Two tuning forks with frequencies of 256 Hz and 512 Hz are struck. Which of the sounds will move faster through the air?

The initial kinetic energy of marble M based on the information is D. 7.2 × [tex]10^{3}[/tex]gcm/s²

Substituting the masses and velocities from the problem statement, we get:

K₂ = 1/2 * 8.2 g * (23.9 cm/s)²

K₂ = 8.3 × [tex]10^{3}[/tex] g/cm/s²

p₂ = 4.1 g * ((m₁/m₂) * v3 + v₃)

p₂ = 4.1 g * (1 + m₁/m₂) * v₃

Since p1 = p2, we can equate the expressions for p₁ and p₂ and solve for v₃:

m₁ * v1 = 4.1 g * (1 + m₁/m₂) * v₃

v₃ = (m1 * v1) / (4.1 g * (1 + m₁/m₂))

Substituting the masses and velocities from the problem statement, we get:

v3 = (4.1 g * 23.9 cm/s) / (4.1 g * 2)

v3 = 11.95 cm/s

K₁ = 1/2 * 4.1 g * (23.9 cm/s)²

K₁ = 7.2 ×  [tex]10^{3}[/tex]g/cm/s²

Therefore, the initial kinetic energy of marble M is 7.2 × 10³g cm/s². Thus, the correct option is 7.2 × [tex]10^{3}[/tex] g cm/s²

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The speed of the running shaft driving the machine, given that the main shaft to drive the machine has a pulley of diameter 140 mm is 111.4 rev/min

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

The speed of the running shaft can be obtain as shown below:

S₁D₁ = S₂D₂

183 × 140 = S₂ × 230

183 × 140 = S₂ × 230

25620 = S₂ × 230

Divide both sides by 230

S₂ = 25620 / 230

S₂ = 111.4 rev/min

Thus, we can conclude that the speed of the running shaft driving the machine is 111.4 rev/min

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The wavelength of the sound wave with a frequency of 415.3 Hz is approximately 3.565 m.

The speed of sound in water is approximately 1482 m/s. Use the formula v = f × λ, where v = velocity (speed of sound), f = frequency, and λ = wavelength.

Given:

Frequency of the first sound wave (f₁) = 257.2 Hz

Wavelength of the first sound wave (λ₁) = 3.25 m

Velocity of sound in water (v) = 1482 m/s

Rearrange the formula to solve for λ₂ (wavelength of the second sound wave):

v = f × λ

λ = v / f

Substituting the values:

λ₂ = v / f₂

= 1482 m/s / 415.3 Hz

Calculating:

λ₂ ≈ 3.565 m

Therefore, the wavelength of the sound wave with a frequency of 415.3 Hz is approximately 3.565 m.

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Answer:

6,063.63637 kg m/s²

Explanation:

First you have to find the acceleration

a = velocity changes / time changes

(a stands for acceleration)

so we have 52-23 = 29 m/s

we know acceleration took 11 seconds so the time changes = 11 seconds

a= 29 / 11 = 2.63636364 m / s²

and we know

F = m × a

( F stands for force and m stands for mass)

so we have 2300kg × 2.63636364 m/s = 6,063.63637 kg m/s² or 6,063.63637 Newton

hope you understand ♥️

part a) If Q increases by 5 times its original value, the electrostatic force (F) will increase5 times as well.

part b) If r is halved (reduced by 2), the force will become four times stronger (since 2² = 4).

part c) If Q1 is positive and Q2 is negative, the charges will attract each other.

part d) If the force that Q1 exerts on Q2 is 5 times larger than the force that Q2 exerts on Q1 is same.

The electrostatic force is described as the force of attraction or repulsion between two charged particles.

With regards to Coulomb's Law, we have that the electrostatic force between two charges separated by a distance is :

Force = k * (Q1 * Q2) / r²

Where:

F_ =  electrostatic force

k = electrostatic constant

Q1 and Q2 =  magnitudes of the charges

r = distance

for case a:

If one of the charges, Q1 or Q2, increases by 5 times then the electrostatic force  will also increase by 5 times.

case b)

If the distance between the charges, r, is halved, the electrostatic force   will become four times stronger because (1/r²).

for case c.

if Q1 is positive and Q2 is negative, the charges will attract each other because of magnetic laws.

for case d.)

If the force that Q1 exerts on Q2 is 5 times larger than the force that Q2 exerts on Q1 is same as there is a resulting stronger gravitational or electromagnetic force.

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Answer:

d

Explanation:

reversing the current, reverses the poles of the electromagnet....this keeps the rotor spinning in the stationary mag field

Answer:

As can be seen from the above animation, the package follows a parabolic path and remains directly below the plane at all times.

Explanation:

hope it helps

This observation demonstrates the principle of electrostatics, which is the study of electric charges at rest. It highlights the fact that charged objects can interact with each other, and that opposite charges attract while like charges repel.

When a plastic rod is rubbed with cotton, electrons from the rod are transferred to the cotton, leaving the rod with an excess of positive charges, and the cotton with an excess of negative charges. This results in the rod acquiring a negative charge.

When the same cotton is brought near the cap of a positively charged electroscope, the leaves of the electroscope will diverge. This happens because the positively charged cap attracts the negative charges on the cotton, causing the electrons to move towards the cap. As a result, the leaves of the electroscope acquire a negative charge, and they repel each other due to their like charges.

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a. The rock's gravitational potential energy, just before touching the ground is 0 J.

b. The rock's kinetic energy, just before touching the ground is 24,500 J.

The rock's gravitational potential energy, just before touching the ground is calculated as follows;

Just before touching the ground, the rock will have maximum velocity, and the kinetic energy of rock will be maximum while the gravitational potential energy will be minimum or zero.

P.E (top height) = K.E (minimum or zero height)

P.E = mgh

where;

P.E = 10 x 9.8 x 250

P.E = 24,500 J

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The amount of Sertaline will you give to the patient is 30 mg that is half of the given 60mg tablet.

To give the patient a 30mg measurement of Sertraline when the accessible dose is 60mg tablets, one-half of the tablet ought to be given. The tablet ought to be part in half employing a pill cutter and after that one of the parts oughts to be managed to the persistent. This will give the persistent the precise 30mg measurements that have been requested. 

Sertraline is an antidepressant pharmaceutical utilized to treat depression, obsessive-compulsive disorder, freeze clutter, post-traumatic stretch clutter, social uneasiness clutter, and premenstrual dysphoric disorder. It belongs in the course of drugs known as selective serotonin reuptake inhibitors (SSRIs) and works by expanding the sum of serotonin, a natural substance within the brain, which makes a difference to preserve mental adjustment. Sertraline is as a rule taken once day by day, with or without nourishment, and ought to be taken as coordinated by a healthcare supplier. 

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The radius of curvature of the mirror is 761.9 cm or 7.619 meters.

Assuming the mirror is a spherical mirror, use the mirror equation:

1/f = 1/di + 1/do

where f = focal length, di = image distance (distance from the mirror to the image), and do = object distance (distance from the mirror to the object).

Since the mirror magnifies the face by a factor of 1.32, the image distance is 1.32 times the object distance:

di = 1.32 × do

The object distance is given as 19.5 cm, so substitute to get:

di = 1.32 × 19.5 cm = 25.74 cm

The mirror magnifies the face by a factor of 1.32, so the magnification is:

m = -di/do = 1.32

Since the mirror is concave (it magnifies the image), the magnification is negative. Substituting di and do:

-1.32 = -25.74 cm/do

Solving for do:

do = 19.5 cm × 25.74 cm / 1.32 / 25.74 cm = 380.95 cm

The object distance is the distance from the mirror to the object, which is half the radius of curvature (R) of the mirror:

do = R/2

So we can solve for R:

R = 2 × do = 2 × 380.95 cm = 761.9 cm

Therefore, the radius of curvature of the mirror is 761.9 cm or 7.619 meters.

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The coefficient of static friction between a 20 kg weight and a football turf is .85. Force of approximately 166.6 Newtons (N) is needed to make the weight start moving.

The force needed to make the 20 kg weight start moving can be determined using the coefficient of static friction. The equation for static friction is:

Frictional force = coefficient of static friction * normal force

The normal force is the force exerted by the surface perpendicular to the weight. In this case, it is equal to the weight of the object, which can be calculated as the mass (20 kg) multiplied by the acceleration due to gravity (9.8 m/s^2):

Normal force = mass * gravity = 20 kg * 9.8 m/s^2 = 196 N

Now, we can calculate the force needed to make the weight start moving:

Frictional force = 0.85 * 196 N ≈ 166.6 N

Therefore, a force of approximately 166.6 Newtons (N) is needed to overcome the static friction and make the 20 kg weight start moving on the football turf. This force must be applied in the opposite direction to the frictional force to initiate motion.

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The work done to lift a man and a 44-pound box up 10 meters of stairs is 11,772 J, and the power required to do this in 1 minute is 196.2 W.

a. First, we need to convert the units of the weight of the box to kilograms: 44 pounds = 20 kg. The total mass that the man needs to lift up the stairs is therefore 100 kg + 20 kg = 120 kg.

The force required to lift this mass against gravity is given by F = mg, where g is the acceleration due to gravity (9.81 m/s^2). So, F = 120 kg x 9.81 m/s^2 = 1177.2 N. The work done is then given by W = Fd, where d is the distance moved (10 meters).

Thus, W = 1177.2 N x 10 m = 11,772 J.

b. To find the power required, we need to divide the work done by the time taken. As the time is given in minutes, we need to convert it to seconds: 1 minute = 60 seconds. Therefore, the power required is P = W/t = 11,772 J / 60 s = 196.2 W.

Therefore, the work done to lift the man and the box up a flight of stairs 10 meters high is 11,772 J, and the power required to do this in only 1 minute is 196.2 W.

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If two mass dampers on a Lagos tower consist of a 373mg concrete block.that complete one oscillation in.6.80 secs. the oscillation amplitude in a high wind is 110cm. Then the spring constant of the mass-spring system is  6.90 N/m.

The spring constant is a measure of the stiffness of a spring, which describes how much force is required to stretch or compress the spring by a certain amount. It is typically measured in units of newtons per meter (N/m).

We can use the formula for the period of oscillation of a mass-spring system:

T = 2π√(m/k)

where T is the period of oscillation, m is the mass of the block, and k is the spring constant.

We can rearrange this formula to solve for k:

k = (4π²m) / T²

where we substitute the values given in the problem.

m = 373mg = 0.373g = 0.000373kg (convert milligrams to kilograms)

T = 6.80 s

π ≈ 3.14159

Plugging in these values, we get:

k = (4π² × 0.000373) / (6.80)²

≈ 6.90 N/m

Therefore, the spring constant of the mass-spring system is approximately 6.90 N/m.

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if the values of mass (m) and radius (R) are provided, the moment of inertia of the body about an axis through the center of disk A can be calculated as (3/2) * m * R^2, and the kinetic energy of the rotating body would be 162 * m * R^2 Joules.

To calculate the moment of inertia of the body about an axis through the center of disk A, we need to consider the moment of inertia contributions from each individual disk and add them up.

Let's denote the moment of inertia of each disk as I_A, I_B, and I_C, respectively. The moment of inertia of a disk rotating about its center can be calculated using the formula:

I = (1/2) * m * r^2

Where m is the mass of the disk and r is its radius.

Since the struts have negligible weight, we can assume that each disk has the same mass.

Let's assume the mass of each disk is m and the radius of each disk is R.

The moment of inertia of disk A (I_A) is given by:

I_A = (1/2) * m * R^2

The moment of inertia of disk B (I_B) and disk C (I_C) will be the same since they have the same mass and radius:

I_B = I_C = (1/2) * m * R^2

The total moment of inertia of the body about the axis through the center of disk A (I_total) is the sum of the individual moment of inertias:

I_total = I_A + I_B + I_C

= (1/2) * m * R^2 + (1/2) * m * R^2 + (1/2) * m * R^2

= (3/2) * m * R^2

To calculate the kinetic energy of the rotating body, we can use the formula:

Kinetic Energy = (1/2) * I_total * ω^2

Substituting the given values:

Kinetic Energy = (1/2) * ((3/2) * m * R^2) * (6.0 rad/s)^2

Simplifying further, if the values of m and R are given, we can calculate the moment of inertia and kinetic energy.

Assuming that the values of mass (m) and radius (R) are given, we can calculate the moment of inertia (I_total) and kinetic energy.

For the given values of ω = 6.0 rad/s and the previously calculated I_total:

I_total = (3/2) * m * R^2

Kinetic Energy = (1/2) * I_total * ω^2

= (1/2) * [(3/2) * m * R^2] * (6.0 rad/s)^2

= (9/2) * m * R^2 * (36.0 rad^2/s^2)

= 162 * m * R^2 Joules

Therefore, if the values of mass (m) and radius (R) are provided, the moment of inertia of the body about an axis through the center of disk A can be calculated as (3/2) * m * R^2, and the kinetic energy of the rotating body would be 162 * m * R^2 Joules.

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(a)Since the integral does not converge to 1, we can conclude that the wave function is not normalized, (b) The normalization constant for the given wave function is A = √10.

In quantum mechanics, the wave function is a mathematical description of the state of a quantum system. It encodes the probability amplitude for a particle or collection of particles to have certain properties, such as position or momentum.

a- To check if the wave function is normalized, we need to calculate the integral of the absolute value squared of the wave function over all space and check if it equals 1. Mathematically, this can be written as:

∫|Ψ(x,t)|^2dx = ∫Ψ*(x,t)Ψ(x,t)dx

where Ψ*(x,t) is the complex conjugate of the wave function.

Substituting the given wave function, we get:

∫|Ψ(x,t)|^2dx = ∫e^(−5x) e^(iwt) e^(5x) e^(−iwt) dx

= ∫1dx

= x

Since the integral does not converge to 1, we can conclude that the wave function is not normalized.

b- To normalize the wave function, we need to find the normalization constant A such that the integral of the absolute value squared of the normalized wave function over all space equals 1. Mathematically, this can be written as:

∫|AΨ(x,t)|^2dx = 1

where Ψ(x,t) is the given wave function.

Substituting the given wave function and the definition of the normalization constant A, we get:

∫|AΨ(x,t)|^2dx = ∫|A|^2 e^(−10x)dx = |A|^2 ∫e^(−10x)dx = |A|^2 * 1/10

For the integral to equal 1, we need |A|^2 * 1/10 = 1, which gives us:

|A|^2 = 10

Taking the positive square root, we get:

|A| = √10

So, the normalization constant for the given wave function is A = √10.

Therefore, The wave function is not normalised since the integral does not converge to 1, and the normalisation constant for the specified wave function is A = √10.

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The correct matches are Production line - Televisions, Continuous flow - Flu vaccines, Custom - Kitchen cabinets, Fixed - Submarines.

1. Production line: A production line is a manufacturing process that involves a series of workstations where individual operations are performed to create a final product. Each workstation is responsible for a specific task, and the product moves from one station to another until it is completed. The production line is used for mass production of standardized products, and it is characterized by a high level of automation and a high production rate.

2. Continuous flow: Continuous flow is a manufacturing process where raw materials or components are continuously fed into the production process, and the finished product is continuously outputted without interruption. This process is used for products that are made in large quantities and have a high demand. The continuous flow process is characterized by a high degree of automation and a low level of labor involvement.

3. Custom: Custom manufacturing is a production process where products are made to meet the specific needs and requirements of individual customers. This process involves the customization of products based on the customer's specifications, and it is characterized by a high level of flexibility and customization. The custom manufacturing process is often used for products that require a high degree of customization, such as furniture or clothing.

4. Fixed: Fixed manufacturing is a production process where products are made using a fixed set of specifications and processes. The fixed manufacturing process is characterized by a low level of customization and a high degree of repeatability. This process is often used for products that require a standardized manufacturing process, such as electronic components or automotive parts.

Therefore, The correct Answers are Production line - Televisions, Continuous flow - Flu vaccines, Custom - Kitchen cabinets, Fixed - Submarines.

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The derivation of Green's function for the Schrödinger wave equation involves using the concept of superposition of solutions to find a particular solution for a given initial condition.

Green's function is a  fine tool that's used to  break  discriminational equations, including the Schrödinger equation. The idea behind Green's function is to find a  result to the  discriminational equation that satisfies a given  original condition.   In the  environment of the Schrödinger equation, Green's function represents the probability  breadth of chancing  a  flyspeck at a particular position at a particular time, given that it started from a known  original position and time.

The Green's function is  attained by  working the Schrödinger equation for a delta function source at the  original position.   To  decide Green's function, one can consider the Schrödinger equation with a delta function source at some  original position. This leads to the  result for the  surge function as a sum of two terms- a free  flyspeck term and a term due to the delta function source.

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a. the resistance of the parallel pair of resistors is  4.71Ω.

b.  the total resistance of the circuit is 7.71Ω.

c. the total current flow of the circuit is  1.55A.

d. The voltage drop across each resistor is 12V.

e. he current flowing through the 2Ω resistor is 1.55A.

f. the current flowing through the 6Ω resistor is 1.55A.

Equivalent resistance :

1/Req = 1/R1 + 1/R2

1/Req = 1/22Ω + 1/6Ω

1/Req = (6 + 22)/(22 * 6)

1/Req = 28/132

Equivalent resistance = 132/28

Equivalent resistance = 4.71Ω

b) The total resistance of the circuit:

total  resistance   = equivalent resistance  + R3

total  resistance = 4.71Ω + 3Ω

total resistance  = 7.71Ω

c) The total current flow of the circuit:

We use Ohm's law

I = V / R

I = 12V / 7.71Ω

I =  1.55A

d) The voltage drop across each resistor is the same as the total voltage

e) The current flowing through the 2Ω resistor is same as all resistors.

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The statement "Many different scientists have added data from their own experiments to build the theory" is correct of the question.

Scientific theory involves thoroughly examining a specific event or collection of events and developing an intricately detailed conclusion backed up by significant data.

As such, this ultimate level represents our unsurpassed comprehension concerning how nature operates - offering us unparalleled clarity that exceeds any other form of understanding.

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Answer:

Approximately [tex]1.75\; {\rm s}[/tex] (assuming that [tex]g = 9.81\; {\rm m\cdot s^{-2}}[/tex] and that air resistance is negligible.)

Explanation:

Find the velocity of the ball right before landing using the following SUVAT equation:

[tex]\displaystyle v^{2} - u^{2} = 2\, a\, x[/tex],

Where:

Rearrange this equation to find [tex]v[/tex]:

[tex]\begin{aligned}v &= \sqrt{u^{2} + 2\, a\, x} \\ &= \sqrt{(8.45)^{2} + 2\, (9.81)\, (29.8)}\; {\rm m\cdot s^{-1}} \\ &\approx 25.61\; {\rm m\cdot s^{-1}}\end{aligned}[/tex].

Divide the change in velocity by acceleration to find the time elapsed:

[tex]\begin{aligned}t &= \frac{v - u}{a} \\ &\approx \frac{25.61 - 8.45}{9.81} \; {\rm s}\\ &\approx 1.75\; {\rm s}\end{aligned}[/tex].

Answer:

Yeah

Explanation:

Thermoproteota is a prokaryote.

Prokaryotes are unicellular

Answer:

Friction plays a crucial role in the operation of a bicycle, both in terms of its performance and maintenance. Here are some ways that friction affects moving parts on a bicycle and ways to reduce or increase friction:

Friction in the chain: The chain is one of the most critical components of a bicycle, and friction can cause significant wear and tear on it. Lubricating the chain regularly can help reduce friction and prolong its lifespan.

Friction in the brakes: The brake pads are designed to increase friction on the wheel rims to slow the bike down or bring it to a stop. Over time, the brake pads wear down, reducing their effectiveness. Replacing the pads regularly can help ensure the brakes work correctly.

Friction in the bearings: Bearings help reduce friction and keep the wheels spinning smoothly. However, if they are not adequately lubricated or are worn out, they can create significant friction. Keeping the bearings clean and lubricated is essential for reducing friction and ensuring the bike runs smoothly.

Friction in the tires: The tire pressure and the surface of the road can affect the level of friction between the tires and the ground. If the tire pressure is too low or too high, it can cause uneven wear on the tire and reduce traction. It is essential to keep the tires inflated to the recommended pressure for optimal performance.

Friction in the pedals: The pedals are where the rider applies force to move the bike forward. If the pedals are not lubricated, they can create friction and reduce the rider's efficiency. Regularly cleaning and lubricating the pedals can help reduce friction and increase the rider's power.

In summary, maintaining a bicycle involves reducing friction in some areas and increasing it in others. Regular cleaning, lubrication, and replacement of worn-out parts can help keep a bicycle running smoothly and safely

Explanation:

The particle's average speed after 10 seconds is 110 m/s, and its average velocity is zero.

When a particle is thrown upwards, its initial velocity is in the upward direction and its acceleration is in the downward direction due to gravity. The acceleration due to gravity is approximately 10 m/s² near the surface of the Earth. Therefore, the particle's velocity decreases at a rate of 10 m/s² until it reaches its highest point, where its velocity is zero. After that, the particle's velocity becomes negative and it starts to fall back to the ground.

To find the particle's average speed after 10 seconds, we need to calculate the total distance traveled by the particle in 10 seconds. The formula to calculate the distance traveled by a particle under constant acceleration is:

distance = initial velocity * time + (1/2) * acceleration * time²

Substituting the given values, we get:

distance = 60 m/s * 10 s + (1/2) * 10 m/s² * (10 s)²

distance = 600 m + 500 m

distance = 1100 m

Therefore, the average speed of the particle after 10 seconds is:

average speed = total distance / total time

average speed = 1100 m / 10 s

average speed = 110 m/s

To find the particle's average velocity after 10 seconds, we need to calculate the displacement of the particle in 10 seconds. Displacement is the change in position of the particle, which is equal to the difference between its final and initial positions. Since the particle is thrown upwards and then falls back to the ground, its displacement after 10 seconds is zero. Therefore, the average velocity of the particle after 10 seconds is also zero.

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It takes approximately 0.00000144/45 = [tex]3.2\times 10^{-8}[/tex] seconds, or 32 nanoseconds, for the capacitor to lose 20% of its initial energy when it discharges through a 45Ω resistor.

To determine how long it takes a charged capacitor to lose 20% of its initial energy when it discharges through a resistor, we need to use the formula for the energy stored in a capacitor, which is given by:

[tex]E = (1/2)CV^2[/tex]

where E is the energy in joules, C is the capacitance in farads, and V is the voltage across the capacitor in volts. The energy stored in a capacitor is proportional to the square of the voltage across it.

When the capacitor discharges through a resistor, the voltage across it decreases over time, and the energy stored in the capacitor is converted into heat energy in the resistor. The rate at which the energy is dissipated is given by:

[tex]P = IV = V^2/R[/tex]

where P is the power in watts, I is the current in amperes, and R is the resistance in ohms.

Using the above equations, we can determine the time it takes for the capacitor to lose 20% of its initial energy as follows:

First, calculate the initial energy stored in the capacitor:

[tex]Ei = (1/2)(80\times 10^{-6})(V^2)[/tex]

Next, calculate the final energy stored in the capacitor when it has lost 20% of its initial energy:

Ef = 0.8Ei

Using the equation for power, we can find the current in the circuit:

[tex]P = IV = V^2/R[/tex]

I = V/R

We can use the formula for the rate of change of energy to find the time taken to lose 20% of the initial energy:

dE/dt [tex]= -P = -(V^2/R)[/tex]

dt/dE = [tex]-R/(V^2)[/tex]

t = -R/(V^2) * ∫ (Ei-Ef) dE

Substituting the values from steps 1-4, we can solve for the time taken:

t = -45/([tex]V^2[/tex]) * ∫ (0.8(1/2)([tex]80\times 10^{-6}[/tex])(V^2) - 0) dE

t = -45/([tex]V^2[/tex]) * [0.8(1/2)([tex]80\times 10^{-6}[/tex])V^2]

t = 0.00000144/R seconds

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The acceleration can be calculated using the formula:

Acceleration = (Final velocity - Initial velocity) / Time taken

Given that the bus starts from rest, the initial velocity is 0 m/s.

Acceleration = (20 m/s - 0 m/s) / 21 sec = 20/21 m/s².

The distance travelled at maximum speed can be calculated by subtracting the distances covered during acceleration and deceleration from the total distance.

Distance during acceleration = (1/2) * acceleration * time² = (1/2) * (20/21 m/s²) * (21 sec)² = 210 m.

Distance during deceleration is the same as distance during acceleration.

Distance travelled at maximum speed = Total distance - 2 * distance during acceleration = 270 m - 2 * 210 m = -150 m.

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Answer: The correct answer is:

the area of the trapezoid under the line

To explain this, let's consider the velocity vs. time graph again. Since the object moves with constant acceleration, the graph will be a straight line with a positive slope. The area under the line represents the distance traveled by the object, which is equal to the displacement if the initial position is zero.

The area under the line is a trapezoid because the velocity is changing over time. The base of the trapezoid is the time interval, and the heights are the initial and final velocities. The formula for the area of a trapezoid is:

Area = (base1 + base2) / 2 * height

where:

base1 = initial velocity

base2 = final velocity

height = time interval

Substituting the given values, we get:

Area = (v_i + v_f) / 2 * t

where v_i = 3 m/s, v_f = 10 m/s, and t is the time interval over which the velocities change.

Therefore, the correct answer is the area of the trapezoid under the line.

Answer:

1) = approximately 74 km/hr
2) = 9:30 AM
3) Avg speed = 28 km/hr
   vel = 0.

Explanation:

Here is how you do it:

1) To find the student's speed, we can use the formula:

Speed = Distance / Time

The student traveled a total distance of 40 km south and 15 km north, which gives a total distance of 40 km + 15 km = 55 km. The total time of travel was 0.75 hours.

Speed = 55 km / 0.75 hr ≈ 73.33 km/hr

Therefore, the student's speed is approximately 73.33 km/hr or 74 km/hr.

To calculate the student's velocity, we need to consider both magnitude and direction. Since the student ended up at the same position as the starting point, the displacement is zero. Therefore, the velocity is also zero.

2) The distance between Houston and Austin is 190 miles. The bus is traveling at a constant speed of 54.3 miles/hour. We can use the formula:

Time = Distance / Speed

Time = 190 miles / 54.3 miles/hour ≈ 3.50 hours

The bus will arrive in Austin approximately 3.50 hours after leaving Houston.

If the bus leaves Houston at 6:00 am, it will arrive in Austin around 9:30 am.

3) The girl rode 5 km east and then turned around and rode 2 km west. The total distance traveled is 5 km + 2 km = 7 km. The entire trip took fifteen minutes, which is equal to 15/60 = 0.25 hours.

Average Speed = Total Distance / Total Time

Average Speed = 7 km / 0.25 hr = 28 km/hr

Therefore, the girl's average speed is 28 km/hr.

To calculate the girl's velocity, we need to consider both magnitude and direction. The girl's initial direction was east, and her final direction was west. Since the starting and ending points are the same, the displacement is zero. Therefore, the velocity is also zero.

Answer:

The correct answer is option B: 47.11°.

Explanation:

To calculate the angle of refraction when light passes from air to water, we can use Snell's law, which states:

n₁ * sin(θ₁) = n₂ * sin(θ₂)

where:

n₁ = refractive index of the medium of incidence (in this case, air) = 1.0

n₂ = refractive index of the medium of refraction (in this case, water) = 1.33

θ₁ = angle of incidence

θ₂ = angle of refraction (what we want to find)

Given:

θ₁ = 77º

Let's plug in the values into Snell's law and solve for θ₂:

1.0 * sin(77º) = 1.33 * sin(θ₂)

sin(77º) = (1.33 * sin(θ₂)) / 1.0

Now, isolate sin(θ₂) by multiplying both sides by 1.0:

sin(77º) * 1.0 = 1.33 * sin(θ₂)

sin(θ₂) = (sin(77º) * 1.0) / 1.33

Now, take the inverse sine (arcsin) of both sides to find θ₂:

θ₂ = arcsin((sin(77º) * 1.0) / 1.33)

Calculating the value:

θ₂ ≈ 47.11º

Therefore, the angle of refraction in the water when the angle of incidence is 77º is approximately 47.11º.