derive dynamic equations of the electrical system shown below (use current i1 and i2 as states). then derive dynamic equations of an analogous mechanical system and draw a schematic diagram.

A 20.0 kg cannonball is fired from a cannon with a muzzle speed of 100 m/s at an angle of 20.0°. Using conservation of energy, the maximum height reached by the cannonball is approximately 510.2 meters.

A cannon ball weighing 20.0 kg is launched from a cannon with an initial velocity of 100 m/s at an angle of 20.0° above the horizontal.

To determine the maximum height reached by the cannonball using the conservation of energy principle, we consider the conversion of kinetic energy into gravitational potential energy.

Initially, the cannonball has only kinetic energy, given by the equation KE = (1/2)mv², where m is the mass and v is the velocity.

At the highest point of its trajectory, the cannonball has no vertical velocity, meaning it has no kinetic energy but possesses gravitational potential energy, given by the equation PE = mgh, where h is the height and g is the acceleration due to gravity (approximately 9.8 m/s²).

Using the conservation of energy, we equate the initial kinetic energy to the maximum potential energy:

(1/2)mv² = mgh

Canceling the mass and rearranging the equation, we find:

v²/2g = h

Plugging in the given values, we have:

(100²)/(2*9.8) = h

Simplifying the equation, we find:

h ≈ 510.2 m

Therefore, the maximum height reached by the cannonball is approximately 510.2 meters.

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Given parameters:

Mass of load = 20kg

Height of man = 1.4m

Unknown:

Work done by man = ?

Work done is the force applied to move a body in a particular direction.

Often times, it is mathematically expressed as;

           Work done  = Force x distance

In this problem, we use the formula of potential energy to find the work done;

     Work done  = Potential energy  = mgh

where m is the mass of the load

            g is the acceleration due to gravity  = 9.8m/s²

            h is the height of the body

Now, input the parameters, and solve for work done;

        Work done = 20 x 9.8 x 1.4  = 274.4J

The work done by man is  274.4J

The current in each experiment increases with increase in the voltage. Similarly, the association between resistance and the current in a circuit shows that increase in the resistance shows a reduction in the current, vice versa.

Ohm's Law states that the voltage across an electric conductor is directly proportional to the current(I) passing through it provided the resistant is constant.

So;

V ∝ I

V = IR  

where

The objective of this question want us to determine: How did the current change for each test provided that Avery uses a 1.5-volt battery, then she uses a 3-volt battery and lastly she uses a 9-volt battery, given that the resistance is constant through out the whole process.

In the first experiment;

In the second experiment;

In the third experiment;

Therefore, we can conclude that the current in each experiment increases with increase in the voltage. Similarly, the association between resistance and the current in a circuit shows that increase in the resistance shows a reduction in the current, vice versa.

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The displacement of the ball is zero.

What is displacement?

The smallest distance between the initial and final position of an object.

What are the equations of motion?

There are three equations of motion that completely describes the motion of an object.

The first equation of motion gives the relationship between the initial velocity, final velocity, acceleration, and time.

The second equation of motion gives the relationship between the initial velocity, displacement, acceleration, and time.

The third equation of motion gives the relationship between the initial velocity, final velocity, acceleration, and displacement.

Given time, initial velocity, and acceleration, the displacement can be calculated using the second equation of motion. The second equation of motion is,

s=u*t+(1/2)*a*t^2

Here, u=25 m/sec, a=-25 m/sec and t=2.0 sec.

Put the values in the formula and calculate the displacement.

s= (25)*(2.0)+(1/2)*(-25)*(2.0)^2

s=50-50

s=0 m.

Hence the displacement of the ball is zero.

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Answer:

○ 0 \(\checkmark\)

Explanation:

Even if the athelete runs four laps of a 400 m track, its displacement will be 0 because the displacement is the shortest distance from its to final position. And, here the final and initial position is same since he comes to its initial position after covering certain distance. So, displacement is 0.

Answer:

The __law__ conservation

of state that either energy may produced nor destroyed

Deposition is when a gaseous state changes to solid state by escaping liquid state. So I think it is 3. Liquid glass cools and hardens

On motorized solar panel arrays, the panels are moved in order to track the movement of the sun. The correct answer is option b.

A motorized solar panel array is a device that can adjust the solar panel's orientation to the sun to maximize electricity production. As the sun moves across the sky, photovoltaic solar panels must adjust their orientation to remain perpendicular to the sun's rays.

By tilting or turning solar panels, solar panels can increase energy production. Motorized solar panel arrays enable solar panels to be tracked using an algorithm that considers the time of day, year, and latitude.

Solar panel tracking systems keep solar panels facing the sun to increase energy generation. The most basic tracking systems involve manually adjusting the solar panels' orientation. Motorized solar panel arrays, which automatically adjust the panels' angles based on the time of day, year, and location, are more sophisticated.

Dual-axis tracking systems can adjust the panels both vertically and horizontally. The result is an increase in the amount of energy generated by the solar panels. Therefore option b is correct.

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Answer:

Relative density is proportional to the frequency of a material's density to its water density. Because both have had the same proportions, their proportion is also dimensionless.

Explanation:

The dimension of relative density:-

Relative Density of a Substance (R.D.) = Substance Density / Water Density.

Therefore, R.D. Is just a ratio or a number. There are no units or dimensions to it.

For example:- The density of iron is 8.5 GM's/cm^3 & the density of water is 1 gm/cm^3 (in cgs units).

Tension:-   Surface tension is the propensity of the new worlds and infographics to reduce to the particle size which is least appropriate. Atmospheric pressure helps insects (e.g. water striders) can travel or move and on a water surface, typically object is sensed rather than water.

Answer:42.41

Explanation:

Given data:

Speed of baseball, v = 22 m/s

(a) Calculation of the height reached by baseball: We can use the formula for height: `h = u^2/(2*g)`where u is the initial velocity and g is acceleration due to gravity. u = 22 m/s (initial velocity)g = 9.8 m/s² (acceleration due to gravity)h = ?Now, put the given values in the above formula and solve it: h = (22 m/s)²/(2 * 9.8 m/s²) = 25.05 m

Therefore, the height reached by baseball is 25.05 m.

(b) Calculation of the time taken by baseball: We can use the formula for time: `t = v/u` where v is the final velocity and u is initial velocity. u = 22 m/s (initial velocity)v = 0 m/s (final velocity)Now, put the given values in the above formula and solve it: t = v/u = 0/22 = 0 s

Therefore, the time taken by baseball is 0 s.

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Answer:A heavier body has more inertia than a lighter body. So, “ the larger the mass, the larger is inertia, and the smaller the mass, the smaller is the inertia”

Explanation:

We can say that “ the mass of a body is a measure of its inertia ”.

Answer:

The kinetic energy of an object is the energy it has because of its motion.

Explanation:

Answer:

Wave frequency

Explanation:

Wave frequency is the number of waves that pass a fixed point in a given amount of time.

The pure resonance initial value problem can be solved by finding the particular solution using the method of undetermined coefficients.

To solve the pure resonance initial value problem x ′′ + ω^2x = F₀sin(ωt), x(0) = 0, x′(0) = 0, we begin by finding the homogeneous solution. The homogeneous equation x ′′ + ω^2x = 0 corresponds to a simple harmonic oscillator with angular frequency ω. Its general solution is \(x_h(t)\) = A*cos(ωt) + B*sin(ωt), where A and B are constants determined by the initial conditions.

Next, we find the particular solution. Since the forcing function F₀sin(ωt) has the same form as the homogeneous solution, we assume a particular solution of the form\(x_p(t)\)= t*(C*sin(ωt) + D*cos(ωt)). By substituting this into the differential equation and solving for the coefficients C and D, we obtain the particular solution.

Finally, the complete solution is given by the sum of the homogeneous and particular solutions: x(t) =\(x_h(t) + x_p(t)\). Applying the initial conditions x(0) = 0 and x′(0) = 0 allows us to determine the values of the constants A, B, C, and D. Once these values are known, the solution to the pure resonance initial value problem can be fully determined.

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The water outflow in 30 secs through 200 mm of the capillary tube is mathematically given as

\(Qo=1.6 \times 10^{2} \mathrm{~mL}\)

\(\begin{aligned}\Delta P &=6660 \mathrm{~m} / \mathrm{m}^{2} \\\mu &=8.01 \times 10^{-4} \text { Pas } \\t &=30 \mathrm{~s} \\L &=200 \mathrm{~mm}=200 \times 10^{-3} \mathrm{~m} \\D &=1.5 \mathrm{~mm}=1.5 \times 10^{-3} \mathrm{~m} \Rightarrow \gamma=\frac{1.5 \times 10^{-3}}{2} \mathrm{~m}\end{aligned}\)

Generally, the equation for Rate of flow of Liquid is  mathematically given as

\(\\$$Q=\frac{\pi r^{4} \times \Delta P}{8 \mu L}\)

$$

Where dP is pressure difference r is the radius

\(\mu\) is the viscosity of water

L is the length of the pipe

\(Q=\frac{\pi \times\left(\frac{1.5 \times 10^{-3}}{2}\right)^{4} \times 6660}{8 \times 8.01 \times 10^{-4} \times 200 \times 10^{-3}}\)

\(Q=5.2 \mathrm{~mL} / \mathrm{s}\)

In $30s the quantity that flows out of the tube

\(&Qo=5.2 \times 30 \\&Qo=1.6 \times 10^{2} \mathrm{~mL}\)

In conclusion, the quantity that flows out of the tube

\(Qo=1.6 \times 10^{2} \mathrm{~mL}\)

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The pressure also doubled when the temperature did. answer P2=2atm.

According to Gay-Lussac Law, pressure and temperature have a direct relationship: P1/T1=P2/T2.

As long as the volume is kept constant, pressure and temperature will both rise or fall together.

The pressure would also double if the temperature did. The energy of the molecules would grow with increased temperature, and more collisions would occur, increasing pressure.

Double the temperature of a sample of gas that is at STP 1 atm and 273 K.

1atm/273K=P₂/546K\sP₂=2atm

The pressure increased by the same factor as the temperature.

Everything we eat, drink, or use contains energy. The fundamental body functions of the body are powered and governed by energy.

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Answer:

Elements in a family have the same

Ans C. number of valence electrons

Given:

The applied force is,

The mass of the object is,

The constant velocity of the object is,

To find:

The coefficient of friction between the object and the surface

Explanation:

The object is moving with a constant velocity which means the object is under equilibrium. So, the applied force is equal to the frictional force on the object.

If the coefficient of friction between the object and the surface is

we can write the frictional force as,

For equilibrium condition,

Hence, the coefficient of friction between the object and the surface is 0.47.

When a lens is focussed at infinity, its focal length is calculated. The focal length of a lens indicates the angle of view (how much of the scene will be caught) and magnification.

(a) Using the mirror equation:

1/f = 1/do + 1/di

where f is the focal length, do is the object distance, and di is the image distance. Plugging in the given values:

1/-5.5 = 1/6 + 1/di

Solving for di:

di = -3.3 m

The image distance of the truck is -3.3 m, which means it is behind the mirror and virtual.

(b) Using the magnification equation:

m = -di/do

Plugging in the values:

m = -(-3.3)/6

m = 0.55

The magnification of the mirror is 0.55, which means the image of the truck is smaller than the actual truck.

So, the image distance of the truck is -3.3 m, and the magnification of the mirror is 0.55.

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Suppose a lion is in free fall.  The lion covers the same distance as the second before.

In free fall, an object falls with a constant acceleration of 9.8 meters per second squared (9.8 m/s^2) due to the force of gravity. This means that the lion's speed increases by 9.8 m/s every second it falls. However, since the lion starts from rest, its initial speed is 0 m/s. Therefore, after one second of free fall, the lion's speed is 9.8 m/s, after two seconds it's 19.6 m/s, and so on. Despite the increase in speed, the lion's displacement (i.e., the distance it covers) in each second of free fall is the same, as the acceleration due to gravity is constant. Hence, the lion covers the same distance as the second before.

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Answer:

Explanation:

A train travels at a speed of 30 mi/hr and travels a distance of 240 miles.

distance = 240 miles

velocity = 30 mi/hr.

time = distance / velocity

       =   240 miles    

            30 miles/hr.

       =  8 hours

Answer:

∆p.e = mg∆h

Explanation:

Take height reference be h1 while height final be h2.

∆h = (h2 - h1)

m = m

g = g

•°• ∆p.e = mg(h2 - h1)

=> ∆p.e = mg∆h

it would be on the right end I believe. Forgive me if I am incorrect.

Switching is a technique commonly used to control general light levels in buildings.

It involves the use of individual switches to control the lamps or groups of lamps within a multi-lamp fixture separately. This enables the user to control the amount of light produced in different areas of a room or building according to their needs. Switching can be done manually or automatically, using various technologies such as timers, motion sensors, and light sensors. It offers a simple and cost-effective way to improve energy efficiency and reduce energy consumption, as well as to create more comfortable and flexible lighting environments that meet the specific needs of different users. Switching is a technique commonly used to control general light levels in buildings.

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The many volcanic and geyser-like eruptions on Jupiter's moon Io are caused by tidal forces exerted on the moon by its host planet Jupiter and the other moons in its vicinity.

The many volcanic and geyser-like eruptions on Jupiter's moon Io are caused by tidal forces exerted on the moon by its host planet Jupiter and the other moons in its vicinity.

These forces cause the moon's interior to flex and heat up, leading to volcanic activity on its surface. Additionally, Io's unique composition, with a high concentration of sulfur and other volatile materials, makes it more prone to volcanic eruptions compared to other moons in our solar system.

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Answer:

the answer is c

Explanation: