Q8 (10pts)
You are working with cartesian unit vectors and ŷ in the plane of the board. Your friend is introducing a
new unit vector  = 0.52 + qŷ, but isn't sure what value q should have. Solve for q and make a
recommendation for what value they could use. If you determine more than one possible value for g,
mention this in your recommendation.

Answer:

To solve this problem, we can use the equations of motion for projectile motion:

- Vertical displacement: Δy = v₀sinθt - 1/2gt²

- Vertical velocity: v = v₀sinθ - gt

- Time of flight: T = 2v₀sinθ/g

- Horizontal displacement: Δx = v₀cosθt

where v₀ is the initial speed, θ is the angle of projection, g is the acceleration due to gravity (9.81 m/s²), t is the time of flight, and Δy and Δx are the vertical and horizontal displacements, respectively.

First, we can find the maximum height by using the equation for vertical displacement:

Δy = v₀sinθt - 1/2gt²

At the maximum height, the vertical velocity is zero, so we can find the time of flight by setting the vertical velocity equation to zero:

v = v₀sinθ - gt = 0

Solving for t, we get:

t = v₀sinθ/g

Substituting this into the equation for vertical displacement, we get:

Δy = v₀sinθ(v₀sinθ/g) - 1/2g(v₀sinθ/g)²

Simplifying, we get:

Δy = (v₀²sin²θ)/(2g)

Substituting the given values, we get:

Δy = (23²sin²25)/(2*9.81) ≈ 29.4 m

So the maximum height is approximately 29.4 meters.

Next, we can find the time of flight using the equation for time of flight:

T = 2v₀sinθ/g

Substituting the given values, we get:

T = 2*23*sin25/9.81 ≈ 3.5 s

So the time of flight is approximately 3.5 seconds.

Finally, we can find the horizontal displacement using the equation for horizontal displacement:

Δx = v₀cosθt

Substituting the given values, we get:

Δx = 23*cos25*3.5 ≈ 64.3 m

So Kelly needs to be approximately 64.3 meters away to catch the ball.

To calculate the total resistance of the two resistors in series, we add them:

R_total = R₁ + R₂ = 12 ohm + 24 ohm = 36 ohm

To calculate the total current flowing in the circuit, we use Ohm's Law:

I = V / R_total = 6.0 V / 36 ohm = 0.17 A

The current flowing in R₁ is the same as the total current, since they are in series:

I₁ = 0.17 A

The current flowing in R₂ is also the same, since they are in series:

I₂ = 0.17 A

To calculate the total power consumed by R₁ and R₂, we use the formula:

P = I²R

For R₁:

P₁ = I₁²R₁ = (0.17 A)²(12 ohm) = 0.35 W

For R₂:

P₂ = I₂²R₂ = (0.17 A)²(24 ohm) = 0.71 W

The total power consumed by both resistors is:

P_total = P₁ + P₂ = 0.35 W + 0.71 W = 1.06 W

Answer:

1. The total resistance of the two resistors:

Since the resistors are connected in parallel.

Total resistance = R₁ + R2

Total resistance = 12 ohm + 24 ohm

Total resistance = 36 ohms

2. The total current flowing in the circuit:

I = V/R

where ,

I = 6.0 V /36 ohm

I = 0.17 amperes

3. The current flowing in R₁

Since he two resistance R₁ and R₂ are connected in series. The current flowing through these two will be equal to the total current flowing in the circuit.

Current flowing in R₁ = 0.17 A

4. The current flowing in R2 = total current flowing in the circuit:

The current flowing in R₂ = 0.17 A.

5. The total power consumed by R₁ and R₂

power consumed by R₁

P = I²R

P = (0.17)²/12

P = 0.0289/12

P = 0.35 (approx)

Now, power consumed by R₂

P = (0.17)² × 24

P = 0.0289 × 24

P = 0.70 (approx)

Total power = power consumed by R₁ + R₂

Total power = 0.35 + 0.70

Total power consumed = 1.05 W

the angle between vectors is 1

let,  vector A,B and |A| =5 , |B| =12

According to dot product,

A.B = |A| |B| cos∝

-6 = 5x12cos∝

cos∝ = 0.99

nearly equal to 1

hence the angle between A and B is 1

Answer: Velocity=0

Explanation: At equilibrium the spring system is not moving.

Answer:

The water cycle outlines the continuous water movement in liquid, solid and gaseous state between locations on the Earth's surface.

The glass jar represents the lake while the atmosphere is represented by the space above the water, and the sky is represented by the (clear) plastic wrap

Arrangement description and Processes;

The processes of the water cycle includes;

Evaporation;

Condensation

Precipitation

Sublimation

Runoff

Infiltration

The arrangement of the materials is as follows;

Place the glass jar (the lake) containing water and the lamp (the Sun) side by side, such that the lamp light shines on the water surface

Cover the glass jar by wrapping the plastic wrap (the sky) around it to prevent the escape of water vapor when the water is hot.

Switch on the lamp so that it heats the water by radiation heat transfer

Observed processes;

The processes demonstrated by the above experiment includes;

1) Evaporation: As the water in the glass jar becomes warmer, the level of the water in the jar can be observed to decrease slightly due to evaporation

2) Condensation: Fog formation, Clouds

When hotter, the water surface as seen through the clear plastic wrap becomes less clearer due to evaporation, and condensation of the vapor while floating above the water surface, similar to the clouds seen in the sky.

3. Precipitation: Rain;

The clear plastic wrap covering the top of the glass jar, prevents the movement of the vapor further away, such that the tiny condensed vapor gather together, to form big droplets under the plastic wrap that falls back into the jar, which is similar to the process of rainfall

The above processes are repeated as more water evaporates from the jar condenses on the plastic wrap and falls back into the jar, showing the process by which water is recycled from the lake into the atmosphere and back to the lake.

Explanation:

The adjacent compressions in the sound wave are 0.155 meters apart.

This distance is also known as the wavelength of the wave. We are given the frequency of the vibration and the speed of sound in air. The formula for wavelength is:

wavelength (λ) = speed of sound (v) / frequency (f)

We are given the frequency of the sound wave as 2200 Hz and the speed of sound through air as 340 m/s.

Plugging these values into the formula gives:

λ = 340 m/s / 2200 Hz = 0.155 meters

Therefore, adjacent compressions (i.e., wavelengths) in the sound wave are a distance of 0.155 meters apart.

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The time it will take the block to fall the entire distance is (a) √3t₁.

Use the equations of motion to solve this problem. The equation to use is:

S = (1/2)gt²

where S = distance, g = acceleration due to gravity, and t = time.

First find the time it takes to fall the first third of the distance. The distance fallen is S₁ = x/3, so:

x/3 = (1/2)gt₁²

Solving for t₁:

t₁ = √((2x)/(3g))

Now, find the time it takes to fall the entire distance. The total distance is S₂ = x, so:

x = (1/2)gt₂²

Solving for t₂:

t₂ = √((2x)/g)

Substituting x with 3S₁:

t₂ = √((6S₁)/g)

Substituting t₁:

t₂ = √((4x)/(3g)) = √(4/3)t₁

Therefore, the answer is (a) √3t₁.

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THE INABILITY OF A BODY TO CHANGE ITS STATE OF MOTION BY ITSELF ⚡

The tendency of matter to resist changes in its velocity or direction of motion is known as the inertia of motion. One of the cornerstones of traditional mechanics, it is also known as the law of inertia.

This principle states that, without an external force, an object at rest tends to remain at rest and an object in motion tends to maintain its current speed and direction. This means that until a force acts on the moving item to cause it to modify its motion, it will continue to proceed in a straight path and at a constant speed due to inertia of motion.

An object's mass affects how much inertia of motion it possesses. An object's inertia of motion increases with bulk, making it more challenging to alter its speed or direction of motion. This feature of matter has a wide range of practical uses, including predicting how moving objects will behave and creating and building systems that need to precisely regulate motion and forces.

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Answer:

Approximately [tex]63.2^{\circ}[/tex].

Explanation:

The refractive index [tex]n[/tex] gives the ratio between the speed of light in vacuum and the speed of light in the given material. A larger refractive index means slower speed of light in the medium. In this question, the speed of light is slower in polycarbonate than in quartz.

When light travels from a material of low light speed to a material of higher light speed, the angle of refraction [tex]\theta_{r}[/tex] will exceed the angle of incidence [tex]\theta_{i}[/tex] (both with respect to the normal.)

The critical angle at this interface is the [tex]\theta_{i}[/tex] for which [tex]\theta_{r} = 90^{\circ}[/tex]. Note that since [tex]\theta_{i}\![/tex] cannot exceed [tex]90^{\circ}[/tex], [tex]\theta_{i} < \theta{r}[/tex] and light must be entering a faster medium from a slower medium. In this question, light would be entering quartz ([tex]n = 1.41[/tex], faster) from polycarbonate ([tex]n = 1.58[/tex], slower.)

By Snell's Law:

[tex]n_{i}\, \sin(\theta_{i}) = n_{r}\, \sin(\theta_{r})[/tex],

Where:

Set [tex]n_{i} = 1.58[/tex] (polycarbonate), [tex]n_{r} = 1.41[/tex] (quartz), and [tex]\theta_{r} = 90^{\circ}[/tex]. Rearrange the equation and solve for [tex]\theta_{i}[/tex]:

[tex]\begin{aligned}\sin(\theta_{i}) &= \frac{n_{r}\, \sin(\theta_{r})}{n_{i}} \end{aligned}[/tex].

[tex]\begin{aligned}\theta_{i} &= \arcsin\left (\frac{n_{r}\, \sin(\theta_{r})}{n_{i}} \right) \\ &= \arcsin \left(\frac{1.41\, \sin(90^{\circ})}{1.58}\right) \\ &\approx 63.2^{\circ}\end{aligned}[/tex].

The final velocity of the ball to one decimal place is approximately 10.0 m/s.

From the third equation of motion:

v² = u² + 2as

Where v is final velocity, u is initial velocity, a is acceleration and s is the distance covered.

Given that:

Plug the given values into the abovr formula and solve for the final velocity v.

v² = u² + 2as

v² = 0² + ( 2 × 6.4 m/s² × 7.8 m )

v² =   2 × 6.4 m/s² × 7.8 m

v² = 99.84 m²/s²

v = √(  99.84 m²/s² )

v = 10.0 m/s

Therefore, the final velocity is 10.0 m/s.

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We can see here in one's own words, instantaneous communication would still not be conceivable even if quantum mechanics were predictable and the results of measurements could be predicted in advance. This is because, even if they were entangled, any attempt to change the state of one atom would inevitably change the state of the other atom.

The behavior and interaction of particles at the atomic and subatomic scales is the subject of quantum mechanics, a subfield of physics. It offers a mathematical framework for describing the probabilistic nature of physical occurrences in the microscopic world as well as the wave-particle duality of matter.

Until they are measured or observed, particles in quantum mechanics do not have fixed positions or attributes, and the measurement process might have an impact on the system being examined.

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Answer:

Explanation:

Increased heart rate

The current would decrease if one light bulb is removed from the circuit. Option B is correct.

If one light bulb is removed from a simple circuit with two identical light bulbs that are in series with one another, the total resistance in the circuit would increase. This is because the resistance of the circuit is proportional to the number of resistors in the circuit, and removing one bulb reduces the number of resistors in the circuit.

The total current in the circuit would decrease because the resistance has increased. This is because the current flowing through a circuit is inversely proportional to the resistance of the circuit according to Ohm's law. Option B is correct.

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Answer:

1.53 N

Explanation:

The force required to stretch a spring is given by Hooke's law: F = k*x, where F is the force, k is the spring constant, and x is the displacement from the equilibrium position.

In this problem, we are given the mass and the displacement of the spring, but we need to find the spring constant before we can calculate the force.

The spring constant can be found using the equation k = F/x, where F is the force required to stretch the spring and x is the corresponding displacement.

Given that the 102 g mass stretches the spring by 4.0 cm, we have:

k = F/x = (mg)/x = (0.102 kg)(9.8 m/s^2)/(0.04 m) = 25.5 N/m

where g is the acceleration due to gravity.

Now, to calculate the force required to stretch the spring by 6.0 cm, we use the same equation with the new displacement:

F = kx = (25.5 N/m)(0.06 m) = 1.53 N

Therefore, the force required to stretch the spring by 6.0 cm is 1.53 N.

Answer: 3.99•10⁴ J

Explanation:

The Heat Formula is: Q = m • C • ΔT

Your given C, m, T₀, and T

C = 0.385 J/g•K

m = 1.55 kg or 1,550 g

T₀ = 33.0 °C

T = 99.9 °C

(ΔT = T - T₀)

Your only remaining variable is Q, heat, so you can now plug in your values to solve.

Q = (1550)(0.385)(99.9 - 33.0)

(ΔT(°C) = ΔT(K) because the conversion is linear)

Q = 39,922.575 J

or

3.99•10⁴ J

Answer:

biomass energy, hydropower and wind energy

Robert Boyle demonstrated that sound needs a medium through which to travel by observing that an alarm watch in a vacuum did not make a sound. Option 1 is the answer.

Sound is a form of energy that results from the vibration of matter. When an object vibrates, it creates sound waves that travel through a medium and can be perceived by the human ear.

A medium is a substance or material through which waves can travel. In the case of sound, air, water, and solids such as metal or wood can serve as a medium. Without a medium, sound cannot propagate because there are no molecules to vibrate and transmit the waves.

Robert Boyle demonstrated that sound needs a medium through which to travel by observing that an alarm watch in a vacuum did not make a sound. This led him to conclude that sound requires a medium, such as air or water, to propagate.

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The induced e.m.f is -0.02sin(10^3t) (V) which is option D

Induced voltage refers to the electrical voltage that is generated in a conductor or coil due to a changing magnetic field.

This phenomenon is known as electromagnetic induction and is the basis for many electrical devices such as generators and transformers.

Induced voltage can be calculated using Faraday's law, which states that the induced electromotive force (EMF) is equal to the rate of change of magnetic flux.

The induced voltage can be either positive or negative depending on the direction of the changing magnetic field and the orientation of the conductor or coil.

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The time taken to get up and out of the way before you and the child collide is 2.82 s.

The time taken to get up and out of the way before you and the child collide is calculated as follows;

s = v + ¹/₂at²

s = v + ¹/₂(g sin (31)t²

where;

The time taken to get up is calculated as;

20 = 0 +  ¹/₂(9.8 sin (31)t²

20 = 2.524t²

t² = 20/2.524

t² = 7.925

t = 2.82 s

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Answer:

5866.9 kg

Explanation:

We can use the conservation of momentum to solve this problem. The momentum of the rocket and fuel system is conserved, so:

Initial momentum = Final momentum

The initial momentum of the system is zero since the rocket is at rest initially. The final momentum is the momentum of the rocket after burning the fuel. We can find the final momentum using the rocket equation:

Δv = ve * ln(m0 / mf)

where Δv is the change in velocity (100 m/s), ve is the exhaust speed (1500 m/s), m0 is the initial mass of the rocket and fuel system (what we want to find), and mf is the final mass of the rocket and fuel system (m0 - 100 kg).

Solving for m0, we get:

m0 = mf * exp(Δv / ve) = (m0 - 100 kg) * exp(100 / 1500)

Simplifying this equation, we get:

m0 = 100 kg / (1 - exp(100 / 1500))

m0 = 5866.9 kg (rounded to four significant figures)

Therefore, the initial mass of the rocket and fuel system was approximately 5866.9 kg.

Answer:

Explanation:

The answer is D. 0  ;

As We know when the net external force on an isolated system is absent then the total linear momentum of the system remains conserved.

=> By Conservation of linear Momentum of the system;

=> P1=P2  i.e initial momentum= final momentum;

=>if final momentum is '0' that is they are in rest position velocity is 0;

  So momentum is 0 By p=mv;

Hence initial momentum  will be zero;

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The initial momentum of the girl can be calculated using the formula:

p = mv

where p is the momentum, m is the mass, and v is the velocity.

Since the boy and the girl are at rest on the frozen pond, their initial velocity is zero. Therefore, the initial momentum of the girl is:

p = mv = (40 kg)(0 m/s) = 0 kgm/s

So, the answer is D. 0 kgm/s.

Burning organic waste is often referred to as "incineration.

It is a process in which organic waste is burned at high temperatures to convert it into ash and gas. Incineration is often used as a method of waste management to reduce the volume of waste and to eliminate potentially harmful organic materials, such as medical waste or hazardous chemicals.

However, incineration can also produce air pollution and greenhouse gas emissions, and there are concerns about the impact of incineration on human health and the environment. As a result, many communities and governments are exploring alternative methods of waste management, such as recycling and composting.

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the answer is polarization.

Yes, I would expect a system with objects that have an equal amount of positive and negative charge to have a large amount of electric potential energy.

This is because the electric potential energy of a system of charges is proportional to the product of the charges and inversely proportional to the distance between them. When positive and negative charges are brought close together, the electric potential energy of the system increases because the charges are attracted to each other due to their opposite charges.

As the charges get closer together, the electric potential energy of the system increases even more, because the charges are closer to each other and their attraction is stronger.

Therefore, when there are equal amounts of positive and negative charges in a system, the electric potential energy of the system will be high because there will be many oppositely charged pairs of particles that are close together and attracting each other strongly.

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Ritalin and Demerol are both controlled substances that have a high risk of abuse and dependence.

Schedule II drugs are believed to have a high abuse potential that could lead to severe psychological or physical dependence. They do, however, occasionally have other known medical applications and can be prescribed by a licensed healthcare provider.

Ritalin is an example of a stimulant, whereas Demerol is an example of an opioid. Thus the drugs that have been mentioned here are drugs that are strictly controlled.

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The number of electrons represent a Change of -70 μC is 4.3 × 10¹⁴.

Electric charge is the physical property of matter that experiences force when it is placed in electric field. F = qE where q is amount of charge, E = electric field and F = is force experienced by the charge. there are two types of charges, positive charge and negative charge which are generally carried by proton and electron resp. like charges repel each other and unlike charges attract each other. the flow charges is called as current. Elementary charge is amount of charge a electron is having, whose value is 1.602 x 10⁻¹⁹ C

The value of elementary charge that is charge on 1 electron is 1.6× 10⁻¹⁹ C

-70 μC = N × 1.6× 10⁻¹⁹ C

N = -70 μC / 1.6× 10⁻¹⁹ C

N = -70 μC / 1.6× 10⁻¹⁹ C

N = 4.3 × 10¹⁴ electrons

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Explanation:

The parallel resistors ( 10 and 40 Ω) have an equivalent resistance of

( 40 * 10 ) / ( 40 + 10 )  = 8 Ω

Then you can add all of the series resistances to find the total resistance

15 + 25 + 8 Ω = 48 Ω

Remember V = IR ....then   V/R = I

      Current =    V/ R = 55 v / 48 Ω = 1.15 A

The tourist is standing one-third of the way along the bridge (option c).

Let's denote the distance from the near end of the bridge to the point where the tourist is standing as x and the total length of the bridge as L.

According to the equilibrium condition, the sum of the forces exerted on the bridge is zero.

So, the vertical forces exerted by the two concrete supports should be equal to the weight of the tourist:

F_near + F_far = 705 N

Given that the magnitude of the vertical force exerted by the near end support is 470 N, we can calculate the force exerted by the far end support:

F_far = 705 N - 470 N = 235 N

Now, we can use the moment equilibrium condition, considering moments around the near end support:

Moment = Force × Distance

For the tourist:

Moment_tourist = 705 N × x

For the far end support:

Moment_far = 235 N × L

For equilibrium, the sum of the moments should be zero:

Moment_tourist - Moment_far = 0

Substituting the moments:

705 N × x - 235 N × L = 0

Now, we can solve for x/L, which represents the fraction of the way along the bridge where the tourist is standing:

x/L = (235 N × L) / 705 N

x/L = 235/705 = 47/141 ≈ 1/3

So, the tourist is standing one-third of the way along the bridge (option c).

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