Settings of your device and accessing the Battery menu.

From there you can check what apps are draining the most power and set up the device to reduce power usage.

It is important to maintain the charge of your device in the recommended range while playing games, between 40-90%.

Doing so will help ensure the longevity of your battery and reduce the risk of heat-related damage. Additionally, you should keep an eye on your power settings to ensure that your device is not wasting too much power.

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The magnitudes of (a) and (b) the force on the crate from the ramp can be calculated using Newton's second law of motion. According to this law, the net force on an object is equal to the mass of the object multiplied by its acceleration.

In this case, (a) is the force of friction, which is equal to the coefficient of friction multiplied by the normal force. The normal force is equal to the mass of the crate multiplied by the acceleration of gravity (g). Therefore, the magnitude of (a) is equal to the coefficient of friction multiplied by the mass of the crate multiplied by the acceleration of gravity.

(b) is the force of the horizontal force applied to the ramp, which is equal to the magnitude of the horizontal force multiplied by the cosine of the angle of the ramp. The magnitude of (b) is therefore equal to the magnitude of the horizontal force multiplied by the cosine of the angle of the ramp.

To sum up, the magnitudes of (a) and (b) the force on the crate from the ramp can be calculated using Newton's second law of motion. (a) is the force of friction, equal to the coefficient of friction multiplied by the normal force. (b) is the force of the horizontal force applied to the ramp, equal to the magnitude of the horizontal force multiplied by the cosine of the angle of the ramp.

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The speed of a spacecraft moving in a circular orbit just above the lunar surface is approximately 2,300 m/s, or 2.3 km/s. To maintain a stable orbit around the Moon, the spacecraft must travel at a specific speed, called the orbital velocity, which is dependent on the radius of the orbit and the mass of the object being orbited.

Using the equations of orbital motion, we can calculate that the orbital velocity of the spacecraft is 2,299 m/s. To express this value with two significant figures, we round to 2.3 km/s.

It is important to note that the value given is only an approximation, and in reality the speed of the spacecraft can vary depending on the other objects and forces acting on it.

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The amount of the star's mass converted to energy in the explosion is 1.11 x 10^27 kg.

Calculating energy:

The mass-energy equivalence equation is used to calculate the mass that is converted to energy during a supernova explosion of a 3.2 x 10^31 kg star, producing 1.0 x 10^44 J of energy.

According to Einstein's mass-energy equivalence equation: E = mc² where, E = energy, m = mass, and c = speed of light This equation expresses the relationship between the mass of an object and the amount of energy that can be released from it.

So, to determine the mass that is converted to energy during the supernova explosion, we need to rearrange the equation as m = E/c². Now we have the following data: E = 1.0 x 10^44 Jc = 3.0 x 10^8 m/s² (speed of light). Substitute these values into the equation to get: m = E/c²m = (1.0 x 10^44 J)/(3.0 x 10^8 m/s)²m = 1.11 x 10^27 kg

Therefore, the supernova explosion of a 3.2 x 10^31 kg star converts 1.11 x 10^27 kg of its mass to energy.

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As Kyle caught the ball, it was moving horizontally at a speed of roughly 0.116 m/s.

Momentum, which is the outcome of an object's mass and velocity, is used to represent mass in motion. An impulse is a force that is used to alter an object's velocity. The impulse, J, and the change in momentum of an object, p=m(vfvi), are equivalent.

mgh = (90.0 kg)(9.81 m/s²)(0.589 m) = 520.6 J

Therefore, Kyle's velocity just as he catches the ball is:

√{1}{2}mv² = 520.6 J implies v = √{2(520.6 J)}{90.0 kg} approx 10.4 m/s

Now, we can use Kyle's velocity and the horizontal distance he traveled to find the time he was in the air. The time is given by:

Delta x = vt implies t = {Delta x}{v} = {0.0396 m}{10.4 m/s} approx 0.0038 s

h = {1}{2}gt² implies t = √{2h}{g} = √{2(0.589 m)}{9.81 m/s²} approx 0.341 s

During this time, the ball traveled a horizontal distance of:

Delta x = vt = (v_{x,ball})(t) implies v_{x,ball} = {Delta x}{t} = {0.0396 m}{0.341 s} approx 0.116 m/s

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Yes, the flow near a cylindrical rod of infinite length can be described by the method in example 4.1-l. This example uses the method of images to calculate the velocity field of the axial flow around a cylindrical rod of infinite length.

To calculate the velocity field, we need to take the velocity potential of the image sources and double integrate it with respect to the cylindrical coordinates. This will yield the axial velocity.

The image sources are chosen such that the fluid flow is symmetric about the centerline of the rod. Therefore, when the axial flow is suddenly set in motion, the image sources also have a velocity in the axial direction. This velocity will be equal to the velocity of the original flow at the same position.

Once the velocity of the image sources is known, the velocity potential of the entire flow can be calculated. This velocity potential is then used to calculate the velocity field in the axial direction around the rod.

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When you perform a simple action like answering your phone, the activity of individual neurons in your nervous system enables you to take in information from your environment and coordinate a response.

When a neuron receives a signal from a dendrite, it generates an electrical impulse called an action potential, which travels down the length of the axon. At the end of the axon, the electrical signal triggers the release of neurotransmitters, which are chemical messengers that transmit the signal to other neurons or muscle cells.

The neurotransmitters bind to specific receptors on the dendrites of the next neuron or muscle cell, which generates a new electrical signal and starts the process over again. This process of neurotransmission allows for rapid communication and coordination between neurons, which is necessary for even simple actions like answering your phone.

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The amplitude of the sound from the speaker at the outdoor concert will change by a factor of 4.2 (78 ft/18 ft) when you move from 18 ft away to 78 ft away.

This is because sound intensity decreases as the distance from the source increases, following an inverse square law. The inverse square law states that the intensity of a sound source is inversely proportional to the square of the distance from the source.
Mathematically, the formula is: I = I0 / (r^2), where I is the intensity at a distance r from the source of intensity I0. This means that when you move from 18 ft away to 78 ft away, the intensity of the sound decreases by a factor of 4.2 ((78 ft/18 ft)^2).
Therefore, the amplitude of the sound from the speaker at the outdoor concert will change by a factor of 4.2 when you move from 18 ft away to 78 ft away.

To get a capacitance of 3.00 pF with a plate separation of 4.00 mm and air between the plates, the plate area required is 1.062 × 10⁻⁵ m² (to 3 significant figures).

The plate separation, d = 4 mm. The capacitance, C = 3 pF = 3 × 10⁻¹² F.

We need to find the plate area, If the material between the plates is air, then the capacitance of a parallel plate capacitor can be given as:

[tex]$$C = \frac{\varepsilon_0A}{d}$$[/tex]

where, ε0 = permittivity of free space = 8.854 × 10⁻¹² F/m.

Substituting the given values in the above formula, we get:

[tex]$$\begin{aligned}C &= \frac{\varepsilon_0A}{d}\\ 3 × 10^{-12} &= \frac{8.854 × 10^{-12} \text{ F/m} × A}{4 × 10^{-3} \text{ m}}\\ A &= \frac{3 × 4 × 10^{-3} \text{ m} × 8.854 × 10^{-12} \text{ F/m}}{8.854 × 10^{-12} \text{ F/m} × 10^{-12}}\\ &= 1.062 × 10^{-5} \text{ m}^2 \end{aligned} $$[/tex]

Therefore, the plate area required to provide a capacitance of 3.00 pF is 1.062 × 10⁻⁵ m² (to three significant figures).

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Answer: C) 3M/2

Explanation:

rotational equilibrium at center pivot

mg(R) + Mg(Rcos60°) – 2Mg(R) = 0.

so cos60° = ½  meaning r 3M/2

A wheel of radius r and negligible mass is mounted on a horizontal frictionless axle so that the wheel is in a vertical plane. The value of m in terms of i is m = 2i * r.

The value of m in terms of m, we can use the condition for static equilibrium which states that the sum of all the forces acting on the system must be zero, and the sum of all the torques must also be zero.
Considering the forces acting on the system, we can see that there are only two: the weight of the objects and the tension in the string that connects them to the wheel. Since the system is in static equilibrium, the tension must be equal to the weight of the objects.
Next, let's consider the torques acting on the system. The torques due to weights of the objects are balanced by the torques due to their distances from the axis of rotation. However, the torque due to the tension in the string is not balanced and produces a net torque on the system.
We can calculate the torque due to the tension in the string by multiplying the tension by the radius of the wheel. The torque due to each object can be calculated by multiplying its weight by its distance from the axis of rotation. Since the system is in static equilibrium, the net torque must be zero, which gives us the following equation:
Tension x Radius = (2im) x 2r + m x r - im x r
Simplifying this equation, we get:
Tension x Radius = 4imr + mr - imr
Tension = (5im + m) / r
Since we know that the tension is equal to the weight of the objects, we can equate the tension to the sum of the weights and solve for m:
(5im + m) / r = 5im + m + 2im
m/r = 2im
m = 2i * r
Therefore, the value of m in terms of i is m = 2i * r.

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During a process, if the state of the system does not change, the system energy will stay the same.

Energy is the ability of an object or system to do work on another object or system. There are different forms of energy like kinetic energy, potential energy, thermal energy, and so on. Energy can be converted from one form to another, but it cannot be created or destroyed. This is the law of conservation of energy.

If a process takes place, then the energy of the system may change. Energy can be absorbed by the system or released by the system. If the system state does not change, then there is no energy transfer involved. Therefore, the system energy will stay the same.

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Answer: The main sequence stars lying in different places differ from each other mainly by having different luminosities and temperatures.

What is an H-R diagram?

An H-R diagram is a plot of stars' luminosity (brightness) versus their surface temperature. On the x-axis, surface temperature is represented, while on the y-axis, luminosity is represented. This plot is used to analyze the characteristics of stars and can provide information such as its temperature, radius, mass, and luminosity.

It is a useful tool for astronomers because it can identify different types of stars, including giants, supergiants, and white dwarfs. It can also be used to compare the various stages of a star's life and to predict how stars evolve over time.

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The quantities that represent mass are 12.0 lb, 0.34 g, 120 kg, and 411 cm.

Mass is the amount of matter that an object contains. It is a scalar physical quantity that can be determined by weighing an object. The standard unit of mass is kilogram (kg). Mass is constant regardless of the object's location in the universe.

The following are the quantities that represent mass:12.0 lb: It is a unit of mass used in the US and some other countries. It stands for pounds, which is equal to 0.45359237 kg.0.34 g: It is a unit of mass used in the metric system. It stands for grams, which is equal to 0.001 kg.120 kg: It is a unit of mass used in the metric system. It stands for kilograms, which is equal to 1000 g.411 cm: It is a unit of length used in the metric system. It stands for centimeters, which is equal to 0.01 m.

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The ball which is thrown with a speed of 21 m/s, travels a distance of 129.99 m in the horizontal direction.

Therefore, the vertical component of the ball's motion will be determined by the force of gravity and the initial vertical speed of the balloon.

We can use the following kinematic equation to determine how long it takes for the ball to fall to the ground:

h = ut + 1/2 * g * t^2

where h is the initial height of the ball (equal to the height of the balloon which is 210 m).

u is the initial velocity of the ball in the vertical direction which is 3.5 m/s.

g is the acceleration due to gravity (approximately 9.8 m/s^2),

and t is the time it takes for the ball to fall to the ground.

Plugging in the values we know, we get:

210 = 3.5 * t + 1/2 * 9.8 * t^2

4.9 t^2 + 3.5 t - 210 = 0

t = 6.19 seconds

Now we can use the time it takes for the ball to fall to the ground to determine how far it travels horizontally, given its initial horizontal velocity of 21 m/s. We can use the following equation:

d = v * t

where d is the horizontal distance traveled by the ball, v is its initial horizontal velocity, and t is the time it takes to fall to the ground (which we just calculated).

Plugging in the values we know, we get:

d = 21 * 6.19

d ≈ 129.99 meters

Therefore, the girl will find the ball approximately at a distance of 129.99 meters away from her when she lands after throwing the ball horizontally.

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Answer:

5.95 m/s to the right

Explanation:

Before the collision, the momentum of the system is given by:

p = m1v1 + m2v2

p = (9.00 kg)(14.0 m/s) + (12.0 kg)(-5.00 m/s)

p = 125.0 kg m/s (to the right)

During the collision, the two masses stick together, so their final velocity will be the same. Let's call this final velocity vf. The momentum of the system after the collision is given by:

p' = (m1 + m2)vf

p' = (9.00 kg + 12.0 kg)vf

p' = 21.0 kg vf

Since momentum is conserved in the collision (there are no external forces acting on the system), we can set p = p' and solve for vf:

125.0 kg m/s = 21.0 kg vf

vf = 5.95 m/s (to the right)

Therefore, the final velocity of the combined masses after the collision is 5.95 m/s to the right.