Using energy considerations and assuming negligible air resistance, show that a rock thrown from a bridge 25.0 m above water with an initial speed of 20.0 m/s strikes the water with a final speed of what, independent of the direction thrown.

Given :

Initial speed of car A is 15 m/s and initial speed of car B is zero.

Final speed of car A is zero and final speed of car B is 10 m/s.

To Find :

What fraction of the initial kinetic energy is lost in the collision.

Solution :

Initial kinetic energy is :

\(K.E_i = \dfrac{15^2m}{2} + 0\\\\K.E_i = \dfrac{225 m}{2}\)

Final kinetic energy is :

\(K.E_f = \dfrac{10^2m}{2} + 0\\\\K.E_f = \dfrac{100m}{2}\)

Now, fraction of initial kinetic energy loss is :

\(Loss = \dfrac{\dfrac{225m}{2}-\dfrac{100m}{2}}{\dfrac{100m}{2}}\\\\Loss = \dfrac{125}{100}\\\\Loss = 1.25\)

Therefore, fraction of initial kinetic energy loss in the collision is 1.25 .

Expansion of universe is not a hypothetical one but the universe is expanding in the sense increase distance over the space and dark matter.

The increase in distance over time between any two particular gravitationally unbound regions of the observable universe is known as the universe's expansion. 

As a result, the size of space itself expands intrinsically. It is not necessary for space to exist outside of the cosmos or for it to extend into anything.

The metric changes in scale rather than space or the things in space moving in the conventional sense. Objects move farther apart from one another at ever-increasing speeds as the spatial component of the universe's spacetime metric scales up.

Any viewer in the cosmos would see that all of space appears to be expanding, except for the galaxies receding with a speed proportional to the distance from the observer.

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Answer: part a is e

part b a  

Explanation:

I HOPE THIS HELPS

It's important to know that the heat capacity of water is 4,200 Joules per Kilogram per degree Celsius. In order to answer the problem, we have to use the following formula

Replacing all the given information, we have

Then, we solve the expression

It takes approximately 9.05 seconds to roll the drum a distance of 36 meters.

We can use the formula for the circumference of a circle:

Circumference = 2 * π * radius

Given:

Radius (r) = 0.40 m

Circumference (C) = 2 * π * 0.40 m

We must figure out how many full rotations the drum makes to go 36 meters in order to calculate how long it takes to roll the drum. Since we are aware of the circumference, we can determine the number of full turns as follows:

Number of turns = Distance / Circumference

Given:

Distance = 36 m

Number of turns = 36 m / (2 * π * 0.40 m)

Now that we know how many turns there are, we can calculate the time by multiplying that number by the length of a turn, which is given as 8.0 seconds:

Time = Number of turns * Time per turn

Time = (36 m / (2 * π * 0.40 m)) * 8.0 s

By substituting the values into the equation, we can calculate the time:

Time = (36 / (2 * 3.14159 * 0.40)) * 8.0 s

Time ≈ 9.05 s

So, it takes approximately 9.05 seconds to roll the drum a distance of 36 meters.

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Answer:

6.67 cm

Explanation:

Given

Finding magnification

Finding image distance

Mirror formula

Solving

270 FAST bacteria occupy the culture at time t = 10 s and 318 FAST bacteria occupy the culture at time t = 11 s.

Define FAST bacteria.

A group of bacteria with the property of acid fastness is referred to as acid-fast bacteria, sometimes known as acid-fast bacilli or simply AFB. A bacterium's capacity to withstand acid decolorization during staining methods is known as acid fastness.

Mycobacteria's high mycolic acid concentration, which causes the staining pattern of poor absorption followed by significant retention, is what makes them acid-fast.

At t = 10 s

N(t) = 10+6t+2t^2

N(t) = 10 +6*10 + 2*10*10

      = 270

At t  = 11s

N(t) =  10+6*11+2*11*11

     =  318

Difference between two will be 318 - 270 =  48

Rate of bacterial growth will be (270-10/270) *100%

i.e. 96.2%

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Creating an effective system to solve problems is beneficial in various ways as it enables an individual to come up with a clear and concise solution to any problem or situation that may arise.

Some of the benefits that I would like to see in my own life as I begin to apply the 4-step problem-solving process are:Improved decision making skills- The 4-step problem-solving process will help me to make better decisions since it requires that I identify the problem, gather information, develop solutions, and implement the most suitable solution. This approach will help me to weigh my options carefully and make decisions based on logic rather than emotions.Improved communication skills- The process of problem-solving requires communication between team members. As I begin to apply the 4-step problem-solving process, I would like to develop better communication skills that will enable me to express my ideas clearly and succinctly.

This will be helpful not only in my personal life but also in my professional life where effective communication is a key to success.Improved critical thinking skills- The process of problem-solving requires critical thinking. By applying the 4-step problem-solving process, I would like to improve my critical thinking skills by learning how to analyze information, assess the problem, and develop solutions based on the available information.Improved productivity- The 4-step problem-solving process is a structured approach that helps to identify problems and develop solutions in a systematic manner. By applying this approach in my life, I would like to improve my productivity since I will be able to solve problems more efficiently and effectively.

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Answer:

medial is the answer "nose is medial to the eyes'

Answer:

The magnetic field strength at the center of a solenoid can be found using the formula:

B = u_0 * N * I / L

where B is the magnetic field strength, u_0 is the permeability of free space (4π × 10^-7 T·m/A), N is the number of turns in the solenoid, I is the current flowing through the solenoid, and L is the length of the solenoid.

Given:

N = 500 turns

I = 5 A

u_0 = 4π × 10^-7 T·m/A

Since we don't know the length of the solenoid, we can't calculate the magnetic field strength.

Answer:

D

Explanation:

Solution:-

- The refrigeration cycle contains the target refrigerated place and the warm reservoir.

- The purpose of the refrigeration cycle is to exchange heat in the evaporator that consists of a cooling fluid mostly ( R - 134a ) with the air in the target refrigerated place.

- The cooling gas in the cycle is at a much lower temperature than the temperature in the target place.

- The exchange of heat is directed from the targeted refrigerated place to the working fluid in the cycle.  

- This is also called the cooling load of the refrigerator / refrigeration cycle ( Ql ).

- The super-heated fluid is then taken to the condenser where heat exchanged with the surrounding which is at much lower temperature than the super-heated fluid in the cycle.  

- Since, both the condenser and evaporator work at different pressures. A compressor is installed to pressurize the working fluid to the condenser pressure. Some amount of energy is required to do work on the working fluid of the cycle. This is denoted as the work input to the cycle. ( Win ).

- The performance of a refrigeration cycle is basically expressed as a ratio of desired out-put and the work-input to the cycle ( compressor ).

- The desired output of the refrigeration cycle is to remove heat from the target place via evaporator. So we express the performance of a refrigeration cycle with a parameter known as the coefficient of performance ( COP ):

                               \(COP_r =\frac{Q_l}{W_i_n}\)

- The ratio of cooling load to work-done on the working fluid.

Answer: The heat removed from the inside to the work done to remove the heat.

The sled will slide a distance of 0.5 meters before coming to rest with constant speed and given kinetic friction.

For given kinetic friction:

When the football players stop pushing the sled, the friction force acting on the sled will cause it to decelerate until it comes to rest. The magnitude of the friction force can be found using the formula:

f_friction = friction coefficient * normal force

where the normal force is equal to the weight of the sled, which is:

normal force = m * g

where m: mass of the sled and g: acceleration due to gravity.

Therefore, the friction force acting on the sled is:

f_friction = 0.30 * (60 kg * \(9.81 m/s^2\)) = 176.94 N

The deceleration of the sled can be found using Newton's second law:

F_net = m * a

where F_net is the net force acting on the sled, m is the mass of the sled, and a is the acceleration of the sled.

The sled is under no net force because it is travelling at a constant pace. As a result, the sled is not decelerating at all.

The kinematic equation is used to:

\(d = (v_f^2 - v_i^2) / (2 * a)\)

Since d is the sled's distance travelled, v f is its final velocity, which is zero, v i is its beginning velocity, which is 1.0 m/s, and an is its acceleration, which is zero, we can find d as follows:

\(d = (0 - (1.0 m/s)^2) / (2 * 0 m/s^2) = 0.5 m\)

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1) The velocity of the pin after the collision is 107.4 m/s.

2) The velocity of the two cars as the collision is inelastic is 48.2 m/s.

We know that by the principle of the conservation of linear momentum, the momentum before Collison is equal to the total momentum after collision. Now we have to use this principle in the both questions that we have here.

1) Given that;

Total momentum before collision = Total momentum after collision

(41.7 * 59.1) + (4.17 * 0) = (41.7 * 48.35) + ( 4.17 * v)

We then have;

2464 + 0 = 2016 +  4.17v

2464 - 2016 = 4.17v

v = 2464 - 2016 /4.17

v = 107.4 m/s

2) Given that;

Total momentum before collision = Total momentum after collision

(51.3 * 50.1) + (100 * 47.2) = (100 +  51.3)v

2570 + 4720 = 151.3v

v = 2570 + 4720/151.3

v = 48.2 m/s

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The average velocity of the car is 100 kilometers/hour south. This means that, on average, the car is traveling 100 kilometers per hour in the south direction relative to its starting point.

To determine the average velocity of the car, we need to calculate the displacement and divide it by the time taken. Velocity is defined as the rate of change of displacement with respect to time.

In this case, the car is traveling south, and its displacement is 200 kilometers from its starting point after 2 hours.

The average velocity is given by the formula:

Average velocity = Displacement / Time

The displacement is 200 kilometers south, and the time is 2 hours. Therefore, we have:

Average velocity = 200 kilometers south / 2 hours

Simplifying the calculation:

Average velocity = 100 kilometers/hour south

Hence, the correct answer is B. 100 kilometers/hour south. This indicates that the car's average velocity is 100 kilometers per hour towards the south direction.

It's important to note that velocity is a vector quantity and includes both magnitude (speed) and direction. In this case, the direction is specified as south, which indicates that the car is moving towards the south relative to its starting point.

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The height of the hill is approximately 0.128 meters.

The total energy of the ball at the top of the hill is equal to its kinetic energy:

E_top = K = 15 J

At the bottom of the hill, the total energy of the ball is the sum of its kinetic and potential energies:

E_bottom = K + U = 70 J + 5 J = 75 J

The potential energy of the ball at the top of the hill is zero, since it is at the highest point. Therefore, the potential energy at the bottom of the hill is:

U = E_bottom - K = 75 J - 70 J = 5 J

The potential energy of an object at a height h is given by:

U = mgh

where m is the mass of the object, g is the acceleration due to gravity (9.8 m/s^2), and h is the height. Rearranging this equation gives:

h = U/(mg)

Substituting the values given in the problem, we get:

h = 5 J / (4 kg * 9.8 m/s^2) ≈ 0.128 m

Therefore, the height of the hill is approximately 0.128 meters.

What is kinetic energy?

Kinetic energy is the energy possessed by a moving object due to its motion. It is defined as the energy an object has by virtue of its motion, and is directly proportional to the mass of the object and the square of its velocity (speed).

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Answer:  a stretch of 2

Explanation: because it 2 (x) - 3

Explanation:

Given that,

Work done to stretch the spring, W = 130 J

Distance, x = 0.1 m

(a) We know that work done in stretching the spring is as follows :

\(W=\dfrac{1}{2}kx^2\\\\k=\dfrac{2W}{x^2}\\\\k=\dfrac{2\times 130}{(0.1)^2}\\\\k=26000\ N/m\)

(b) If additional distance is 0.1 m i.e. x = 0.1 + 0.1 = 0.2 m

So,

\(W=\dfrac{1}{2}kx^2\\\\W=\dfrac{1}{2}\times 26000\times 0.2^2\\\\W=520\ J\)

So, the new work is more than 130 J.

A parallel circuit is an electrical circuit with more than one current path and all circuit components are connected between the same two sets of electrically common points. The current supplied by the source in a parallel circuit is equal to the sum of all branch currents in the circuit.

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Answer: 20

Explanation: cause

Explanation:

When two or more atoms link up, they create a molecule. e.g, A molecule of water is made of two atoms of hydrogen (H) and one atom of oxygen (O).

Answer:

The word is "wind".

Explanation:

The sentence would be:

"The sun is also the reason wind exists. The wind is moving air."

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The current that flows through the 75 ohm resistor in the circuit shown below is 0.12A.

The current flowing through a circuit can be calculated using the Ohm's law equation as follows;

V = IR

Where;

According to this question, a circuit is shown in the above image. A 75 ohm resistor is given alongside a voltage of 9V. The current can be calculated as follows;

9 = I × 75

I = 0.12A

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The energy that a substance contains is known as heat. Thus, the correct option for this question is B.

Entropy may be characterized as the measurement of the degree of randomness or in other words, it is the increase in the disorganization within a system. It is the measure of a system's thermal energy per unit temperature that is unavailable for doing useful work.

Equilibrium is a state of balance between opposing forces or actions that is either static or dynamic. It symbolizes the circumstance of being balanced in nature.

Thermal energy is a type of energy that is significantly contained within a system that is responsible for its temperature. Heat is the flow of thermal energy.

Therefore, the energy that a substance contains is known as heat. Thus, the correct option for this question is B.

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The energy stored in the circuit at any time t is given by \(U = (1/2)L*I^{2} + (1/2)Q^{2} /C = (1/2)L*(V_{0} /R)^{2} *e^{(-2t/(R*C))} + (1/2)C*V_{0} ^{2} *(1 - e^{(-2t/(R*C)})).\)The units are in seconds.

The total energy stored in the circuit can be calculated using the formula: U = (1/2)L*I² + (1/2)Q²/C, where L is the inductance, I is the current, Q is the charge on the capacitor, and C is the capacitance.

Initially, the capacitor is uncharged, so the second term is zero.

Therefore, the initial energy stored in the circuit is U₀ = (1/2)L*I₀², where I₀ is the initial current, which is zero.

When the magnetic field is switched on, a current begins to flow in the solenoid.

This current increases until it reaches its maximum value, given by I = V/R, where V is the voltage across the solenoid and R is its resistance.

Since the solenoid is connected in series with the capacitor, the voltage across the solenoid is equal to the voltage across the capacitor, which is given by V = Q/C, where Q is the charge on the capacitor.

The charge on the capacitor is given by Q = C*V, where V is the voltage across the capacitor at any time t.

Therefore, we have I = V/R = Q/(R*C) = dQ/dt*(1/R*C), where dQ/dt is the rate of change of charge on the capacitor.

This is a first-order linear differential equation, which can be solved to give \(Q(t) = Q_{0} *(1 - e^{(-t/(R*C)}))\), where Q₀ is the maximum charge on the capacitor, given by Q₀ = C*V₀, where V₀ is the voltage across the capacitor at t=0.

The current in the solenoid is given by I(t) = \(dQ/dt*(1/R*C) = (V_{0} /R)*e^{(-t/(R*C)}).\)

The energy stored in the circuit at any time t is given by\(U = (1/2)L*I^{2} + (1/2)Q^{2} /C = (1/2)L*(V_{0} /R)^{2} *e^{(-2t/(R*C))} + (1/2)C*V_{0} ^{2} *(1 - e^{(-2t/(R*C)})).\)

The time t at which the energy stored in the circuit drops to 10% of its initial value can be found by solving the equation U(t) = U₀/10, or equivalently, \((1/2)L*(V_{0} /R)^{2} *e^{(-2t/(R*C)}) + (1/2)C*V_{0} /R)^{2}*(1 - e^{(-2t/(R*C)})) = (1/20)L*I_{0} /R)^{2}.\)

This equation can be solved numerically using a computer program, or graphically by plotting U(t) and U₀/10 versus t on the same axes and finding their intersection point.

The solution is t = 1.74 ms.

The units are in seconds.

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Answer:

a: 0.25 ohms

Explanation:

The resistance of the circuit can be calculated by using Ohm's Law:

\(V = IR\\\\R = \frac{V}{I}\)

where,

R = Resistance of the circuit = ?

V = Voltage = 12 volts

I = Current = 48 A

Therefore,

\(R = \frac{12\ V}{48\ A} \\\\R = 0.25\ ohms\)

Hence, the correct option is:

a: 0.25 ohms

Answer:

a natural mixture of sand, gravel, and crushed stone

Explanation:

Soil formation occurs as a result of the the decay or the remains of plants and animals which are used up.

Weathering can be defined as the physical and chemical breakdown of rock into smaller pieces called sediment. Weathering can be classified into two categories namely;

I. Physical weathering : it is the process of breaking rocks into pieces without affecting its chemical composition e.g temperature, abrasion and frost action.

II. Chemical weathering : it is the process of breaking rocks into pieces by chemical action which leads to changes in its chemical composition e.g carbonation, hydration, plant acid and oxidation.

In Science, one of the type of land resource is generally referred to as an aggregate.

Typically, an aggregate is a natural mixture of sand, gravel, and crushed stone. It's a heterogeneous mixture that is commonly mixed with bitumen, gypsum, cement, lime and several other adhesive to form mortar or concrete which are used in building and constructions.

Answer:

C

Explanation:

It's correct have a nice day

B. The reactants have higher potential energy, and energy is absorbed is the statement that best describes the total energy change of the system.

The difference in the amounts of chemical energy that are stored in the products and reactants accounts for the energy change in a chemical reaction. Enthalpy refers to the system’s heat content or stored chemical energy.

Potential energy can be described as the energy which a body possess because of its position. The potential energy can also be said as stored energy. The energy diagram that shows the changes in energy is called as a chemical reaction.

Potential energy and the Reaction progress are shown in the problem and from this the reactants are seen as the substance which reacts and form one or more than one product.

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