Two hockey players are skating toward each other on a frictionless ice. One is moving at 1 m/s while the other is traveling at 2 m/s. The players collide and stick together. Find their combined speed.

Mugger and a victim meet on a dark street. The mugger previously decided whether to bring a gun and, if he did, whether to show it during the robbery. If the mugger does not show a gun - either because he doesn't have one or has one and hides it- then the victim has to decide whether to resist.

The strategic form of this situation is shown below. Note that all payoffs have been specified, except for the mugger's payoff when he chooses to have a gun and show it.We know that there is a Nash Equilibrium in which the mugger randomizes over the two pure strategies gun, hide and no gun and the victim randomizes over resist and do not resist.

The mugger will have no incentive to change his strategy if the victim will not change his. So, let's first take a look at the victim's best response to the mugger's strategies.

Assume the mugger is going to bring a gun with probability x. If the mugger shows the gun, the victim will not resist because the payoff from resisting is -10, which is less than -5. If the mugger doesn't show the gun, then the victim will resist if his payoff from resisting is at least equal to his payoff from not resisting. That is, if:2p - 5(1 - p) ≥ 0The mugger will choose to show the gun if and only if his payoff from showing the gun is greater than his payoff from not showing the gun.

That is, if:3x + 5(1 - x) ≥ 0Simplifying this inequality: 8x - 5 ≥ 0x ≥ 5/8So, there is a Nash Equilibrium in which the mugger randomizes over the two pure strategies gun, hide and no gun and the victim randomizes over resist and do not resist, when x is greater than or equal to 5/8.

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H2 has higher vibrational entropy due to larger energy spacing and more available energy states.

Problem 1:

To calculate kg T for T = 500 K in various units:

\(erg: kg T = 1.3807 × 10^-16 erg/K * 500 K eV: kg T = 8.6173 × 10^-5 eV/K * 500 K cm-t: kg T = 1.3807 × 10^-23 cm-t/K * 500 K Wavelength: kg T = (6.626 × 10^-34 J·s) / (500 K) Degrees Kelvin: kg T = 500 K Hertz: kg T = (6.626 × 10^-34 J·s) * (500 Hz)\)

Problem 2:

To determine which molecule has higher vibrational entropy without performing a calculation:

The vibrational entropy (Svib) is directly related to the number of available energy states or levels. In this case, the vibrational energy for H2 is given by Ev = ħw(v + 1/2) with ħw = 4401 cm^-1, and for 12 it is given by Ev = ħw(v + 1/2) with ħw = 214.52 cm^-1.

Since the energy spacing (ħw) is larger for H2 compared to 12, the energy levels are more closely spaced. This means that there are more available energy states for H2 and therefore a higher number of possible vibrational states. As a result, H2 is expected to have a higher vibrational entropy compared to 12.

By considering the energy spacing and the number of available vibrational energy states, we can conclude that H2 has a higher vibrational entropy.

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Answer:

it yields a derived unit known as Newton, which is the unit of Force.

Explanation:

The formula for force is given by Newton's Second Law, which states that whenever an unbalanced force is applied to a body, it produces an acceleration in the body in the direction of force.

\(F = ma\\\)

where, F = Force

m = mass

a = acceleration

Now, we substitute the respective S.I units of each quantity in equation:

F = Newton (N)

m = kilogram (kg)

a = acceleration = m/s²

Therefore,

\(N = (kg)(m/s^2)\)

So, it is clear from above expression that:

When kilogram is multiplied by meter per second squared, it yields a derived unit known as Newton, which is the unit of Force.

The mass of a golf ball can be calculated using the principle of conservation of mass.

The mass of a golf ball can be determined through the principle of conservation of mass by weighing the ball before and after a process that does not change its mass and subtracting any mass change from the total mass to find the mass of the golf ball alone.

To do this, you need to weigh a golf ball before and after a process that does not change its mass, such as immersing it in water or exposing it to a different temperature.

For example, to find the mass of a golf ball using the principle of conservation of mass, you would first weigh the ball on a scale to find its dry mass, then immerse it in water and weigh it again to find its mass in water. The difference between the two masses would be the mass of water that the golf ball displaced, which can be subtracted from the total mass to find the mass of the golf ball alone.

It's important to note that the accuracy of the measurement will depend on the precision of the scale used and the controlled conditions of the experiment, such as the temperature and pressure of the water and the room. Additionally, it's essential to consider the buoyant force that acts on an object immersed in a fluid, which can affect the accuracy of the measurement.

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The total work done by the force of friction on the block as it moves a distance L up the incline is given by the formula:

Wfric = −f × L

The work done by the force of friction on the block as it moves a distance L up the incline is equal to the product of the force of friction and the distance moved. Work is the measure of the amount of energy transferred by a force when an object is moved a certain distance. If a force acts on an object and the object moves, work is done by the force. Therefore, work can be defined as the product of force and displacement.

Mathematically, it can be expressed as follows:

W = F × S

where W is work, F is force, and S is displacement. The SI unit of work is joules (J). When a block moves on an inclined plane, friction is one of the forces acting on the block. As the block moves up the plane, the force of friction acts opposite to the direction of motion of the block. Hence, the work done by the force of friction is negative. This means that the force of friction acts to decrease the energy of the block.

The work done by the force of friction on the block as it moves a distance L up the incline is given by the formula:

Wfric = −f × L

where Wfric is the work done by the force of friction, f is the force of friction, and L is the distance moved by the block up the incline. Therefore, the total work done by the force of friction on the block as it moves a distance L up the incline is given by the formula:

Wfric = −f × L

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Answer:

the same

Explanation:

if that is what you are asking

Answer:

B

Explanation:

your answer is B. 2. 5 m/s to the left

A student with a mass of 50 kg is standing in a canoe the initial velocity of the canoe is 2.5 m/s to the left. The correct option is option (B).

Given that the mass of the student is 50 kg, the mass of the canoe is 30 kg, and the velocity of the student is 1.5 m/s to the right, we can calculate the velocity of the canoe.

Before the jump, the total momentum is the sum of the momentum of the student and the momentum of the canoe, since they are initially at rest.

Total momentum before the jump = (mass of the student + mass of the canoe) × (initial velocity)

= (50 + 30) × 0 = 0

After the jump, the total momentum is the sum of the momentum of the student and the momentum of the canoe.

Total momentum after the jump = mass of the student × velocity of the student + mass of the canoe × velocity of the canoe

Total momentum after the jump = (50 ×  1.5) + (30 × velocity of the canoe)

0 = (50 × 1.5) + (30 ×  velocity of the canoe)

-75  = 30 ×  velocity of the canoe

velocity of the canoe = -75  / 30 = -2.5 m/s

Therefore, the initial velocity of the canoe is 2.5 m/s to the left. Hence, the correct option is (B).

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Answer:

added in picture

Explanation:

added in the picture

A hydraulic jack is used to lift objects such as automobiles. If the input force is 200 N over a distance of 1 meter, the output force over a distance of 0.1 meter is ideally 2000 N. This is due to the fact that the hydraulic jack is a mechanical device that utilizes a hydraulic mechanism to multiply the force applied to it.

A hydraulic jack is a mechanical device that utilizes a hydraulic mechanism to multiply the force applied to it. It works on the principle of Pascal's law, which states that when pressure is applied to an enclosed fluid, it is transmitted uniformly in all directions.

The fluid exerts pressure on the surface of a piston, which causes the piston to move upward. The output force of a hydraulic jack is determined by the ratio of the areas of the two pistons and the pressure exerted on the input piston.The output force of a hydraulic jack is ideally more significant than the input force. The ratio of the output force to the input force is referred to as the mechanical advantage of the hydraulic jack.

The mechanical advantage is determined by the ratio of the area of the output piston to the area of the input piston. If the area of the output piston is ten times larger than the area of the input piston, the mechanical advantage of the hydraulic jack is ten. The output force is ten times greater than the input force.

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Answer:

stretching and compression

The strength of the magnetic field is increased by adding more coils to the wire and placing a metal bar within the coils.

The given problem is based on the concept and fundamentals of the magnetic strength in a current-carrying coil of wire. The current-carrying wire in a coiled form is known as Solenoid.

And the mathematical expression for the magnetic field in a solenoid is,[\(B = \dfrac{\mu_{0} \times N \times i}{L}\)

Here,

B is the strength of the magnetic field.

\(\mu_{0}\) is the magnetic permeability of free space.

N is the number of coils.

The strength of the magnetic field will increase by increasing the number of coils and placing the metallic slab (it will increase magnetic permeability) within the coils.

Thus, we can conclude that the strength of the magnetic field is increased by adding more coils to the wire and placing a metal bar within the coils.

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Answer:

C

Explanation:

ANSWER:

a. 1200 lb/ft^3

b. Gold

STEP-BY-STEP EXPLANATION:

Given:

Weight (W) = 96 lb

Volume (V) = 0.08 ft^3

a.

Weight density is equal to the quotient of weight to volume, therefore:

b.

We can say that this weight density is equal to the weight density of Gold

Answer:

2.25 billion years

Explanation:

i am smort

Answer:

Surface tension is a fundamental property of the surface of liquid. Surface tension is responsible for the curvature of the surfaces of air and liquids. Surface tension is responsible for the ability of some solid objects to “float” on the surface of a liquid.

hope it helps

Surface tension is the tendency of liquid surfaces at rest to shrink into the minimum surface area possible.Surface tension is what allows any object that is denser than water to float on water

hope this will help out

Answer:

I = 50 A

Explanation:

The magnetic field created by a wire with a current can be calculated as:

Where μ is a constant equal to 4π x 10^(-7) T m/A, I is current, and r is the distance from the wire. So, replacing the values, we get:

Then, solving for I, we get:

Therefore, the current that is traveling through the wire is 50 A.

On the other hand, if the current is moving upward, the direction of the magnetic field can be found by the rule of the right hand, so the magnetic field will have the following direction:

Answer: it’s c

Explanation:

Given parameters:

Rate of acceleration of the box = 0.08m/s²

Force applied to the box = 47N

Unknown:

Mass of the box  = ?

The force applied on a body is push or pull on it to move it in a specific direction. Force causes the motion of a body.

Mathematically, force is expressed as the product of mass and acceleration;

             Force  = mass x acceleration

Input parameters and solve for mass;

              47  = mass  x  0.08

                 mass  = \(\frac{47}{0.08}\)

                mass  = 587.5Kg

The mass of the box is  587.5Kg

Explanation:

Final velocity=Initial velocity+(acceleration×time)

4 ways to find initial velocity:

1) Initial velocity=Final velocity-(acceleration×time)

2) Initial velocity=(Distance/Time)-((acceleration×time)/2)

3) Initial velocity=√Final velocity-(2×(acceleration×distance))

4) Initial velocity=2(distance/time)-Final velocity

Total force = Mass×Acceleration

(F=ma)

The speed of the cart is 4.67 m/s.

The momentum is conserved in the absence of any external force. The total momentum before any interaction between two objects is equal to the total momentum after the interaction. Hence, the final momentum is equal to the initial momentum. We can use this law to solve the given question.

Therefore, the initial momentum of the system is = m1v1+m2v2

(m1, v1, m2, v2 are the masses and velocities of the objects)Here, m1=1000 kg, v1=5.0 m/s, m2=70 kg, and v2=0 (man is at rest)Initial momentum = 1000 x 5.0 + 70 x 0 = 5000 kg m/s. The man starts running to the left with a speed of 10 m/s relative to the cart. It means the man is moving at (5-10) = -5 m/s relative to the ground. Here, we need to find the final velocity of the cart. The man will have a velocity of -5 m/s relative to the ground. We need to calculate the final velocity of the cart.

Considering the conservation of momentum,

Initial momentum = final momentum(1000+70)v

final = 1070(vfinal) = 5000/1070

The final velocity of the cart is 4.67 m/s.

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Answer:

Work done = 838470 Joules.

Explanation:

Given the following data;

Power = 19 hp

Time = 1 minute to seconds = 60 seconds.

Next, we would convert the unit of power in "hp" to "Watt."

1 Watt = 0.00135962 horsepower

x Watt = 19 horsepower

Cross-multiplying, we have;

19 = 0.00135962x

x = 19/0.00135962

x = 13974.5 Watts.

Now, to find the work done in moving the mower;

Work done = power * time

Substituting into the formula, we have;

Work done = 13974.5 * 60

Work done = 838470 Joules.

The conclusion you make about the relative orientation of the mirrors is that multiple images are created by multiple reflections between two flat mirrors.

What are mirrors: The law of reflection helps explain how a mirror is characterized as a reflecting surface.

In conclusion, When two mirrors are parallel to each other, the number of reflecton is infinite.This also depends on your point of view.

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The probability that the item actually has a flaw given that it passed the first inspector is approximately 0.021, or 2.1%.

To calculate the probability that an item actually has a flaw given that it passed the first inspector, we need to use Bayes' theorem.

Let's define the events as follows:

A: The item has a flaw.

B: The item is passed by the first inspector.

We are given:

P(A) = 0.02 (probability that an item has a flaw)

P(B|A) = 1 (probability that the item is passed by the first inspector given that it has a flaw)

We want to calculate:

P(A|B) = ? (probability that the item has a flaw given that it is passed by the first inspector)

According to Bayes' theorem:

P(A|B) = (P(B|A) * P(A)) / P(B)

To calculate P(B), we need to consider both scenarios: the item has a flaw (A) and the item does not have a flaw (A').

P(B) = P(B|A) * P(A) + P(B|A') * P(A')

Given that P(B|A') is the probability that the item is passed by the first inspector given that it does not have a flaw, we can assume this probability to be high, such as 0.95. Therefore, P(B|A') = 0.95.

Using these values, we can calculate P(B) as follows:

P(B) = P(B|A) * P(A) + P(B|A') * P(A')

= 1 * 0.02 + 0.95 * (1 - 0.02)

= 0.02 + 0.95 * 0.98

= 0.02 + 0.931

= 0.951

We can calculate P(A|B) using Bayes' theorem:

P(A|B) = (P(B|A) * P(A)) / P(B)

= (1 * 0.02) / 0.951

= 0.02 / 0.951

≈ 0.021

Therefore, the probability that the item actually has a flaw given that it passed the first inspector is approximately 0.021, or 2.1%.

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Answer:

Explanation:

Given:

V₁ = 20 m/s

ΔS = 200 m

V₂ = 15 m/s

___________

S - ?

Car motion equation:

X₁ = V₁*t = 25*t

X₂ = ΔS  + V₂*t = 200 + 15*t

Since the second car overtook the first, then:

X₁ = X₂

25*t = 200 + 15*t

5*t = 200

t = 200 / 5 = 40 с

Distance:

S = ΔS + V₂*t = 200 + 15*40 = 200 + 600 = 800 m

Correct answer:

A) 800 m

The ball that is thrown directly downward with an initial speed of 7.05 m/s, from a height of 29.9 m. takes 3.29 s to strike the ground

The formula for the downward vertical launch and the procedure we will use is:

t = {V₀ + \(\sqrt{}\)[(V₀)² + 2*g*y]}/ g

Where:

Information about the problem:

With the information gave, we can calculate the time from the ball is thrown, using the formula of downward vertical launch:

t = {V₀ + \(\sqrt{}\)[(V₀)² + 2*g*y]}/ g

t = {7.05 m/s + \(\sqrt{}\)[(7.05 m/s)² + 2*9.8 m/s²*29.9 m]}/ 9.8 m/s²

t = {7.05 m/s + \(\sqrt{}\)[49.70 m²/s² + 586.04m²/s² ]}/ 9.8 m/s²

t = {7.05 m/s + \(\sqrt{}\)[635.74 m²/s² ]}/ 9.8 m/s²

t = {7.05 m/s + 25.214 m/s}/ 9.8 m/s²

t = 32.26 m/s/ 9.8 m/s²

t = 3.29 s

In physics vertical launch is the motion described by an object that has been launched vertically in which the acceleration is the earth's gravitational force.

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Answer:

Defined below

Explanation:

Climate change is simply the long term change in the average weather patterns that are associated with the local, regional and global climates of the earth. Climate change is usually driven by human activities like burning of fossils; natural processes like cyclic ocean patterns; external factors like volcanic eruptions.

120 ccf of natural gas converted to kWh electricity is equivalent to approximately 3,646.19 kWh of electricity

To convert 120 ccf of natural gas to kWh of electricity:

1. Convert ccf to BTU (British Thermal Units): 1 ccf (100 cubic feet) of natural gas contains approximately 103,700 BTU.
2. Convert BTU to kWh: 1 BTU is equal to 0.000293071 kWh.

Multiply the amount of natural gas in ccf by the BTU content:
120 ccf * 103,700 BTU/ccf = 12,444,000 BTU

Convert the BTU to kWh:
12,444,000 BTU * 0.000293071 kWh/BTU ≈ 3,646.19 kWh

So, 120 ccf of natural gas is equivalent to approximately 3,646.19 kWh of electricity after the conversion calculations(to two decimal places).

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