A) In the figure below, a cylinder is compressed by means of a wedge against an elastic constant spring = 12 /. If = 500 , determine what the minimum compression in the spring will be so that the pad does not move. Disregard the weight of the blocks and . The coefficient of friction between and the pad and between the floor and the pad is s = 0.4. Consider that the friction between the cylinder and the vertical walls is negligible


Answer: 4.08 cm.


B) Determine the lowest force required to lift the weight of 750 . The static coefficient of friction between and and between and is s= 0.25, and between and is 's = 0.5. Disregard the weight of the shims and .


Answer : 1095.4 N.

Answer:

The answer is "\(4,500 - 225 \ V\)".

Explanation:

Using formula for calculating the Voltage:

\(M_1=12.5\\\\M_2=250\\\\V_1=4,500 \\\\\bold{\text{Formula: }}\\\\\to \bold{\frac{m_1}{m_2}=\frac{V_2}{V_1}}\\\\\to \frac{12.5}{250}=\frac{V_2}{4,500}\\\\\to 0.05=\frac{v_2}{4,500}\\\\\to 0.05\times 4,500= V_2\\\\\to V_2=225\\\\\)

Hence the range of accelerating in voltage is \(4,500 - 225 \ V\)

Answer:

645 times 4.55 whatever the hell that is you jard and energy comes from change from kinetic energy (climbing up slide) like a frejard!

Explanation:

Writing in an online journal is different from writing in a paper one in the following way: it is easier to communicate online (option B).

A journal is a newspaper or magazine dealing with a particular subject.

A journal is an efficient medium to communicate the findings or results of an investigation to the public.

However, a journal can be virtual (online) or paper (hard copy). In this 21st century, it is easier to communicate to the masses online because more audience will be captured.

Therefore, writing in an online journal is different from writing in a paper one in the following way: it is easier to communicate online.

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Answer:

4.8 m/s

Explanation:

Given: angular velocity of wheel ω = 2.5 rev/sec

radius r = 30 cm

length of arrow = 24 cm

For arrow to pass through spinning ring it has to pass between any two spokes of the wheel.

angle between two spokes = π/4

time taken by a spook to reach the position of adjacent spoke t =θ/ω

=  π/4/(2.5×2π) = 1/20 sec

for the arrow to pass through the spokes of the wheel it should take time t <1/20 sec to pass through the wheel

a) therefore, minimum speed = (24/100)/(1/20) = 4.8 m/s

C. No.

The Roman soldier model for refraction assumes that light travels faster in air than in water. When light passes from a medium of lower refractive index (air) to a medium of higher refractive index (water), it bends towards the normal (a line perpendicular to the surface of the water at the point of incidence).

In the case of the muddy stream crossing the road at an angle of 45 degrees, the soldiers in the front row will hit the water first, and then the soldiers behind them will hit the water progressively later. This is because the light from the front of the stream reaches the soldiers' eyes first, while the light from the back of the stream takes a longer path and reaches their eyes later.

Therefore, the soldiers in the front row will not hit the water at the same time.

\(|A|=\sqrt{4^2+3^2}=5\\ |B|=\sqrt{5^2+(-2)^2}=\sqrt{29} \\\)

At pH = 8, the ratio of H+ ions to OH- ions is 1:1, indicating a neutral solution. The concentration of H+ ions and OH- ions is approximately 1 x 10^(-8) mol/L. The calculated and approximated ratios should match.

To calculate the ratio of H+ ions to OH- ions at pH = 8, we need to use the relationship between pH and the concentration of H+ ions. The pH scale is a logarithmic scale that measures the acidity or alkalinity of a solution based on the concentration of H+ ions.

The formula to calculate the concentration of H+ ions (\(C_H\)+) from pH is:

\(C_H\)+ = \(10^(^-^p^H^)\)

Substituting pH = 8 into the formula:

\(C_H\)+ = \(10^(^-^8^))\)

Using the properties of logarithms, we can calculate the concentration of H+ ions:

\(C_H\)+ ≈ 1 x \(10^(^-^8^))\) mol/L

According to the concept of neutrality in water, the concentration of H+ ions is equal to the concentration of OH- ions. Therefore, the concentration of OH- ions (\(C_O_H\)-) is also approximately 1 x \(10^(^-^8^))\)mol/L.

To calculate the ratio of H+ ions to OH- ions, we divide the concentration of H+ ions by the concentration of OH- ions:

Ratio = \(C_H\)+ / \(C_O_H\)-

Ratio = (1 x \(10^(^-^8^))\) / (1 x \(10^(^-^8^))\))

Ratio = 1:1

The ratio of H+ ions to OH- ions at pH = 8 is 1:1, indicating a neutral solution. This means that the concentration of H+ ions is equal to the concentration of OH- ions, resulting in a balanced ratio.

When comparing the calculated ratio of 1:1 to the approximated ratio at pH = 8, they should be the same because the ratio of H+ ions to OH- ions is determined solely by the pH value, which is consistent and mathematically derived. Therefore, the approximated and calculated ratios should match.

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B) A pendulum is a mass suspended on the bottom of a string.

A pendulum is a simple mechanical device that consists of a mass (known as the bob) suspended from a fixed point by a string, wire, or rod. When the bob is pulled to one side and released, it swings back and forth under the influence of gravity, forming a regular pattern of motion. The time it takes for the pendulum to complete one full swing (i.e., from one extreme position to the other and back again) is known as its period. The period of a pendulum is affected by the length of the string and the strength of gravity. The longer the string, the longer the period, and the stronger the gravity, the shorter the period.Pendulums have a wide range of practical applications, such as timekeeping, as seen in grandfather clocks. They are also used in scientific experiments to measure time intervals and gravitational acceleration.

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Answer:

power

Explanation:

Answer:

power

Explanation:

The phenomenon known as the Emission Spectra.

Emission spectrum is the phenomenon provides evidence that the hydrogen atom has discrete energy levels.

Emission spectrum is the spectrum of the different energy levels. The occurrence of emission spectrum gives proof that the hydrogen atom has distinct energy levels.

Emission spectrum is the phenomenon provides evidence that the hydrogen atom has discrete energy levels

Hence, the phenomenon is known as emission spectrum.

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Bluetooth works through radio waves in the ISM band, that is, they work by radio frequency. For that use the wireless networks of personal area (WPAN).

Bluetooth is a form of communication that works through radio waves by which there can be a transfer of data such as music, documents, images, etc. It works at a short distance so the devices must be close for the data transfer to occur correctly

Therefore, we can confirm that Bluetooth works through radio waves in the ISM band, that is, they work by radio frequency. For that use the wireless networks of personal area (WPAN).

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For the following are four electrical components:

a. For components A and B, both of which obey Ohm's law, the current-voltage characteristics would be a straight line passing through the origin. The slope of the line for component B would be steeper than that of component A, indicating higher resistance.

b. The shape of the characteristic for component C, the filament lamp, can be explained by its construction. A filament lamp consists of a filament made of a resistive material, typically tungsten, which heats up and emits light when an electric current passes through it.

c. The component chosen for D, which does not obey Ohm's law, could be a diode. A diode is a two-terminal electronic component that allows the current to flow in only one direction.

For the following are four electrical components:

a. Sketches of current-voltage characteristics:

For components A and B, both of which obey Ohm's law, the current-voltage characteristics would be a straight line passing through the origin. The slope of the line for component B would be steeper than that of component A, indicating higher resistance.

  Current (I)

     ^

     |          B

     |         /

     |        /

     |       /

     |      /

     |     /

     |    /

     |   /

     |  /

     | /

     |/

     +------------------> Voltage (V)

     Current (I)

     ^

     |          A

     |         /

     |        /

     |       /

     |      /

     |     /

     |    /

     |   /

     |  /

     | /

     |/

     +------------------> Voltage (V)

For component C, a filament lamp, the current-voltage characteristic would be a curve that is not linear. It would exhibit a non-linear increase in current with increasing voltage. At lower voltages, the lamp would have low resistance, but as the voltage increases, the resistance of the filament also increases due to the phenomenon of thermal self-regulation. This leads to a slower increase in current at higher voltages.

For component D, a component that does not obey Ohm's law, the current-voltage characteristic could be any non-linear curve depending on the specific component chosen. Examples of components that do not obey Ohm's law include diodes and transistors.

b. The shape of the characteristic for component C, the filament lamp, can be explained by its construction. A filament lamp consists of a filament made of a resistive material, typically tungsten, which heats up and emits light when an electric current passes through it. As the voltage across the filament increases, the temperature of the filament increases as well, causing its resistance to increase. This increase in resistance results in a slower increase in current with increasing voltage, leading to the characteristic non-linear curve observed.

c. The component chosen for D, which does not obey Ohm's law, could be a diode. A diode is a two-terminal electronic component that allows the current to flow in only one direction. It exhibits a non-linear current-voltage characteristic where it conducts current only when the voltage is above a certain threshold, known as the forward voltage. Below this threshold, the diode has a high resistance and blocks current flow in the reverse direction. The characteristic curve of a diode would show negligible current flow until the forward voltage is reached, after which it exhibits a rapid increase in current with a relatively constant voltage.

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Answer:

Sv = 1/2 a t^2         equation describing vertical distance traveled

Sv = 1/2 F / m * t^2       need to find t

Sh = .029m     horizontal distance traveled

.029 m = Vh t     time to travel 29 mm

t = 29E-3 m / 1.1E7 m/s = 2.64E-9 s

Sv = 1/2 * 5.1E-16 / 9.11E-31 * (2.64E-9)^2 = 5.1 / 2 * 2.64^2 / 9.11 * 10^-3 m

Sv = .00195 m = 1.95 mm

Electromagnetic spectrum:

When first E.M. waves were discovered and researched the scientists coped up with a lots of benefits of it especially in the telecommunication industry. Later, when the E.M. spectrum was started using in industry the people came to know about its harmful disadvantages which it cause. They are as follows:

Advantages of E.M. spectrum:

Disadvantages of E.M. waves:

(PS: E.M. waves do become beneficial and harmful when it's usage is done. Basically, they come with both it's advantages (benefits) and disadvantages (harmfulness) when we use it. Especially it is commonly seen in industrial areas or communication sector)

Classical mechanics describes the motion of objects on a macroscopic scale, while quantum mechanics deals with the behavior of particles on a microscopic scale. Classical mechanics is deterministic, meaning that it predicts precise outcomes based on initial conditions, while quantum mechanics is probabilistic, providing probabilities of different outcomes. Classical mechanics follows the principle of causality, where every effect has a specific cause, whereas quantum mechanics introduces inherent uncertainty and wave-particle duality. Classical mechanics is well-suited for describing everyday objects, while quantum mechanics is necessary to explain the behavior of particles at the atomic and subatomic levels.

~~~Harsha~~~

The answers are (a) |q| = 58.2 cm, M = -1.50, virtual, upright, shrunk; (b) |q| =, M = -, actual, substantially magnified; and (c) |q| = 6.5 cm, M = -1.68, virtual, upright, enlarged.

We can use the magnification formula and the thin lens equation to solve:

Where f is the lens's focal length, d_i is the image distance, and d_o is the object distance, the equation is: 1/f = 1/d_i + 1/d_o.

The formula for magnification is M = -d_i/d_o, where M stands for magnification.

For part (a), the object distance is d_o = -38.8 cm and the focal length is f = -19.4 cm.

1/-19.4 = 1/d_i + 1/-38.8

|d_i| = 58.2 cm

The image is virtual and smaller than the object (since the magnification is less than 1)

For part (b), the object distance is d_o = -19.4 cm, and the focal length is f = -19.4 cm.

1/-19.4 = 1/d_i + 1/-19.4

|d_i| = ∞

The image is at infinity, which means it is a real image and highly magnified (since the object distance is close to the focal length).

For part (c), the object distance is d_o = -9.70 cm, and the focal length is f = -19.4 cm.

1/-19.4 = 1/d_i + 1/-9.70

|d_i| = 6.5 cm

The image is virtual and larger than the object (since the magnification is greater than 1).
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At 30°C, the rms speed of a sample of oxygen with a molar mass of 16 g/mol is approximately 482.34 m/s.

The root mean square (rms) speed of a gas molecule is a measure of the average speed of the gas particles in a sample. It can be calculated using the formula:

vrms = √(3kT/m)

Where:

vrms is the rms speed

k is the Boltzmann constant (1.38 x 10^-23 J/K)

T is the temperature in Kelvin

m is the molar mass of the gas in kilograms

To calculate the rms speed of oxygen at 30°C (303 Kelvin) with a molar mass of 16 g/mol, we need to convert the molar mass to kilograms by dividing it by 1000:

m = 16 g/mol = 0.016 kg/mol

Substituting the values into the formula, we have:

vrms = √((3 * 1.38 x 10^-23 J/K * 303 K) / (0.016 kg/mol))

Calculating this expression yields the rms speed of the oxygen sample:

vrms ≈ 482.34 m/s

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The scenario presented is an example of negative punishment.

Negative punishment involves the removal of a desirable stimulus or the addition of an aversive stimulus in response to a behavior, with the goal of decreasing the likelihood of that behavior occurring again in the future.

In this case, the desirable stimulus that was removed is the son's ability to engage in leisure activities like playing hockey, and the aversive stimulus that was added is the scolding from the parent. By experiencing this consequence, the son may be less likely to forget his chores in the future in order to avoid the negative outcome.

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Option C. The heat absorbed or lost by a substance while it's changing state  correctly describes latent heat

Latent heat is the heat absorbed or lost by a substance while it is changing state.

The latent heat is a type of heat that is transferred during phase change, i.e., while a substance undergoes a change of state.

For example, when ice melts into liquid water, or when liquid water evaporates into water vapor, heat is absorbed from the surroundings.

Latent heat is not associated with a temperature change; rather, it's associated with a change of state.

For instance, the temperature of water remains at 100°C while boiling.

When water is boiling, the latent heat of vaporization is absorbed and utilized to break the hydrogen bonds holding water molecules together to change water from the liquid phase to the gaseous phase.

When the water is boiling, adding more heat won't increase the water's temperature, instead, the extra heat will be absorbed to change the phase of water molecules.

Therefore, the correct answer to the given question is option C: The heat absorbed or lost by a substance while it is changing state.

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Answer:

There are three different ways that the equation is represented visually when it is balanced. First, the scale is at equilibrium when it is balanced. The balance turns yellow and a smiley face appears. Second, the graph shows equal amounts on both the reactant and product side of the equation. Third, within the individual molecule box, there should be the same number of each element on both the product and a reactant side of the equation.

Reaction Total Number of Molecules

 Reactant Side (left) Product Side (right)

Make Ammonia  4  2

Separate Water  2  3

Combust Methane  3  3

No, the number of total molecules on the left side of a balanced equation is not equal to the number of total molecules on the right side of the equation. A molecule is the smallest number of atoms bonded together for a chemical reaction. The total number of atoms must be the same, but not molecules. The reactants and products will bond together in different ways leading to different numbers of reactants and products.

Reaction Total Number of Atoms

 Reactant Side (left) Product Side (right)

Make Ammonia  1C, 4H, 4O  1 C, 4H, 4O

Separate Water  2H, 4O  2H, 4O

Combust Methane  2N, 6H  2N, 6H

Yes, in order for the equation to be correct, the total number of atoms on the left side of the balanced equation must always equal the total number of atoms on the right side of the balanced equation.

Answers to this question vary. A good answer could say start with the chemical with the smallest amount on each side of the equation and balance that. Alternatively, you could start with the largest and balance that first. You also could say that you examined the visual representation in the reactant and product box to see if there was an equal number of atoms. Sometimes, it does require trial and error to get an equal number of atoms on each side of the equation. You could also use math concepts such as greatest common factors to use the smallest number possible of each molecule.

No, you could not use a non-integer number.

Explanation:

PF

Answer: There are three different ways that the equation is represented visually when it is balanced. First, the scale is at equilibrium when it is balanced. The balance turns yellow and a smiley face appears. Second, the graph shows equal amounts on both the reactant and product side of the equation. Third, within the individual molecule box, there should be the same number of each element on both the product and a reactant side of the equation.

Reaction Total Number of Molecules

 Reactant Side (left) Product Side (right)

Make Ammonia  4  2

Separate Water  2  3

Combust Methane  3  3

No, the number of total molecules on the left side of a balanced equation is not equal to the number of total molecules on the right side of the equation. A molecule is the smallest number of atoms bonded together for a chemical reaction. The total number of atoms must be the same, but not molecules. The reactants and products will bond together in different ways leading to different numbers of reactants and products.

Reaction Total Number of Atoms

 Reactant Side (left) Product Side (right)

Make Ammonia  1C, 4H, 4O  1 C, 4H, 4O

Separate Water  2H, 4O  2H, 4O

Combust Methane  2N, 6H  2N, 6H

Yes, in order for the equation to be correct, the total number of atoms on the left side of the balanced equation must always equal the total number of atoms on the right side of the balanced equation.

Answers to this question vary. A good answer could say start with the chemical with the smallest amount on each side of the equation and balance that. Alternatively, you could start with the largest and balance that first. You also could say that you examined the visual representation in the reactant and product box to see if there was an equal number of atoms. Sometimes, it does require trial and error to get an equal number of atoms on each side of the equation. You could also use math concepts such as greatest common factors to use the smallest number possible of each molecule.

No, you could not use a non-integer number.

The 10/90 principle can be a powerful tool for taking control of your situation and improving your life. By taking responsibility for what you can change and focusing on your reaction to the situation, you can make positive changes in your life and become the master of your own destiny.

The 10/90 principle refers to the idea that life is made up of 10% of what happens to you and 90% of how you respond to it. In other words, you may not be able to control what happens to you, but you can control your reaction to it. By taking responsibility for what you can change rather than being a victim of what you cannot change, you can take control of your situation and improve your life.One example of a situation where the 10/90 principle could be applied is losing a job. Losing a job can be a devastating experience, and it can be easy to feel like a victim in this situation. However, by applying the 10/90 principle, you can take control of your situation and make positive changes in your life.The first step in applying the 10/90 principle in this situation would be to take responsibility for what you can change. This could mean updating your resume, networking with others in your field, and applying for new jobs. By taking action and doing what you can to find a new job, you are taking control of your situation and improving your chances of finding a new job.
The second step would be to focus on your reaction to the situation. Instead of dwelling on the negative aspects of losing your job, try to focus on the positive aspects. This could mean using the extra time to pursue a new hobby or spend more time with family and friends. By focusing on the positive aspects of the situation, you are taking control of your reaction and improving your overall well-being.
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Answer:

Weight = 17780.82 N

Explanation:

The weight of the heaviest invertebrate = 2 tons

It is spread out over its length of 70 feet.

We need to find its weight in newtons.

We know that,

1 ton = 907.185 kg

2 ton  = 1814.37 kg

Weight of a body is given by :

W = mg

Where

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

So,

W = 1814.37 kg × 9.8 m/s²

W = 17780.82 N

Hence, the weight of heaviest invertebrate is 17780.82 N.

The weight will be "19600 Newtons".

Given values:

Length,

Mass,

            = 2 × 1000

            = 2000 kg

As we know,

→ \(W = mg\)

By substituting the values, we get

       \(= 2000\times 9.8\)

       \(= 19600 \ N\)

Thus the response above is appropriate.

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A cell of inter resistance of 0.5 ohm is connected to coil of resistance 4 ohm and 8 ohm joined in parallel.If there is current of 2A in 8 ohm, the electromotive force (emf) of the cell is approximately 14.5 volts.

To find the emf of the cell, we can apply Ohm's Law and Kirchhoff's laws to analyze the circuit.

Given:

Resistance of the coil, R1 = 4 ohm

Resistance of the other resistor, R2 = 8 ohm

Current passing through the 8-ohm resistor, I = 2A

First, let's analyze the parallel combination of the 4-ohm and 8-ohm resistors.

The total resistance of two resistors in parallel can be calculated using the formula:

1/Rp = 1/R1 + 1/R2

Substituting the given values, we have:

1/Rp = 1/4 + 1/8

1/Rp = 2/8 + 1/8

1/Rp = 3/8

Rp = 8/3 ohm

Now, let's consider the total resistance in the circuit, which includes the internal resistance of the cell (0.5 ohm) and the parallel combination of the resistors (8/3 ohm).

R_total = R_internal + Rp

R_total = 0.5 + 8/3

R_total = 1.833 ohm

Now, we can find the emf of the cell using Ohm's Law:

emf = I * R_total

emf = 2 * 1.833

emf ≈ 3.667 volts

Therefore, the emf of the cell is approximately 3.667 volts.

However, it is worth noting that the given current of 2A passing through the 8-ohm resistor does not affect the emf calculation since the emf of the cell is independent of the current in the circuit.

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The earthquake would occur 13 minutes before 10:05 a.m. which will be at 9.52 am.

The p-waves travel with a constant velocity of 7 km/s

The time can be calculated by using the formula

t = d / v

where

T1 =  10:05 a.m

d is the distance they take to travel from the epicenter

v is the speed of the p-waves

On average, the speed of p-waves is

v = 7 km/s

d = 5600 km (given)

Substituting the values in the formula;

t = d / v

t = 5600 ÷ 7

t = 800 seconds

Converting into minutes,

t = 800 ÷ 60

t = 13.3

≈ 13 mins

T1 -  13 mins = T2

10:05 - 13 mins = 9.52 am

It means the earthquake occurred prior 13 minutes, that is at 9.52 am.

Therefore, the earthquake occurred at 9.52 am.

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Answer:

a) 3.36 sec

b) 23.9 m/s

c) 1.52 sec

Explanation:

maximum height

H = 25 +v_y^2/2g

H=25+9^2/2*9.81 =29.13 m

time taken to reach maximum height = t_1 =v_y/g = 9/9.81 =0.92 seconds

time taken to fall back to ground from maximum height = √(2gH)/g

= √(2*9.81*29.13)/9.8 = 2.439 seconds

a) Total time taken to reach ground T = t_1+t_2 =0.92+2.439=3.36 sec

b) objects final speed = √2gH = 23.9 m/s

c) let total time be t then

25 = 9t +0.5gt^2

Solving we get t= 1.52 seconds

a) The object will take a time of 3.355 seconds to reach the ground.

b) The final velocity of the object as it impacts the ground is -23.902 meters per second.

c) The object will take a time of 1.520 seconds to reach the ground.

a) The height of the object (\(h\)), in meters, as a function of time (\(t\)), in seconds, is described below:

\(y = y_{o} + v_{o}\cdot t + \frac{1}{2}\cdot g \cdot t^{2}\) (1)

Where:

Now we proceed to determine the time needed for the object to reach the ground: (\(y_{o} = 25\,m\), \(y = 0\,m\), \(v_{o} = 9\,\frac{m}{s}\), \(g = -9.807\,\frac{m}{s^{2}}\))

\(-4.904\cdot t^{2}+9\cdot t +25 = 0\) (2)

Then, we solve this second order polynomial by quadratic formula:

\(t_{1} \approx 3.355\,s\), \(t_{2} \approx -1.520\,s\)

Only the former solution offers a realistic indicator. Hence, we conclude that the object will take a time of 3.355 seconds to reach the ground.

b) The final velocity of the object (\(v\)), in meters per second, is determined by this expression:

\(v = v_{o}+g\cdot t\) (3)

Now we proceed to find the final velocity of the object as it impact the ground: (\(v_{o} = 9\,\frac{m}{s}\), \(g = -9.807\,\frac{m}{s^{2}}\), \(t \approx 3.355\,s\))

\(v = 9+(-9.807)\cdot (3.355)\)

\(v = -23.902\,\frac{m}{s}\)

The final velocity of the object as it impacts the ground is -23.902 meters per second. \(\blacksquare\)

c) In this part we shall apply the same approach in a), that is: (\(y_{o} = 25\,m\), \(y = 0\,m\), \(v_{o} = -9\,\frac{m}{s}\), \(g = -9.807\,\frac{m}{s^{2}}\))

\(-4.904\cdot t^{2}-9\cdot t +25 = 0\)

Then, we solve this second order polynomial by quadratic formula:

\(t_{1} \approx 1.520\,s\), \(t_{2} \approx -3.355\,s\)

Only the former solution offers a realistic indicator. Hence, we conclude that the object will take a time of 1.520 seconds to reach the ground.

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Answer:

the answer is B.

Answer:

light

Explanation:

you can see stuff in space but cant hear it

The time of flight is 1.8 seconds, the horizontal component of the velocity is 11.2 m/s, and the distance from the catapult to where it lands is 20.2 meters.

When an object accelerates positively, it moves more quickly than it did earlier. In the first case, the moving car showed positive acceleration. The car is moving forward positively.

The rate at which displacement changes is known as velocity. The rate at which velocity changes is known as acceleration. Because it includes both magnitude and direction, velocity is classified as a vector quantity. Since acceleration is merely the rate at which velocity changes, acceleration additionally serves as a vector quantity.

To solve this problem, we can use the kinematic equations of motion. We can break the initial velocity into its horizontal and vertical components, and then use the equations to solve for the time of flight, horizontal velocity, and horizontal displacement.

Vertical component:

The initial vertical velocity is given by:

v0y = v0 sin(θ)

where v0 is the initial velocity (14.6 m/s) and θ is the angle of elevation (39◦).

v0y = 14.6 m/s × sin(39◦) = 9.0 m/s (approx)

Time of flight:

The time of flight can be found using the vertical motion equation:

\(y = v_0y t + (1/2)at^2\)

where y is the vertical displacement (which is zero at the peak of the trajectory), a is the acceleration due to gravity (-9.8 m/s^2), and t is the time of flight.

Setting y to zero, we get:

\(0 = (9.0 m/s) t + (1/2)(-9.8 m/s^2)t^2\)

Solving for t using the quadratic formula, we get:

t = 1.8 s (approx)

Horizontal component:

The initial horizontal velocity is given by:

v0x = v0 cos(θ)

v0x = 14.6 m/s × cos(39◦) = 11.2 m/s (approx)

Horizontal displacement:

The horizontal displacement can be found using the equation:

x = v0 x t

x = (11.2 m/s)(1.8 s) = 20.2 m (approx)

Therefore, the time of flight is 1.8 seconds, the horizontal component of the velocity is 11.2 m/s, and the distance from the catapult to where it lands is 20.2 meters.

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