a device that sends out sound waves to detect objects is called

The advantage of the larger diameter of JWST is the light gathering ability of the JWST is 7.3 times better than it is for the HST. Hence, the correct option is (b).

The advantage of the larger diameter of the James Webb Space Telescope (JWST) over the Hubble Space Telescope (HST) is that the light gathering ability of the JWST is 7.3 times better than that of the HST. This is because the diameter of the JWST's primary mirror is 6.5 meters, while the diameter of the HST's primary mirror is only 2.4 meters. The greater the diameter of a telescope's mirror, the more light it can collect and focus, which leads to better image resolution and sensitivity.

Option (a) is incorrect, because a better light-gathering ability does not necessarily translate to a better resolution. The resolution of a telescope depends on a number of factors, including its optics, the size of its detector, and the amount of light that it can gather.

And options (c), (d), (e), and (f) are also incorrect, as the light-gathering ability of the JWST is 7.3 times better than that of the HST, not 2.7 times.

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a solid ok thank you

hope it helps

The mass of an atom is less than the sum of the masses of its component protons, neutrons and electrons. The mass defect is 0.0423 amu. The correct option is B.

The mass defect is equal to the mass lost as an equivalent amount of energy during the formation of a given nucleus from the component nucleons.

Δm = M°- M

Δm = Mass defect

M° = Expected total mass

M = Experimentally determined mass

Here 'Li' has 3 protons and 4 neutrons.

The mass of proton = 3 × 1.0073 = 3.0219 amu

The mass of neutron = 4 × 1.0087 = 4.0348 amu

The sum of masses of protons and neutrons = 7.0567

Mass defect = 7.0567 - 7.0144 = 0.0423 amu

Thus the correct option is B.

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The velocity of the gripped part P is -0.4i_hat + 0.293j_hat m/s, and the acceleration is -0.05i_hat - 3.93j_hat m/s^2. The magnitude of the velocity is 0.5 m/s, and the magnitude of the acceleration is 3.93 m/s^2.

Tangential acceleration is the component of acceleration that is parallel to the instantaneous velocity of an object moving along a curved path. It represents the rate of change of the magnitude of the velocity vector of the object. Mathematically, the tangential acceleration at any instant is given by the formula:

a_t = r * d²(theta)/dt²

To compute the velocity and acceleration of the gripped part P, we can use the equations for velocity and acceleration of a particle in planar motion:

v = v_i + a_t, where v_i is the initial velocity and a_t is the tangential acceleration a = a_t + a_n, where a_n is the normal acceleration

First, let's find the position of the gripped part P at the given instant. We can use the law of cosines to find the length of the arm:

l² = i² + 2ilcos(theta) + l² cos(theta) = (l² + i² - l²)/(2il) = (i²)/(2il) = 0.2/(20.5) = 0.2

Therefore, theta = arccos(0.2) = 78.46 degrees.

Next, let's find the position vectors of the gripped part P at the given instant. We can use the polar coordinates of P:

r = l theta = theta x = rcos(theta) = 0.5cos(78.46) = 0.13 m y = rsin(theta) = 0.5sin(78.46) = 0.47 m

Now, let's find the velocity vector v. We can find the tangential acceleration using the formula:

a_t = ld^2(theta)/dt^2 = l(-0.3)*cos(theta) = -0.15 m/s^2

Therefore, the velocity vector is:

v = v_i + a_t = ltheta_dot(-sin(theta)*i_hat + cos(theta)j_hat) + (-0.15(-sin(theta)*i_hat + cos(theta)j_hat)) = (-0.25(-sin(30)*i_hat + cos(30)j_hat)) + (-0.15(-sin(30)i_hat + cos(30)j_hat)) = (-0.4i_hat + 0.293j_hat) m/s

The magnitude of the velocity is:

|v| = sqrt((-0.4)^2 + (0.293)^2) = 0.5 m/s

Next, let's find the acceleration vector a. We can find the normal acceleration using the formula:

a_n = l × (d^2(theta)/dt^2)sin(theta) = -0.30.5×sin(78.46) = -0.145 m/s^2

Therefore, the acceleration vector is:

a = a_t + a_n = (-0.15*(-sin(30)*i_hat + cos(30)j_hat)) + (-0.145sin(78.46)*cos(30)i_hat + (-0.145sin(78.46)sin(30) - 9.81)j_hat) = (-0.05i_hat - 3.93j_hat) m/s²

The magnitude of the acceleration is:

|a| = √((-0.05)² + (-3.93)²) = 3.93 m/s²

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Here are three ways to make the ball look red:

   Use a red light: Shine a red light directly onto the white ball while the ball is in the ON position. This will cause the ball to reflect only the red light and appear red.

In regards to the Use a magenta filter: Shine a white light onto the white ball while the ball is in the ON position, and place a magenta filter in front of the light source. This will cause the ball to reflect both red and blue light, which will combine to create the appearance of red.

Lastly, Combine green and blue light with a yellow filter: Shine a white light onto the white ball while the ball is in the ON position, and use green and blue lights to illuminate the ball. Place a yellow filter in front of the ball, which will absorb the green and blue light and allow only red light to pass through. This will create the appearance of a red ball.

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Answer: 81 1/2 moons would be needed to equal the amount of mass of Earth

Explanation:

Answer:

20 meters

Explanation:

The initial velocity of the ball can be determined using the equation for kinetic energy:

K = (1/2)mv^2

100 J = (1/2) * 0.5 kg * v^2

So, v^2 = 200 J / 0.5 kg = 400 m^2/s^2

The velocity can be determined from the square root:

v = sqrt(400 m^2/s^2) = 20 m/s

Now we can use the velocity to determine the maximum height. The maximum height is reached when the velocity is zero, so we can use the formula for vertical motion under constant acceleration to find the time when this occurs:

v = v0 - gt

0 = 20 m/s - 10 m/s^2 * t

t = 2 s

We can use this time to find the maximum height:

h = v0 * t - (1/2)gt^2

h = 20 m/s * 2 s - (1/2) * 10 m/s^2 * 2 s^2

h = 40 m - 20 m

h = 20 m

So, the maximum height reached by the ball is 20 meters.

The specific heat of a  3. 78 kg object that absorbs 678 J is 42.2 J/(kg-K).

As per the given information in the question:

Specific heat = 3.78 kg

Absorption of the object = 678 J

Temperature increase = 4.25 K

Specific heat has units of J / (kg C).

Substituting the values in the formula,

Specific Heat = 678 / 3.78 kg * 4.25 C) = 42.2   J/(kg-K)

The specific heat is defined as the amount required to raise the temperature of a unit mass of a substance by 1 degree Celsius.

This is expressed mathematically as

Q= mc∆T

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Electric charge is not possible on an oil droplet

How do charged oil drops form?

When radiation (such as X-rays) ionizes the area between the metal plates, electrons from the air attach to the falling oil droplets and give them a negative charge.

They could only gain or lose electrons, which are the only charged particles. The "elementary charge" of an electron is 1.60 • 10-19 C, and it is present on every electron. Therefore, any oil droplet's charge needs to be a multiple of this quantity. Due to their typically low conductivity, lubricants can act as insulators in transformers and switches. Oils can conduct electrical current, though. Their conductivity is influenced by a number of variables, including as the base oil, additives, and polarity.

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The peak wavelength of radiation from a 2800 K incandescent bulb is 1.035 μm, outside the visible range. Most energy is infrared.

The fraction of the radiant energy emitted by the filament that falls in the visible range can be calculated using Wien's displacement law and the Stefan-Boltzmann law.

Wien's displacement law states that the peak wavelength of the radiation emitted by a blackbody is inversely proportional to its temperature. The formula is:

peak wavelength = constant / temperature

where the constant is approximately equal to 2.898 × [tex]10^(-3)[/tex] meters-kelvin.

Substituting the temperature of the filament (2800 K) into the formula, we get:

peak wavelength = 2.898 × [tex]10^(-3)[/tex]m-K / 2800 K = 1.035 × [tex]10^(-6)[/tex] meters

This means that the peak wavelength of the radiation emitted by the filament is in the infrared range, and is not visible to the human eye.

The fraction of the radiant energy emitted by the filament that falls in the visible range can be approximated by integrating the Planck radiation law over the visible spectrum (approximately 400-700 nm) and dividing by the total radiant energy emitted by the filament. The formula for the radiant flux density emitted by a blackbody is:

radiant flux density = σ[tex]T^4[/tex]

where σ is the Stefan-Boltzmann constant ([tex]5.67 *10^(-8) W/m^2-K^4[/tex]) and T is the temperature of the filament in kelvin.

Integrating this formula over the visible spectrum, we get:

radiant flux in visible range = ∫(400 nm to 700 nm) [2πh[tex]c^2 / λ^5[/tex]] / [exp(hc/λkT) - 1] dλ

where h is Planck's constant, c is the speed of light, and k is the Boltzmann constant.

Evaluating this integral gives the radiant flux in the visible range. Dividing this by the total radiant flux emitted by the filament (which is just σ[tex]T^4[/tex]), we can find the fraction of the radiant energy emitted by the filament that falls in the visible range. This calculation is quite involved, and would require numerical integration, but in general, only a small fraction of the energy emitted by a filament at 2800 K falls in the visible range. Most of the energy is emitted in the infrared and ultraviolet ranges.

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Isaac Newton described the idea that the  universe as a giant clock with unified rules for gravity and motion.

The clockwork universe is commonly stated  with Sir Isaac Newton but it turns out that both he and his close philosophical supporter Samuel Clarke both strongly criticized the notion of the clockwork universe, because it left no room for Divine Providence.

The faster a clock moves, the slower time passes according to someone in a different frame of reference.

In the history of science, the clockwork universe compares the universe to a mechanical clock. It continues ticking along, as a perfect machine, with its gears governed by the laws of physics, making every aspect of the machine predictable.

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The full range of frequencies of electromagnetic radiation is called the electromagnetic spectrum. So, the correct answer is C.

The electromagnetic spectrum includes all types of electromagnetic radiation, including visible light, radio waves, microwaves, infrared radiation, ultraviolet radiation, X-rays, and gamma rays. Each type of electromagnetic radiation has a different frequency and wavelength, and they all travel at the speed of light in a vacuum. Each type of electromagnetic radiation has a unique wavelength and frequency, which determine its properties and the way it interacts with matter. Radio waves have the longest wavelength and the lowest frequency in the electromagnetic spectrum, followed by microwaves, infrared radiation, visible light, ultraviolet radiation, X-rays, and gamma rays.

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If a 240 volt voltage source is connected to a wire with 10 ohms of resistance, then the current is 24 amp.

Given data as per the question is:

Voltage given - 240 V

Resistance = 10 ohm

The formula to be used in such numerical is,

V=IR --------------------- (A)

where V in the equation is the voltage, I in the equation is the current and R in the equation is the resistance.

Substituting the values in the equation (A)

240=I(10)

I= 240/10 = 24 amp

The current is 24 amp.

The formula V=IR is the ohm's law.  The current which is flowing through the wire is directly proportional to the potential difference applied across its ends of it ,provided that the temperature and all the other physical conditions of the wire like stresses and strains remains absolutly constant.

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The maximum height of a projectile given its original position and initial velocity is, h = (v^2)/(2g).

Maximum height of a projectile given its original position and initial velocity in the vertical direction,

h = (v^2*sin^2(theta))/(2g)

where v is the initial velocity in the vertical direction, theta is the angle of the initial velocity and g is the acceleration due to gravity.

If the projectile is launched straight up, then theta = 90 degrees,

h = (v^2)/(2g)

To use this formula, you need to know the value of v, the initial velocity of the projectile in the vertical direction. This can be found by analyzing the initial conditions of the problem or by measuring the initial velocity directly.

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Nitrogen and helium have the highest average kinetic energy because they are maintained at the highest temperature.

Kinetic energy is the energy possessed by molecules in motion. Average kinetic energy corresponds to the total kinetic energy of the molecules of a gas. Now, as temperature has a direct influence on the motion of the particles in a gas, it therefore, influences the average kinetic energy. Thus, nitrogen and helium, when at 100° C, have the highest average kinetic energy.

We can now say that hotter objects tend to have greater average kinetic energy and also the higher temperatures, and vice-versa. The average energy of the gas particles impacting the container walls grows as the temperature rises. The force the particles per unit area apply to the container is known as pressure. Pressure must increase as the temperature does.

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The ecologist was comparing the density of white-tailed deer, Odocoileus virginianus, between two woodlots.

A population's density is calculated as the number of people in a given area or volume. It is a key parameter for comprehending the dynamics of populations and one of the most fundamental ideas in population ecology.

The number of people per unit area, such as per square meter or per square kilometer, is a common way to represent population density in the context of ecology. As an illustration, it is possible to compute the density of a certain species in a particular habitat by counting the number of individuals inside a given area and dividing that number by the area.

The dynamics of the population are significantly influenced by density. Increased resource competition brought on by a high population density may have an impact on population growth, survival, and reproduction. A low population density, on the other hand, may lead to less competition for resources and more food availability, which may encourage human growth and reproduction.

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The forces acting on a mass in a coordinate system include gravitational forces, electromagnetic forces, frictional forces, and tension forces.

The equations you provided are the equations of motion for a particle with mass m moving in a straight line under the influence of a net force Ftot. The equation Ftot = md²r/dt² represents Newton's Second Law of Motion, which states that the net force acting on an object is equal to its mass times its acceleration.

The second equation, r = (d²r/dt²)t², gives the position of the particle as a function of time. It is the second derivative of the position vector r with respect to time t, which corresponds to the acceleration of the particle.

Together, these equations describe the motion of a particle under the influence of a net force and can be used to calculate the position, velocity, and acceleration of the particle as a function of time.

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The question is -

What forces work on the mass in the new coordinate system? suppose the mass is a height y in the new coordinates. the total force on it is given: [tex]F_{tot}[/tex] = md²r/dt²

A resistance of 140 ohm is needed to be added in parallel connection with 480 ohm resistor to fix the existing circuit.

It was revealed in the close inspection of an electric circuit that a 480 ohm resistors was inadvertently soldered in the place where 350 ohm resistor was needed.

Now because the 480 ohm resistor cannot be removed we have to fix the existing circuit by adding an another resistance in parallel with the 480 ohm resistance to make it equal to 350 ohm.

So, we write, let us say we added R in parallel,

1/350 = 1/R + 1/480

R = 1400ohm.

So, we need to add a 1400 ohm resistor in the existing circuit.

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The PE of the spring at the maximum is [tex]375J[/tex] and Temperature  T is [tex]0.907s[/tex]

The potential energy of the spring at the maximum is the elastic potential energy. This is equal to the work done on the spring (the product of force and displacement) and is given by the equation:

[tex]PE =\frac{ 1}{2}kx^2[/tex], where k is the spring constant, and x is the displacement.

In this case, the displacement is equal to the amplitude of the spring, given by the equation:

[tex]A = (\frac{v^{2}}{k})^{1/2}[/tex], where v is the velocity.

Substituting this into the equation for PE, we get:

[tex]PE =\frac{ 1}{2}k(\frac{v^{2}}{k})^{2 }\\\\=\frac{ 1}{2}kv^{2}[/tex]

Plugging in the values for k and v given in the question, we get [tex]PE = \frac{1}{2}*150N/m*(5m/s)^2\\ \\PE= 375J.[/tex]

The equation provides the spring's duration:

[tex]T = 2\pi (m/k)^{1/2}[/tex]

where m is the mass of the object.

Substituting the values for m and k given in the question, we get:

[tex]T = 2\pi(\frac{2kg}{150N/m})^{1/2}\\\\ T= 0.907s.[/tex]

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Ptolemy. Ptolemy was a Greek astronomer who developed the Ptolemaic system of astronomy.

Astronomer is an individual who studies the universe and its components such as stars, planets, galaxies, and other celestial bodies. They use observational data, mathematical models, and theoretical principles to understand the physical properties, evolution and origin of the universe. Astronomers often work in teams, and employ a variety of techniques to observe and analyze the data they collect. Astronomers may use ground-based telescopes, spacecraft, or other instruments to observe the universe and the objects within it.

This system used a combination of observational data and mathematical calculations to accurately predict the positions of the planets. This system was used for around 1500 years, until the invention of the telescope in the 17th century.

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a. The intersections of the field lines with a side of the cube are not uniformly distributed due to the symmetry of electric field lines that converge near the corners of the cube.

b. i. The number of field lines passing through surface element A and surface element B is the same due to the symmetry of electric field lines.

ii. The flux passing through surface element A and surface element B is equal due to the relationship between flux and the number of field lines.

c. The  element will be roughly the same, but as the surface area becomes smaller, the number of field lines passing through each element will become increasingly random and difficult to predict.

What does symmetry of electric field mean?

The symmetry of an electric field refers to the property that the electric field at a point in space is the same regardless of the direction in which it is measured. In other words, if you rotate the coordinate system or change the direction in which you are measuring the electric field, the electric field will have the same magnitude and direction.

For example, the electric field generated by a point charge is spherically symmetric, meaning it has the same magnitude and direction at all points on a spherical surface centered on the charge. This is because the electric field lines emanate radially from the charge in all directions, and the magnitude of the field decreases with the square of the distance from the charge. The symmetry of the electric field can simplify calculations and help predict the behaviour of charges in electric fields.

a. The intersections of the field lines with a side of the cube are not uniformly distributed across that side. This is because the electric field lines emanate from the positive charge in all directions, and as they approach the sides of the cube, they bend and converge toward the corners of the cube. Therefore, the electric field is stronger near the corners of the cube, and the field lines are more closely spaced there. This means that the density of field lines intersecting a given surface area on the cube will be greater near the corners than it is elsewhere.

b. i. The number of field lines through surface element A is equal to the number of field lines through surface element B. This is because the electric field lines emanating from the positive charge are symmetrical in all directions. Therefore, if we consider a small area element on the left side of the cube (such as surface element A), the same number of field lines will pass through that element as will pass through an equal area element on the opposite side of the cube (such as surface element B).

ii. The flux through surface element A is equal to the flux through surface element B. This is because the flux is proportional to the number of field lines passing through a given area, and as stated in (b.i), the number of field lines passing through equal area elements on opposite sides of the cube is equal.

c. If considering the surface element A itself as composed of many even smaller pieces, the number of field lines passing through each small surface element will be roughly the same. This is because the electric field lines are symmetrical and emanate from the point charge in all directions, and so the field lines will be distributed fairly uniformly over the surface area of the element. However, as the surface area of each small element becomes very small, the number of field lines passing through each element will become increasingly random and difficult to predict, due to the statistical nature of electric field lines.

When the region over which looked becomes sufficiently small, the field lines for the positive point charge appear to be radially distributed, emanating from the charge in all directions like the spokes of a wheel. The closer we look to the charge, the more tightly spaced the field lines will become, until they appear to converge toward the charge itself.

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A plane flies 72 x 105 m north and then another 15 x 105 m west in a total time of 6 h. the magnitude of your average velocity for the entire trip is 340 m/s.

Displacement = [(72 x 10⁵]² + [15 x 10⁵]²

= 10⁵ x √72² + 15²

= 10⁵ x √5.409

= 73.545 x 10⁵

Time = 6 hours = 6 x 3600 sec

Velocity = 73.545x10⁵/36x6x100

V= 0.34044 x 10³

V = 340.49

V = 340 m/s

Magnitude of average velocity is 340 m/s.

The terms haste and speed give us an idea of how fast or decelerate an object is moving. relatively frequently, we come across situations where we need to identify which of the two or further objects is moving briskly. One can fluently tell the faster of the two if they're moving in the same direction on the same road. still, if their direction of stir is in the contrary direction, also it's delicate to determine the fastest.

In similar cases, the conception of haste is helpful. In this composition, let us learn the haste meaning, the unit of haste, the illustration of haste, and the difference between speed and haste.

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Option B is correct.

Kinetic energy is the energy that a body possesses as a result of its movement. Potential energy is the energy that a body possesses as a result of its location or state.

While an object's kinetic energy is relevant to the state of other items in its environment, potential energy is fully independent of its surroundings. As a result, the acceleration of an item is not visible in the movement of a single object when other objects in the same environment are also moving.

Here potential energy is being used so work done will be mgh

Where,

M = mass

G = acceleration due to gravity

H = height

Since there is no change in kinetic energy,

So,

W1/W2 = mgh1/mgh2

Now, here mass and acceleration due to gravity are the same

Therefore,

W1/W2 = h1/h2

W2 = 0.5 × 146000J = 73000J

Therefore, the work done to lift the block halfway to the top is 73,000 joules.  

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The density of mercury at 166 °C would be approximately 13203 kg/m³.

A substance's density is a physical characteristic that indicates how much mass there is per unit volume. In other terms, it is a measurement of how close together a substance's particles are packed. The density equation is:

Mass / Volume equals density.

Where an object's volume is the amount of space it takes up and its mass is the amount of substance it contains.

Depending on the measurement system being used, the units for density may vary. The unit of density in the International System of Units (SI) is kilograms per cubic meter (kg/m3). However, additional measurements can also be made, such as grams per cubic centimeter (g/cm3) or pounds per cubic foot (lb/ft3).

To calculate the density of mercury at 166 °C, we can use the following formula:

ρ2 = ρ1 / [1 + β (T2 - T1)]

where:

ρ1 = 13600 kg/m³ is the density of mercury at 0 °C

β = 182 x 10^-6/°C is the coefficient of volume expansion for mercury

T1 = 0 °C is the initial temperature

T2 = 166 °C is the final temperature

Substituting these values into the formula, we get:

ρ2 = 13600 kg/m³ / [1 + (182 x 10^-6/°C) x (166 °C - 0 °C)]

ρ2 = 13600 kg/m³ / [1 + (182 x 10^-6/°C) x (166 °C)]

ρ2 = 13600 kg/m³ / 1.030012

ρ2 = 13203 kg/m³

Therefore, the density of mercury at 166 °C would be approximately 13203 kg/m³.

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The point that will vibrate the most when one of the friends speaks into the cup is point Q as vibration dampens and energy is lost due to friction.

In a toy telephone, sound is transmitted through a string that connects two plastic cups. When one person speaks into one cup, the sound waves vibrate the cup, which in turn vibrates the string and causes the other cup to vibrate as well.

Assuming that the string is held taut, the vibration of the cups will depend on the placement of the points P, Q, and R, as shown in the figure. If the string is not taut, the cups may not vibrate at all, or the vibrations may be too weak to transmit the sound effectively.

Point P is located at the midpoint of the string, and it will not vibrate much because the two cups are attached to it and there is no space for it to move.

Point Q is located at one end of the string, and it will vibrate the most when one of the friends speaks into the cup. This is because the cup will vibrate the string, and the vibration will be transmitted all the way to the other end of the string, where point Q is located.

Point R is located between P and Q, and it will vibrate to some extent, but not as much as point Q. This is because the vibration will be damped as it travels along the string, and some of the energy will be lost due to friction.

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The correct answer is 0 N.

There will be no current in the rod and thus no magnetic force resisting the motion. Without any resistance, it will keep moving until acted on by an outside force according to Newton's first law.

What is motion?

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The technology is perhaps the most dramatic force now shaping our world.

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Indeed, through a method known as induction, a negatively-charged electroscope can be used to identify whether an object is positive or negative.

When a negatively-charged object is brought near the electroscope, the negative charges in the electroscope will be repelled by the negative charges on the object, and move to the far end of the electroscope. This will leave the near end of the electroscope with a net positive charge.

If the object is then brought into contact with the electroscope, some of the negative charges on the object will flow onto the electroscope, neutralizing the positive charge on the near end of the electroscope. However, some of the negative charges on the object will remain on the far end of the electroscope, leaving a net negative charge on the electroscope.

At this point, the electroscope has a negative charge that is due in part to the negative charges on the object. If the object is then moved away from the electroscope, the negative charges on the far end of the electroscope will be less strongly repelled, and will move back towards the near end of the electroscope. This will leave the near end of the electroscope with a net positive charge again, but the charge will be less than the original positive charge. The net charge on the electroscope after this process will depend on the initial charge on the object. If the object is positively charged, it will attract negative charges to the near end of the electroscope, leaving a net negative charge on the electroscope. If the object is negatively charged, it will repel negative charges to the far end of the electroscope, leaving a net negative charge on the electroscope.

Therefore, by observing the final charge on the electroscope after this process, one can determine whether the object is positive or negative.

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Greetings from Joint Base Lewis-McChord, the base where I Corps and the 62 Airlift Wing are based. The flagship military facility on the West Coast for the Department of Defence is Joint Base Lewis-McChord, which is situated in the Puget Sound area of the Pacific Northwest.

JBLM, the sole Army Power Projection Platform west of the Rocky Mountains, has since expanded to become the largest Army-led joint post in the United States.

Because of the 100 km/h speed, the net spirit of the plane will be in this activity. In order to determine the plane's motion with respect to the north, we first locate the theatre.

The calculation would be 100 km/h divided by 300 km/h. According to the formula, three would win 10 thetas.

Therefore, The plane's motion's angle determines whether it is respectable.

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The required velocity of the box after it is released from the spring is 5.35 m/s.

The mass of the box m is given as 5 kg.

Elastic coefficient k is given as 110 N/m.

Compression of the spring x is given as 0.65 m.

We know the expression for force as,

F = k x

where,

k is the elastic coefficient

x is the compression in spring

Entering the values we have,

F = k x = 110 × 0.65 = 71.5 N ----(1)

Force is nothing but the tension in the spring which is given by the expression,

F = T = 1/2 m v² = 1/2 (5)v² = 2.5 v² ----(2)

Equating (2) and (1), we have,

2.5 v² = 71.5

v² = 28.6

v = 5.35 m/s

Thus, the velocity of the box after it is released from the spring is 5.35 m/s.

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