9. Two objects A and B move toward each other with speeds of 80 cm/s and 20 cm/s, respectively. The
mass of A is 140 g and that of B is 60 g. After a head-on, perfectly elastic collision, the speed of
object B is
8.0 cm/s
20 cm/s
92 cm/s
a.
b.
C.
d. 1.2 m/s
m₁
Hom
m2
hinnt of mass m= 4.0 kg by a compressed

Answer:

The angle of refraction be 3.21°

Explanation:

Let the angle of refraction = r

Given,

Angle of incidence, i = 0.5°

Refractive index of amber, n = 1.55

Refractive Index can be calculated by  n = sin i/sin r

⇒ n = sin i/sin r

⇒ 1.55 = sin 0.5°/sin r

⇒ sin 0.5° =  0.0087

⇒ 1.55 =  0.0087/ sin r

⇒ sin r = 0.0087/1.55

⇒ sin r = 0.0056

⇒ r =  sin−1(0,0056)

⇒ r = 3.21°

According to these two figures, the kinetic energy symbol is p^2/2m, and a car with mass m is moving with a momentum of p. due to the fact that kinetic energy is directly proportional to the mass of an item.

It is possible to say the following: KE =  p^2/2m where V denotes the changing motion speed of the item and m denotes the body's mass. Newtonian mechanics states that an object's mass and velocity together determine its momentum, more specifically its linear momentum or translational momentum. It is a vector quantity since it has both a magnitude and a direction. A essential quality of a body is its mass. It was believed to be related to the amount of matter in a physical body.

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The direction of the velocity of the other part in the instant after the explosion is:  up and to the left.

When a particle is hurled obliquely near the surface of the earth, it travels along a curved path while accelerating continuously in the direction of the planet's center. Such a particle's motion is known as projectile motion.

As one part falls straight down with no horizontal motion, the total component of horizontal momentum will be in the another part and due to law of conservation of momentum, a upward momentum will be introduced after the collision. the direction of the velocity of it will be  up and to the left.

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The height of the object when it first started falling is 0 meters.

The equation used to calculate the height of an object in freefall is h = (1/2)gt2, where h is the height, g is the acceleration due to gravity (9.8 m/s2) and t is the time in seconds.

What is velocity?

Velocity is a vector quantity that measures the rate and direction of an object's motion. It is the rate at which an object's position changes over time, measured in meters per second (m/s).

Since the starting velocity is 0, the height when it first started falling is 0.

h = (1/2)gt2

h = (1/2)(-9.8 m/s2)(5s)2

h = 0 m

Therefore, The height of the object when it first started falling is 0 meters.

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The wave's speed is 85 m/s if its wavelength is 5 meters and its frequency is 17 Hz.

A waveform signal that is propagated in space or down a wire does have a wavelength, that is the separation between two equal places (adjacent crests) in the consecutive cycles. This length is typically specified in wireless systems in metres (m), centimetres (cm), or millimeters (mm) (mm).

given data,

frequency of the wave v = 17 Hz

Wavelength of the wave = 5m

speed of the wave s = ?

Calculating the speed of wave

We know that,

Speed= frequency × wavelength

Thus,

s= 17 × 5 m/s

s= 85 m/s

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The orbital speed of a satellite that is orbiting the earth at an altitude where the gravitational acceleration is 8.70 m/s^2 is 7.68×10^3m/s.

Given the centripetal acceleration of satellite (a) = 8.70 m/s^2

The mass of earth (M) =  5.98×10^24 kg

Let the radius of satellites orbit = R

The satellites orbital speed = v

We know that the satellite's centripetal acceleration (a = v²/R ) is equal to its gravitational acceleration.

v²/R = GM/R² here G is the gravitational constant 6.674×10-11 m3⋅kg-1⋅s-2

v² = GM/R

From centripetal acceleration we have R = v²/a. Then,

v² = GMa/v²

v = (GMa)^1/4

v = (6.674×10^-11 x 5.98×10^24 x 8.70)^1/4 = 7.68×10^3m/s

Hence the orbital speed of a satellite is 7.68×10^3m/s

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The distance is inversely proportional to the magnitude of the gravitational force. As the distance increases, the magnitude of force decreases.

The gravitational force on an object can be defined as the force of attraction or the attractive force which attracts all the physical forms which are having some mass. Gravitational force is by far the weakest recognized natural force of all.

Since, the gravitational force is inversely proportional to the square of the separation between the force and the object distance between the two interacting objects, there is more separation distance will result in weaker gravitational forces of attraction. So, as the two objects are separated from each other, the force of gravitation attraction between them also decreases.

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1) The maximum speed is 4.98 m/s

2) The maximum speed is 3.984 m/s.

3) The maximum height is 2.81 m.

Speed is the rate at which a object travels along a path over time, whereas velocity is the speed & direction of an object's movement. In other words, speed is a scalar quantity, but velocity is a vector.

Part (a) → [tex]v^{2} =vi^{2} -2gh[/tex]

=8^2-2×9.8×2.00

=64-39.2

=24.8

v=4.98 m/s

Therefore, Speed is 4.98m/s upwards

Part (b) → From the conversion of momentum

60×4.98=(60+15)V

v= (60×4.98)/75

=3.984m/s

Therefore, speed is 3.984m/s upwards

Part (d) → Hmax=2.00+((3.984)^2)/2g

Or Hmax =2.00+15.8723/19.6

=2.00+0.81 m

=2.81 m

Therefore, the height Hmax is 2.81 m.

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The molecular electron configurations describe an excited state are listed below.

What is electronic configuration?

Electronic configuration, also known as electronic structure or electron configuration, refers to the way that electrons are arranged in orbitals around an atomic nucleus.

What is excited state?

An excited state of an electron is one in which it momentarily possesses an energy state higher than its ground state. If an electron receives extra energy, for as via absorbing a photon, or packet of light, or from colliding with an atom or particle nearby, it might become excited.

The increasing energy of the molecular orbits (electrons < 16) according to the molecular orbital theory is:

σ1s < σ*1s < σ2s < σ*2s < σ2px < π2py = π2pz < π*2py = π*2pz <σ*2px

(a) Given:

(σ1s)2(σ*1s)2(σ2s )2(σ*2s)2(π2p)4(π*2p)1

This is an excited state because the electronic configuration given is not filled in increasing energy orbitals which should be the way of filling in ground state as there is no electron in σ2px but upper orbitals has electrons which means that it is an excited state.

(b) Given:

(σ1s)2(σ*1s)2(σ2s )1(σ*2s)1

This is an excited state because the electronic configuration given is not filled in increasing energy orbitals which should be the way of filling in ground state as there is only one electron in σ2s and it can accommodate 1 more electron but upper orbitals has electrons which means that it is an excited state.

(c) Given:

(σ1s)2(σ*1s)2(σ2s )2(σ*2s)2(σ2p)2(π2p)4

This is a ground state because the electronic configuration given is filled in increasing energy orbitals which should be the way of filling in ground state.

(d) Given:

(σ1s)2(σ*1s)2(σ*2s)1

This is an excited state because the electronic configuration given is not filled in increasing energy orbitals which should be the way of filling in ground state as there is no electron in σ2s but upper orbitals has electrons which means that it is an excited state.

Therefore,  molecular electron configurations describe an excited state are listed above.

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A ring with radius r and a uniformly distributed total charge Q lies in the xy plane, centered at the originPart a What is the potential V(z)

The potential V(z) on the z axis due to the ring can be expressed as: V(z) = ke*Q/(2*r) * ln(z/r + (z/r)^2 + 1).

Potential is a term used to describe the ability of something or someone to achieve a desired outcome or result. It is the capacity to do or become something in the future. Potential is often used to refer to a latent or undeveloped ability, talent, or capability.

Part A:
The potential V(z) on the z axis due to the ring can be expressed as:
V(z) = ke*Q/(2*r) * ln(z/r + (z/r)^2 + 1)
where ke = 1/4 phi e0, Q is the total charge, and r is the radius of the ring.

Part B:
The magnitude of the electric field E on the z axis for z > 0 can be expressed as:
E = ke*Q/(2*r^2) * (z/r + 1/z)
where ke = 1/4 phi e0, Q is the total charge, and r is the radius of the ring. This expression follows from the definition of the electric field, E = -grad(V). Taking the gradient of V(z) in Part A yields the expression for E.

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The runaway star is farther away from Earth than the sun. the sun is closer to Earth than the runaway star if it seems brighter than the star and the star is 90 times bigger than the sun.

An exceptionally high proper motion, known as a runaway star, is a star that was supposed to have been ejected from a nearby binary system when its companion star exploded supernova. Beyond the Milky Way, these runaway stars seem to be widespread, especially in massive galaxy clusters.

Astronomers have found hundreds of billions of runaway stars in the Virgo cluster. The Milky Way's sun and all of its stars are revolving around its nucleus. Although there are some little local motions within this broader stream of stars, it is largely orderly. Compared to the sun, the runaway star is closer to Earth.

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The total change in energy of the cube of water is -19228.8 J.

The ability to generate a force that causes an item to move is what is meant by the definition of energy as the "power to accomplish work." Although the definition is unclear, the meaning is clear: energy is simply the force that propels things. Potential and kinetic energy are the two kinds of energy.

the solution is -

velocity is also given but if we look for final states so both times it is at rest.

Since it is rest at both positions so the change in energy = m×c×dt + m×g×dz.

Here m = 2 kg.

C = 4185.5 j/kg k.

dt = 22 - 25 = -3

dz = 300 - 0 = 300 m

Total change in energy = -25114.8 + 5886 = -19228.8 J.

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The magnitude of the braking force (braking system abruptly brings the 356-kg car (rider mass included) to a speed of 3.6 m/s over a distance of 6.22 meters.) applied to cray-zee's car = 18,231 N

The force that slows the car when the driver depresses the brake pedal is known as the braking force.

It is impossible to directly quantify this well-known force since it operates on tires that are in touch with the ground, without which nothing would be possible.

It is still feasible to determine its severity, though. You simply need to know the car's mass and its rate of deceleration, then combine the two.

W = [tex]\frac{1}{2}[/tex] mv₁² -  [tex]\frac{1}{2}[/tex] mv₀²

= [tex]\frac{1}{2}[/tex] (356) (25.5)² - [tex]\frac{1}{2}[/tex] (356) (3.6)²

= 115,744 - 2,306

= 113,438 J

Hence, the magnitude of the braking force:

W = F x d

113,438 J = F x 6.22

F = 18,231 N

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Answer:

95

Explanation:

because x × au= 69 +26

which means planet x is destroyed

The bounce height on the 4th bounce is 1.5 m.

The ball will lose some energy with each bounce, so the bounce height will decrease each time.

Assuming the ball starts from rest and the collisions are perfectly elastic, we can use the conservation of energy to find the bounce height on each bounce.

On the first bounce, the ball will reach a height of:

h1 = mgh/2

where m is the mass of the ball, g is the acceleration due to gravity, and h is the height of the first bounce.

On the second bounce, the ball will reach a height of:

h2 = (mgh/2) / 2

On the third bounce, the ball will reach a height of:

h3 = (mgh/2) / 4

On the fourth bounce, the ball will reach a height of:

h4 = (mgh/2) / 8

So the fourth bounce height will be 1.5 m.

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The average velocity of the driver is 80.7 fps. The result is obtained by dividing the displacement by the change in time.

Average velocity is the displacement or change in position of an object (∆x) divided by the change in time (∆t). It can be expressed as

V avg = Δx/Δt

Where

The formula of position can be counted as

x = vt

A vehicle travels at

Find the average velocity in feet per second!

We find the position x₁ and x₂.

x₁ = v₁t₁ = 50(3) = 150 mile

x₂ = v₂t₂ = 25(0.5) = 12.5 mile

The average velocity would be

V avg = Δx/Δt

V avg = (x₁ - x₂)/(t₁ - t₂)

V avg = (150 - 12.5)/(3 - 0.5)

V avg = 137.5/2.5

V avg = 55 mph

V avg = 55 × 5280/3600 fps

V avg = 80.7 fps

Hence, the average velocity of the vehicle is 80.7 feet per second.

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The net charge contained by the cube lies in a electrical field vector region is   1.7 x 10^-19 C.

The electric flux over any closed surface is directly proportionate to the net electric charge q enclosed by the surface, according to Gauss's law of electricity, that also says as = q/0, where 0 is the electric permittivity of free space, which has a value of 8.854 10-12 square coulombs per newton per square metre.

Electric field vector:

E =−3.00i−4.00y^2j+3.00kN/C

Faces +j direction: A = 4m2

E => (-4)x (4^2) x 4 => -256 N.m/c^2

Faces -j direction: A= 4m2

E => (-4) (2^2) x 4 => 64 N.m/c^2

Net flux  => Ф=>  -256 N.m/c^2 + 64 N.m/c^2 = -192 N.m/c^2.

gauss's law

εox Ф => 8.85 x 10^-12 c^2/nm^2 x 192 N.m/c^2

         => 1.7 x 10^-19 C

A vector quantity that exists at every point in space is the electric field E with the vector on top. The force that would be exerted on a unit positive test charge if it were placed at a certain location is indicated by the electric field there.

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The electrical field on the second surface is larger when two identically charged spheres are encircled by identically sized gaussian surfaces. as a result of the second surface's larger area.

The electric field is described as a vector field, where each point in space is associated with the electrostatic (Coulomb) force per unit of charge. This description is based on an infinitesimal positive test charge at rest. The volt per metre (V/m) is the derived SI unit for the electric field, the newton per coulomb (N/C). In the end, the  electrical field that both charges create around them is what drives the force that the two charges apply to one another.

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If the hill's circumference is 30 meters. The centripetal force equals the gravitational force at 9.39 m/s.

Any force that changes the direction of motion towards to center of either a circular motion is known as a centripetal force. The part of the force that produces the rotational motion is the part that is orthogonal to the velocity.

Force acting is used to maintain an object moving in a circle due to gravity. Since gravity generally behaves opposed to motion, it has no effect on an item in a circular path.

Radius, r = 30 m

speed = v.

(Fr = (mv^2)/r

μk mg& = (mv^2)/r

v =√(μ_k gr)

v = √(0.30×9.80×30)

v = 9.39 m/s

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The clock will run fast when the elevator is accelerating downward.

A pendulum clock is a timepiece that keeps time by swinging a weight called a pendulum. Because a pendulum is a harmonic oscillator, it has the advantage of swinging back and forth in a precise time interval that is based on its length and resists swinging at other rates.

The forces experienced in an elevator are applied in this way to Newton's second law. You feel heavy when moving upwards and lighter when moving downwardly when you accelerate. You would feel weightless if the elevator cable snapped since you and the elevator would both be descending at the same speed.

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a) The potential difference between the plates after a sheet of Teflon is inserted between them is 20.0V

b) The potential difference between the plates after a sheet of Teflon is inserted between them is  9.52Volts.

The amount of potential energy that exists between two points in a circuit is what we can refer to as the voltage. While the other points have potential, one has a higher potential. The term "voltage" or "potential difference" refers to the charge difference between higher and lower potentials.

Part a) Capacitor plates have a certain voltage when they are fully charged. ΔV = 20.0V

Considering that the battery is currently disconnected, the potential difference between the plates is given as

ΔV = Q/C

As long as the capacitance remains constant and the charge is conserved on the plates, the potential difference will remain unchanged.

b) Teflon sheet is now placed between the capacitor's plates.

Consequently, the capacitor's capacitance will alter by a factor of the dielectric constant.

Therefore, we will

C' = KC

Kteflon = 2.1

Consequently, the new capacitance given here is

C' = 2.1C

ΔV = Q/C

ΔV = 20/2.1

ΔV = 9.52Volts.

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The car can travel 28 miles on one gallon of gas. Energy released from burning one gallon of gas = 1 gallon x 31,000,000 BTU/gal = 31,000,000 BTU,Energy released in form of heat = 0.9 x 31,000,000 BTU = 27,900,000 BTU,Work required to make the car go one mile = 0.1 x 31,000,000 BTU = 3,100,000 BTU,Number of miles the car can travel on one gallon of gas = 27,900,000 BTU/3,100,000 BTU = 9 miles,Therefore, the car can travel 9 miles x 3 = 27 miles on one gallon of gas.

What is the miles ?

Miles are a unit of measurement used to measure distances. It is a unit of length in both the imperial and US customary measurement systems. One mile is equal to 1.609 kilometers, 1,760 yards, or 5,280 feet. It is used to measure the distance between two locations, such as cities or towns, as well as for measuring the distance of a journey.

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The correct answer is c. 758,000,000. The 7.58e8 is the scientific notation, also known as exponential notation, which is a way of expressing very large or very small numbers

The letter "e" in a decimal number, indicates scientific notation. The "e" stands for the exponent of 10, and the number following it represents the power to which the number 10 is raised.

7.58e8 in scientific notation represents 7.58 x 10^8  .In this case, 8 is the exponent, meaning that the number 7.58 is multiplied by 10 to the power of 8, or 10^8, resulting in 758,000,000.

Using exponential notation, we may delete zeros and represent a number in a compact form by taking use of the fact that multiplication or dividing by multiples of 10 moves the decimal point of a number to the left or right.

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( 1) The speed of each seat is 6.73 m/s

( 2 ) The tension in the chain is 533.37 N.

The speed of each seat is determined by treating the system as a simple harmonic motion.

Apply the law of conservation of mechanical energy as shown below.

kinetic energy of each seat at the bottom = potential energy of each seat at the top

K.E = P.E

¹/₂mv² = mgh

v² = 2gh

v = √ ( 2gh )

where;

The vertical displacement of the seats is calculated from the length of the chain as follows;

h = L cos (24.4)

The speed of each seat is calculated as follows;

v = √ ( 2g L cos (24.4) )

v =  √ ( 2 x 9.8 x 2.54cos (24.4) )

v = 6.73 m/s

The tension in the chain is calculated by applying the formula for centripetal force as follows;

T = mv²/r

where;

T = ( 73.6 x 6.73² ) / ( 6.25 )

T = 533.37 N

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Time to impact the ground is 0.45 seconds. It will land 0.56 meters away from the table. The bullet appears to be traveling straight forward without changing directions, according to the horizontal speed.

By measuring the ball's diameter d and dividing it by the time t it takes for it to cross the photogate, one can also calculate the ball's starting horizontal velocity. Therefore, Vo = d/t.

Typically, horizontal velocity is defined as horizontal displacement divided by time, expressed in units like meters per second or miles per hour. Simply put, displacement is the distance an object has traveled since leaving a starting location.

y=Vyi t + 1/2 gt²

  1 = o+ 1/2 ×9.8×t²

  1=4.9 ×t²

t²= 1/4.9= 0.204081633

==> t = 0.45 sec

x= Vx× t

Here

Vx = 1.25 m/sec

t= 0.45 sec

x=  1.25 × 0.45 = 0.56 m

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Answer:

Explanation:

To determine if the shooter could have come from the penthouse, we need to calculate the angle of elevation from the penthouse to the tree. We can use trigonometry to do this.

We know that the height of the penthouse is 85 feet, and the distance from the penthouse to the tree is 60 feet. We can use the tangent function to calculate the angle of elevation:

tan(angle of elevation) = opposite / adjacent

opposite = height of penthouse = 85 feet

adjacent = distance from penthouse to tree = 60 feet

tan(angle of elevation) = 85 / 60

angle of elevation = arctan(85/60)

Now we have the angle of elevation, we can determine if the shooter could have come from the penthouse. If the angle of elevation is greater than 90 degrees, the shooter would have had to shoot at an impossible angle, and the shots could not have come from the penthouse.

In this case, the angle of elevation is approximately 62.9 degrees, which is less than 90 degrees. So the shots could have come from the penthouse.

It's important to note that this is a simplified calculation based on the data provided, and it is not a conclusive evidence. A detailed investigation is required to gather all the facts and evidence before determining the shooter's location.

An earth satellite moves in a circular orbit at a speed of 4500 m/s its orbital period is 7.665h

Generally, Newton's gravitational law states that the force of attraction between two objects can be formulated as follows:

[tex]F=G \frac{m_1 m_2}{R^2}[/tex]

Let us now tackle the problem

Given:

speed of satellite = v = 4500 m/s.

mass of earth = M = 6 × 10²⁴ kg

[tex]\begin{aligned}& \Sigma F=m a \\& G \frac{M m}{R^2}=m \frac{v^2}{R} \\& G \frac{M}{R^2}=\frac{v^2}{R} \\& G \frac{M}{R}=v^2 \\& R=G \frac{M}{v^2} \\& 2 \pi R=2 \pi G \frac{M}{v^2} \\& \frac{2 \pi R}{v}=\left(2 \pi G \frac{M}{v^2}\right) \div v \\& T=2 \pi G \frac{M}{v^3}\end{aligned}[/tex]

[tex]& T=2 \pi \times 6.67 \times 10^{-11} \times \frac{6 \times 10^{24}}{5000^3} \\[/tex]

T =27594.3 s

T =7.665h

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Answer: if 500 kHz was to be used in sound of a human tissue. Yes it would be taken into 1540 m/s. BUT, if you were to add 500 plus 1540 then you can get your answer

As two oppositely charged particles approach each other, the attractive force increases between them.

Only attraction is possible with gravitational force. It can't be disgusting. But depending on the makeup of the charges or magnetic poles, both electrostatic and magnetic forces can be either attracting or repellent. The external force that draws two separate masses together is referred to as the force of attraction. Gravitation, magnetism, & electric forces are a few examples.

A force that attracts the protons or positive parts of one molecule to the electrons or negative parts of another molecule is known as an intermolecular force. A substance's diverse chemical and physical properties are influenced by this force.

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