A substance takes three minutes in cooling from 50°C to 45°C and takes five minutes and cooling from 45°C to 40°C what is the temperature of the surrounding how much time will it take to cool the substances from 40°C to 35°C

The mass of water in the container is approximately 115.38 kg.

To calculate the mass of water in the container, we can use the formula:

Q = mcΔT

Where:

Q is the heat energy transferred to the water,

m is the mass of the water,

c is the specific heat capacity of water, and

ΔT is the change in temperature.Given:

Resistance of the heating coil (R) = 20 ohms

Voltage (V) = 220 volts

Time (t) = 2 minutes = 2 * 60 seconds = 120 seconds

Specific heat capacity of water (c) = 4.2 x 10^3 J/kg°C

Change in temperature (ΔT) = 100°C - 40°C = 60°C

First, we need to calculate the heat energy transferred to the water using the formula:

Q = IVt

Where:

I is the current flowing through the heating coil.

Using Ohm's Law, we can find the current:

I = V/R

I = 220 V / 20 ohms

I = 11 A

Now, we can calculate the heat energy:

Q = (11 A) * (220 V) * (120 s)

Q = 290,400 J

Substituting the values into the formula for heat energy:

290,400 J = (m) * (4.2 x 10^3 J/kg°C) * (60°C)

Simplifying the equation:

m = 290,400 J / (4.2 x 10^3 J/kg°C * 60°C)

m ≈ 115.38 kg

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The buoyant force exerted by the water on the cylinder is 0.2 N.

To find the buoyancy force exerted by water on the cylinder, we need to understand the concept of buoyancy and Archimedes' principle.

Archimedes' principle states that the buoyant force acting on an object immersed in a fluid is equal to the weight of the fluid displaced by the object. The buoyant force opposes the weight of the object and is responsible for the apparent loss of weight when an object is submerged in a fluid.

In this experiment, the weight of the cylinder (Wac) is 4 N. When the cylinder is immersed in water, the apparent weight of the cylinder (Wap) is 3.8 N. The difference between these two weights is the buoyant force exerted by the water on the cylinder.

Buoyant force (B) = Wac - Wap

B = 4 N - 3.8 N

B = 0.2 N

Therefore, the buoyant force exerted by the water on the cylinder is 0.2 N.

This means that the upward force exerted by the water on the cylinder is 0.2 N, opposing the downward force of gravity. The buoyant force depends on the volume of the fluid displaced by the object. In this case, the weight of the displaced water is equal to the buoyant force, as stated by Archimedes' principle.

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Temperature of planets decreases as they  distance from the Sun increases.

Temperature serves as a physical quantity used to express our perception of hot or cold sensations. Thermometers are used as instruments for measuring this quantity accurately across various scales--each scale utilizing different reference points and materials historically.

A noteworthy fact regarding planetary climates is their dependence on received amounts of solar radiation: planets situated farther away from the sun tend to have lower overall temperatures because they receive less direct sunlight.

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The specific heat of the ingot of metal heated and then dropped into a calorimeter is 100.0 J/kg°C.

The heat lost by the ingot is equal to the heat gained by the water.

Q_ingot = Q_water

The heat lost by the ingot can be calculated as follows:

Q_ingot = m_ingot × c_ingot × (T_ingot - T_f)

The heat gained by the water can be calculated as follows:

Q_water = m_water × c_water × (T_f - T_water)

where:

m_ingot = mass of the ingot (0.050 kg)

c_ingot = specific heat of the ingot (to be determined)

T_ingot = initial temperature of the ingot (200.0°C)

T_f  = final equilibrium temperature (22.4°C)

m_water = mass of the water (0.400 kg)

c_water = specific heat of water (4.184 J/g°C)

T_water = initial temperature of the water (20.0°C)

Substituting these values into the equations:

m_ingot × c_ingot × (T_ingot - T_f) = m_water × c_water × (T_f - T_water)

or

c_ingot = (m_water × c_water × (T_f - T_water)) / (m_ingot × (T_ingot - T_f))

Plugging in the values:

c_ingot = (0.400 kg × 4.184 J/g°C × (22.4°C - 20.0°C)) / (0.050 kg × (200.0°C - 22.4°C))

c_ingot = 100.0 J/kg°C

Therefore, the specific heat of the metal is 100.0 J/kg°C.

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A) These vectors should be drawn with the appropriate scale and labeled. The resulting vector is obtained by adding the two vectors head-to-tail. The tail of the crosswind vector should be connected to the head of the aircraft velocity vector.

B) R ≈ √68125 m/s ≈ 260.98 m/s

C)θ ≈ arctan(0.3)

θ ≈ 16.7°

D)The magnitude of the resultant vector is approximately 260.98 m/s. The direction of the resultant vector is approximately 16.7° south of west.

a) To draw the vector diagram, we represent the velocity of the aircraft as a vector pointing southwest with a magnitude of 250 m/s. We also represent the crosswind as a vector pointing east with a magnitude of 75 m/s. These vectors should be drawn with the appropriate scale and labeled. The resulting vector is obtained by adding the two vectors head-to-tail. The tail of the crosswind vector should be connected to the head of the aircraft velocity vector. The resulting vector represents the resultant velocity.

b) To calculate the magnitude of the resultant vector, we can use the Pythagorean theorem. Let's denote the magnitude of the resultant vector as R. The magnitude of the aircraft velocity vector is 250 m/s, and the magnitude of the crosswind vector is 75 m/s. Therefore,

R^2 = (250 m/s)^2 + (75 m/s)^2

R^2 = 62500 m^2/s^2 + 5625 m^2/s^2

R^2 = 68125 m^2/s^2

Taking the square root of both sides, we find:

R ≈ √68125 m/s ≈ 260.98 m/s

c) To calculate the angle to the resultant, we can use trigonometry. Let's denote the angle between the resultant vector and the southwest direction as θ. We can use the inverse tangent function:

tan(θ) = (75 m/s) / (250 m/s)

θ ≈ arctan(0.3)

θ ≈ 16.7°

d) The magnitude of the resultant vector is approximately 260.98 m/s. The direction of the resultant vector is approximately 16.7° south of west.

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Force of a body is calculated by mass times acceleration.

Acceleration = Velocity/Time

= 25/5

= 5 m/s²

Now,

Force = 1000 × 5

Force = 5000 N

Hence, 5000 N force is required to stop the bus in 5 second

The force required to stop the bus is 5000 N.

Given:

Acceleration (a) can be calculated using the formula:

a = (v' - v) / t

Substituting the given values, we have:

a = (0 - 25) / 5 = -5 m/s²

The force required to stop the bus can be calculated using Newton's second law of motion:

F = ma

Substituting the mass and acceleration, we get:

F = 1000 kg * (-5 m/s²) = -5000 N

Since the force cannot be negative, the magnitude of the force required to stop the bus is 5000 N.

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The resistivity of the wire of length 1 m and resistance of 3 ohm is  2.12×10⁻⁷ Ω/m.

Resistivity is defined to the electrical resistance of a conductor of a particular unit cross-sectional area and unit length.

To calculate the resistivity of the wire, we use the formula below

Formula:

Where:

From the question,

Given:

Substitute these values into equation 1

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Answer:

I don't actually know, but it has to do with the research they id

Explanation:

to seem precise

Answer:

c

Explanation:

The work done by the pupil librarian on the book is equal to the change in implicit energy of the book.

First, we need to calculate the implicit energy of the book when it's on the bottom

Ep1 = mgh1 = (2.2 kg)(9.81 m/ s2)( 0 m) = 0 J

where m is the mass of the book, g is the acceleration due to graveness, and h1 is the original height of the book( on the bottom).

Next, we need to calculate the implicit energy of the book when it's on the shel

f Ep2 = mgh2 = (2.2 kg)(9.81 m/ s2)(0.35 m) = 7.637 J

The total work done by the pupil librarian on the book is the difference in implicit energy

W = Ep2- Ep1 = 7.637 J- 0 J = 7.637 J

So the pupil librarian does 7.637 J of work on the book.

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Answer: The centripetal force acting on the car is 4752 Newtons

Explanation:

The formula for centripetal force (F) is:

[tex]F = m * v^2 / r[/tex]

where:

m is the mass,

v is the velocity, and

r is the radius.

Given that the mass (m) of the car is 990 kg, the velocity (v) of the car is 12 m/s, and the radius (r) of the curve is 30 m, we can substitute these values into the formula:

[tex]F = 990 kg * (12 m/s)^2 / 30 m[/tex]

Solving this gives:

[tex]F = 990 kg * 144 m^2/s^2 / 30 m[/tex]

This simplifies to:

[tex]F = 4752 N[/tex]

Therefore, the centripetal force acting on the car is 4752 Newtons.

The height of the object, given that the potential energy of the object doubled will be double (option D)

First, we shall list out the given parameters. Details below:

Potential energy is given as:

PE = mgh

Keeping mg constant, we have

PE₁ / h₁ = PE₂ / h₂

Inputting the given parameters, we have

P / h = 2P / h₂

Cross multiply

P × h₂ = h × 2P

Divide both sides by P

h₂ = (h × 2P) / P

h₂ = h × 2

h₂ = 2h

Thus, we can conclude that the new height of the object will also double (option D)

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The football left the kicker's foot with an initial vertical speed of 19.62 m/s.

The initial vertical velocity of a football kicked straight up into the air can be calculated using the kinematic equation:
v_f = v_i + a*t
where v_f is the final velocity (0 m/s in this case, as the football stops at its highest point before falling), v_i is the initial velocity (which we want to find), a is the acceleration due to gravity (-9.81 m/s^2, negative because it acts downward), and t is the time taken to reach the highest point.
First, we need to determine the time taken to reach the highest point, which is half of the total time (4 seconds):
t = 4 seconds / 2 = 2 seconds
Now we can substitute the values into the equation:
0 m/s = v_i - 9.81 m/s^2 * 2 seconds
Rearrange the equation to solve for v_i:
v_i = 9.81 m/s^2 * 2 seconds = 19.62 m/s
Therefore, the football left the kicker's foot with an initial vertical speed of 19.62 m/s.

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Answer:

2.94 s

Explanation:

v = u + at

where:

v = final velocity = 9 m/s

u = initial velocity = 0 m/s (rest)

a = acceleration

t = time taken to reach final velocity

We can rearrange the equation to solve for time:

t = (v - u) / a

Substituting the given values, we get:

t = (9 m/s - 0 m/s) / a

Now, we need to find the acceleration. We can use another kinematic equation:

s = ut + (1/2)at^2

where:

s = displacement = 1500 m

u = initial velocity = 0 m/s

a = acceleration

t = time taken to cover the displacement

We can rearrange the equation to solve for acceleration:

a = 2(s - ut) / t^2

Substituting the given values, we get:

a = 2(1500 m - 0 m) / (1500 m / 9 m/s)^2

Simplifying, we get:

a = 3.06 m/s^2

Now, we can substitute this value of acceleration in the earlier equation to find the time taken:

t = (9 m/s - 0 m/s) / 3.06 m/s^2

Simplifying, we get:

t = 2.94 s

Given that the original force is 10 newtons, the new force when the distance is doubled would be 2.5 newtons. Option A

Based on Newton's law of  gravitation, the force of gravity between two objects is inversely proportional to the square of the distance between them.

What this means is that if the distance between two objects is doubled, the force of gravity between them is reduced by a factor of four.

In this case, the distance between the two objects is doubled, so the force of gravity between them is reduced from 10 newtons to 2.5 newtons.

We can calculate it by saying 10 N / 4 = 2.5 N.

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Answer: A.

2.5 newtons

Explanation: edmentum

The electric conductivity of the wire is 0.05 siemens per meter (S/m).

To calculate the speed of sound in the air, you can use the formula:

Speed of sound = Distance / Time

In this case, the distance is 10 meters and the time is 0.05 seconds:

Speed of sound = 10 m / 0.05 s = 200 m/s

Therefore, the speed of sound in the air is 200 meters per second (m/s).

To calculate the electric current flowing through a wire, you can use Ohm's Law:

Current = Voltage / Resistance

In this case, the voltage is 50 volts and the resistance is 10 ohms:

Current = 50 V / 10 Ω = 5 A

Therefore, the electric current flowing through the wire is 5 amperes (A).

To calculate the electric conductivity of the wire, you can use the formula:

Electric conductivity = 1 / Resistance * (Cross-sectional area / Length)

In this case, the resistance is 10 ohms, the length is 10 meters, and the cross-sectional area is 0.5 square meters:

Electric conductivity = 1 / 10 Ω * (0.5 m^2 / 10 m) = 0.05 S/m

Therefore, the electric conductivity of the wire is 0.05 siemens per meter (S/m).

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Answer: Coulomb's law states that the force between two charged particles is directly proportional to the product of the charges and inversely proportional to the square of the distance between them. Mathematically, it can be represented as:

F = k(q1q2)/r^2

where F is the force, q1 and q2 are the charges of the particles, r is the distance between them, and k is the Coulomb's constant.

In the before scenario, both charges are positive (+q and +q), so they repel each other and the force between them is positive.

In the after scenario, one charge is positive (+q) and the other is negative (-q), so they attract each other and the force between them is negative.

Therefore, the correct answer is option C: The magnitude of the force is the same, but it changes from repulsive to attractive. The magnitude of the force is not affected by the sign of the charges, only the direction of the force changes.

Explanation: :)

Answer:

to shorten the answer

or it's like a code because scientists already know what it means

Answer:

Skyscraper

Explanation:

A human has less inertia than a skyscraper. The ability of matter to resist changes in motion is known as inertia, and it is inversely proportional to mass. A building has more inertia than a person since it has a larger mass.

According to Newton's third law of motion, if you apply a force of 100 N to the side of a skyscraper, the structure will respond by applying an equal and opposing force of 100 N to you. This is due to the fact that the force you exert on the tower is transmitted through your body, to your feet, and then into the ground. The skyscraper experiences an equal and opposite force from the earth, which is reflected back up your body through your feet.

B, Venus has an extremely high surface temperature, in fact, the highest on average of any planet in the solar system is not an effect that might have originated via catastrophic collision.

This is not an effect that might have originated via catastrophic collision. Venus's high surface temperature is due to its thick atmosphere, which is composed mostly of carbon dioxide. The carbon dioxide traps heat from the sun, causing the planet to warm up.

The other effects listed are all possible effects of catastrophic collisions. Uranus's axial tilt of 98° with respect to its orbit could have been caused by a collision with another planet-sized object.

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Answer: 0.2 seconds

Explanation: I took the test

The time period of the given wave is 0.2 seconds.

The speed of the wave, v = 2 m/s

The wavelength of the wave, λ = 0.4 m

The time period of a wave is defined as the amount of time required for one full oscillation in the medium's density.

It may alternatively be described as the amount of time needed for two successive rarefactions or compressions (Trough and Crest, respectively) to pass a given point.

The expression for the velocity of the wave is given by,

v = fλ

So, the frequency of the wave is,

f = v/λ

f = 2/0.4

f = 5 Hz

The time period of the wave can also be defined as the reciprocal of the frequency.

So, the time period of the wave is,

T = 1/f

T = 1/5

T = 0.2 s

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The correct answer to this question is option A, which indicates that the ambulance approaches the learner and then passes the learner.

Based on the information provided in the question, we can determine that the sound waves produced by the siren of an ambulance are detected by a learner standing at a roadside. The frequency-time graph shown in the question indicates that the detected frequency of the sound waves increases and then decreases over time. This suggests that the ambulance is moving towards the learner and then moving away from the learner. Option A in the question suggests that the ambulance approaches the learner and then passes the learner, which is consistent with the interpretation of the frequency-time graph. Therefore, option A is the correct answer. It is important to note that the question specifies that the ambulance is moving at constant velocity along a straight horizontal road. This means that the ambulance is not turning, which eliminates options B and C as possible answers. Option D suggests that the ambulance moves away from the learner and then stops, which is inconsistent with the information provided in the question.

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Answer:

The frequency must be constant to maintain continuity  the boundary.

Answer: The increase in the need for energy is causing significant environmental damage in several ways like fossil fuels, land use, deforestation, water use, and Air and water pollution

Explanation:

The increase in the need for energy is causing significant environmental damage in several ways like in fossil fuels from where the majority of our energy comes from non-renewable sources such as coal, oil, and gas, which release harmful greenhouse gases into the atmosphere when burned, contributing to climate change and global warming.

Land use and deforestation increase the production of biofuels and the construction of power plants requires a significant amount of land, leading to deforestation and habitat loss.

Water uses in energy production consume vast amounts of water, leading to water scarcity and ecosystem degradation

Air and water pollution in the production and transportation of energy and the disposal of waste from energy production result in air and water pollution that harm both humans and wildlife.

To address these issues, we must focus on reducing our energy consumption, promoting renewable energy sources, and implementing energy-efficient practices. Here are several solutions to this ongoing problem:

Promote Renewable Energy: Increase the use of renewable energy sources such as solar, wind, and hydropower, which are cleaner and less harmful to the environment than fossil fuels.

Improve Energy Efficiency: Encourage energy-efficient practices such as using LED lights, insulating buildings, and using energy-efficient appliances, which can significantly reduce energy consumption.

Encourage Conservation: Promote energy conservation, such as turning off lights when not in use, using public transportation, and carpooling, to reduce the need for energy production.

Develop Sustainable Infrastructure: Create sustainable infrastructure such as green buildings and eco-friendly transportation, which reduces the need for energy production and minimizes environmental impact.

Implement Environmental Policies: Governments can implement environmental policies that encourage energy conservation and the use of renewable energy sources, such as incentives for renewable energy and carbon taxes on fossil fuels.

Promote Education: Educate the public on the importance of energy conservation and the benefits of renewable energy, which can lead to behavior change and a reduction in energy consumption.

In conclusion, the increase in the need for energy is causing significant environmental damage, but there are several solutions to this ongoing problem. By promoting renewable energy, improving energy efficiency, encouraging conservation, developing sustainable infrastructure, implementing environmental policies, and promoting education, we can minimize our impact on the environment while still meeting our energy needs.

Answer:

4.06 seconds

148.3 meters

Explanation:

To solve for the time it takes for the projectile to hit the ground, we can use the following kinematic equation:

y = y_0 + v_0y * t + 1/2 * a_y * t^2

where y is the final height (0 m), y_0 is the initial height (also 0 m), v_0y is the initial vertical velocity, and a_y is the acceleration due to gravity (-9.8 m/s^2).

First, we need to find v_0y, the initial vertical velocity:

v_0y = v_0 * sin(theta) = 42 m/s * sin(28 degrees) ≈ 19.6 m/s

Now, we can solve for the time it takes to hit the ground:

0 = 0 + 19.6 m/s * t + 1/2 * (-9.8 m/s^2) * t^2

Simplifying and solving for t, we get:

t ≈ 4.06 seconds

Therefore, it takes about 4.06 seconds for the projectile to hit the ground.

To find the horizontal distance traveled by the projectile, we can use the following kinematic equation:

x = v_0x * t

where x is the horizontal distance traveled, v_0x is the initial horizontal velocity, and t is the time it takes to hit the ground (which we just calculated).

Since there is no air resistance, the horizontal velocity remains constant throughout the motion. Therefore:

v_0x = v_0 * cos(theta) = 42 m/s * cos(28 degrees) ≈ 36.5 m/s

Now, we can plug in the values to find the horizontal distance traveled:

x = 36.5 m/s * 4.06 s ≈ 148.3 meters

Answer:A word equation uses words to represent the reactants and products in a chemical reaction. A formula equation uses chemical symbols or formulas, but does not reveal the ratios of the products and reactants.

Explanation: example of a word equation: Synthesis, magnesium + chlorine → magnesium chloride.

Example of a formula equation:CH4(g) + O2(g) → CO2(g) + H2O(g)

Answer:

Approximately [tex]4.52\; {\rm s}[/tex], assuming that air resistance on the projectile is negligible.

Explanation:

It is given that the initial velocity of the projectile was [tex]u = 30\; {\rm m\cdot s^{-1}}[/tex] with an angle of elevation of [tex]0^{\circ}[/tex]. Decompose this initial velocity into its horizontal and vertical components:

Under the assumptions, the duration of the free fall depends only on the vertical component of initial velocity, [tex]u_{y} = 0\; {\rm m\cdot s^{-1}}[/tex].

Apply the following SUVAT equation to find this duration:

[tex]\displaystyle x_{y} = \frac{1}{2}\, a_{y}\, t^{2} + u_{y}\, t[/tex],

Where:

Since initial vertical velocity was [tex]u_{y} = 0\; {\rm m\cdot s^{-1}}[/tex], this equation simplifies to:
[tex]\displaystyle x_{y} = \frac{1}{2}\, a_{y}\, t^{2}[/tex].

Rearrange this equation to find duration [tex]t[/tex]:

[tex]\begin{aligned}t &= \sqrt{\frac{2\, x_{y}}{a_{y}}} \\ &= \sqrt{\frac{2\, (-100)}{(-9.8)}}\; {\rm s} \\ &\approx 4.52\; {\rm s}\end{aligned}[/tex].

Answer:

The last option, t=4.52 s.

Explanation:

The following information will help you tackle any projectile motion problem (assuming there is zero air friction), so please read carefully.

This projectile motion problem is solvable with some basic knowledge of projectile physics and the use of the 4 kinematic equations that are written below.

[tex]\boxed{\left\begin{array}{ccc}\text{\underline{The 4 Kinematic Equations:}}\\\\1. \ \vec v_f=\vec v_0+\vec at\\\\2. \ \Delta \vec x=\frac{1}{2}(\vec v_f-\vec v_0)t\\\\3. \ \Delta \vec x=\vec v_0t+\frac{1}{2}\vec at^2\\\\ 4. \ \vec v_f^2=\vec v_0^2+2\vec a \Delta \vec x \end{array}\right}[/tex]

Things to note about the above kinematic equations:

In order to use the above equations, two things MUST be true.

i. Acceleration is constant.

ii. You must know at least three pieces of information.

When dealing with 2-D motion, NEVER mix horizontal and vertical components together in the same equation.

Tackling Projectile Motion Problems:

To tackle any projectile motion problem, you will have to split components up into x and y. I personally like to make a table which you will see later as I am solving the question.

Things that are true for all 2-D projectile motion problems:

[tex]\boxed{\left\begin{array}{ccc}\text{\underline{Horizontal Component:}}\\\vec a_x= 0 \ m/s^2\\ \vec v_x=\vec v\cos\theta\end{array}\right} \ \boxed{\left\begin{array}{ccc}\text{\underline{Vertical Component:}}\\\vec a_y= -9.8 \ m/s^2\\\vec v_y=\vec v\sin\theta\end{array}\right}[/tex]

The horizontal component of velocity will be the same throughout the projectiles flight while the vertical component of velocity is variable (always changing). The horizontal component of acceleration will always be zero while the vertical component of acceleration will be the acceleration due to gravity. These things are crucial to understand when dealing with projectile motion problems.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Given:

[tex]\vec v_o=30 \ m/s \ at \ 0 \textdegree\\\\\Delta \vec y= -100 \ m[/tex]

Find:

[tex]t= ?? \ s[/tex]

(1) - Splitting up what we know into it horz. and vert. components

[tex]\boxed{\left\begin{array}{ccc}\text{\underline{Horizontal Component:}}\\\vec a_x= 0 \ m/s^2\\ \vec v_{0x}=(30)cos(0 \textdegree)= 30 \ m/s\\\vec v_{fx}= ?? \ m/s\\ \Delta \vec x= ?? \ m\end{array}\right} \ \boxed{\left\begin{array}{ccc}\text{\underline{Vertical Component:}}\\\vec a_y= -9.8 \ m/s^2\\\vec v_{0y}=(30)sin(0 \textdegree)=0 \ m/s\\\vec v_{fy}= ?? \ m/s\\ \Delta \vec y= -100 \ m\end{array}\right}\\\\t=?? \ s[/tex]

(2) - As you can see from the table above we know three pieces of information for the vertical components. I will use equation 3 to solve for the time, t

[tex]\Delta \vec y=\vec v_{0y}t+\frac{1}{2}\vec a_yt^2\\\\\Longrightarrow -100=(0)t+\frac{1}{2}(-9.8)t^2\\\\\Longrightarrow -100=-4.9t^2\\\\\Longrightarrow t^2=20.4082\\\\\Longrightarrow t=\sqrt{20.4082} \\\\\therefore \boxed{\boxed{t \approx 4.52 \ s}}[/tex]

Thus, it takes about 4.52 seconds for the projectile to hit the ground.

This proves that the motional emf is given by the following equation, emf = Bℓvsinθ when B , ℓ , and v are not mutually perpendicular.

The motional emf is the voltage that is generated when a conductor moves through a magnetic field. The magnitude of the motional emf is given by the following equation:

emf = Bℓvsinθ

where:

B = magnetic field strength

ℓ = length of the conductor

v = velocity of the conductor

θ = angle between the magnetic field and the velocity of the conductor

If v is perpendicular to B, then θ is the angle between l and B. If l is perpendicular to B, then θ is the angle between v and B.

The magnitude of the electric current is given by the following equation:

I = nqvA

where:

n = number of electrons per unit volume

q = charge of an electron

v = velocity of the electrons

A = cross-sectional area of the conductor

The electric current creates a voltage across the conductor, which is given by the following equation:

V = IR

where:

R = resistance of the conductor

The resistance of the conductor is given by the following equation:

R = ρl/A

where:

ρ = resistivity of the conductor

Substituting equations 2, 3, 5, and 6 into equation 1, gives following equation:

emf = Bℓvsinθ

This proves that the motional emf is given by the following equation:

emf = Bℓvsinθ

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Graphs can be used to calculate the displacement of an object by analyzing the relationship between time and position (or distance) on the graph.

Here's how:Position-Time Graph: If you have a position-time graph, the displacement of an object can be calculated by finding the difference between the initial and final positions. The displacement is equal to the change in position between two points on the graph. It can be determined by subtracting the initial position from the final position. The direction of displacement can be inferred based on the slope of the graph.Velocity-Time Graph: If you have a velocity-time graph, the displacement can be calculated by finding the area under the curve. The area under the graph represents the distance traveled, and the displacement is equal to the net area (taking into account the direction). Positive areas above the time axis represent displacement in one direction, while negative areas below the time axis represent displacement in the opposite direction.By utilizing these graphing techniques, one can analyze the position and motion of an object and calculate its displacement accurately. Graphs provide a visual representation of the relationship between time and position, allowing for a more intuitive understanding of displacement.

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a) , the average speed of trolley X is 0.2 m/s and the average speed of trolley Y is 0.4 m/s.

b)  the total momentum after the release of the spring is 0.4m kg·m/s.

To calculate the average speeds of trolleys X and Y, we can use the formula:

Average speed = Distance / Time

For trolley X:

Distance = 100 mm = 0.1 m

Time = 0.5 s

Average speed of trolley X = 0.1 m / 0.5 s = 0.2 m/s

For trolley Y:

Distance = 200 mm = 0.2 m

Time = 0.5 s

Average speed of trolley Y = 0.2 m / 0.5 s = 0.4 m/s

Therefore, the average speed of trolley X is 0.2 m/s and the average speed of trolley Y is 0.4 m/s.

To calculate the total momentum after the release of the spring, we need to consider the principle of conservation of momentum. According to this principle, the total momentum of an isolated system remains constant if no external forces act on it.

The momentum of an object is given by the formula:

Momentum = Mass × Velocity

For trolley X:

Mass = m

Velocity = Average speed of trolley X = 0.2 m/s

Momentum of trolley X = m × 0.2 m/s = 0.2m kg·m/s

For trolley Y:

Mass = 1/2m

Velocity = Average speed of trolley Y = 0.4 m/s

Momentum of trolley Y = (1/2m) × 0.4 m/s = 0.2m kg·m/s

Since the two trolleys are an isolated system and no external forces act on them, the total momentum after the release of the spring is the sum of the individual momenta:

Total momentum = Momentum of trolley X + Momentum of trolley Y

Total momentum = 0.2m kg·m/s + 0.2m kg·m/s

Total momentum = 0.4m kg·m/s

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