if the clown recoils with a speed of 0.485 m/s and the barbell is thrown with a speed of 8.5 m/s, what is the mass, in kilograms, of the barbell?

The percentage contribution of the elastin towards the total force assuming elastic behavior will be 100%.

To calculate the percentage contribution of elastin towards the total force assuming elastic behavior, we need to know the total force and the contribution of elastin to the total force.

Let's assume that the total force is F_total and the contribution of elastin to the total force is F_elastin. In an elastic behavior, the force exerted by elastin is directly proportional to the amount of deformation or stretch, given by Hooke's law, which is, F_elastin = k × x

where k is the spring constant of the elastin and x is the amount of deformation or stretch.

If we know the spring constant of the elastin and the amount of deformation or stretch, we can calculate the force exerted by the elastin.

Assuming that there are no other significant sources of force in the system, we can say that the total force is equal to the force exerted by the elastin:

F_total = F_elastin

Therefore, F_total = k × x

To calculate the percentage contribution of elastin towards the total force, we can use the following formula;

Percentage contribution of elastin = (F_elastin / F_total) × 100%

Substituting F_elastin and F_total from the above equations, we get:

Percentage contribution of elastin = (k × x / k × x) × 100%

The k × x term cancels out, leaving us with:

Percentage contribution of elastin = 100%

This means that in an elastic system where the only significant source of force is elastin, the total force is entirely due to the force exerted by the elastin.

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The most accurate range provided for our spectrum of light that is visible is 380-740 nm. Option c is correct.

The visible spectrum of light refers to the range of electromagnetic radiation that can be detected by the human eye, typically between 380 to 740 nanometers in wavelength. This range is perceived by the human eye as different colors, with violet having the shortest wavelength and red having the longest. The visible spectrum is just a small portion of the electromagnetic spectrum, which includes other forms of radiation such as radio waves, microwaves, X-rays, and gamma rays.

Scientists use various devices to detect and measure the different ranges of the electromagnetic spectrum. Understanding the properties and behaviors of light in different ranges is important in fields such as astronomy, optics, and communications. Hence, option c is correct.

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The number of repetitions that take place during a period of time determines a wave's frequency. It is expressed in cycles per second, or Hertz (Hz), a unit of measurement.

If the wave's radius and speed are known, the frequency of the wave can be calculated using the equation f=v f = v, where is the wavelength in metres and v is the wave speed in m/s.

Frequency is the number of waves that pass through a fixed place in a predetermined amount of time. As a result, a pulse that lasts for half a second has a frequency of 2 seconds per pulse. If it takes 1/100 of an hour, the figure is 100 times per hour.

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Answer:

The answer is time-delay circuit breaker.

An intentional delay between the time when the fault or overload is sensed and the time when the circuit breaker (CB) operates is present in time delay circuit breakers.

What is a circuit breaker?

A circuit breaker is an electrical safety device that is designed to protect an electrical circuit from damage caused by overload, short circuit, or ground fault. A circuit breaker will trip or disconnect the circuit from the power supply when it detects a fault. After resolving the problem, the circuit can be reconnected. The circuit breaker is a critical element of the electrical system. It protects electrical equipment, facilities, and human lives from electrical incidents. It acts as a switch that can be turned off if an electrical fault or damage is detected.

What is a time-delay circuit breaker?

A time-delay circuit breaker is a circuit breaker with an intentional delay between the time when the fault or overload is sensed and the time when the CB operates. It provides time-delay protection against short circuits and overloads. It is used when a motor or other inductive loads are present. In the absence of a time-delay circuit breaker, the breaker may trip immediately due to the high inrush current when an inductive load is switched on. This high current is much greater than the normal full-load current. A time-delay circuit breaker will delay the trip so that the inrush current has time to diminish to normal full-load current levels.

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Three objects are connected by massless wires over a massless frictionless pulley as shown in the figure. the tension in the wire connecting the 10.0-kg and 15.0-kg objects is measured to be 133 n the mass m in the multiple-object system without friction is approximately 13.1 kg.

To find the mass m in this multiple-object system without friction, follow these steps:
1. Analyze the forces acting on each object. For the 10.0-kg and 15.0-kg objects, the forces are tension (T) and gravitational force (weight).
2. Write the equation of motion for each object using Newton's second law (F = ma). For the 10.0-kg object: T - 10.0g = 10.0a, and for the 15.0-kg object: 15.0g - T = 15.0a.
3. Substitute the given tension (133 N) into the equations: 133 - 10.0g = 10.0a and 15.0g - 133 = 15.0a.
4. Solve one of the equations for acceleration (a). For example, from the first equation: a = (133 - 10.0g) / 10.0.
5. Substitute the expression for acceleration into the other equation, and solve for g (the acceleration due to gravity): 15.0g - 133 = 15.0((133 - 10.0g) / 10.0).
6. Solve for g: g ≈ 9.81 m/s^2.
7. Use the value of g to find the acceleration (a) from step 4: a ≈ 0.57 m/s^2.
8. Now, consider the third object with mass m. The forces acting on it are tension (T) and gravitational force (m*g). Write the equation of motion for this object: T - m*g = m*a.
9. Substitute the given tension (133 N) and the calculated acceleration (0.57 m/s^2) into the equation: 133 - m*9.81 = m*0.57
10. Solve for mass m: m ≈ 13.1 kg.

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one way to determine your intensity is to rate how hard you feel you are working is false. The given statement is false.

Intensity is a measure of the amount of effort or energy expended during physical activity. It is typically measured using objective criteria, such as heart rate, oxygen consumption, or power output.

Relying solely on subjective feelings of how hard you feel you are working may not provide an accurate or precise measure of intensity.

Objective measurements are generally more reliable for determining the intensity of physical activity.

Therefore, Rating how hard you believe you are working is a deceptive indicator of your intensity. The assertion is untrue.

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The nozzle pressure is approximately 893892 Pa, or about 129.6 psi.

To determine the nozzle pressure, we can use the Bernoulli's equation, which states that the total pressure of a fluid is constant along a streamline.

Assuming that the fluid is incompressible and the hose is a perfect straight line, the Bernoulli's equation can be simplified as:

P + 0.5rhov^2 + rhogh = constant

where P is the pressure, rho is the density of the fluid, v is the velocity of the fluid, g is the acceleration due to gravity, and h is the height of the fluid above a reference point.

Since the fluid is not moving horizontally, we can assume that the velocity of the fluid is zero at the nozzle, and the velocity head term (0.5rhov^2) can be ignored.

The reference point can be set at the nozzle, where the pressure is the nozzle pressure (P_n). At the pump, the pressure is the pump pressure (P_p), and the height is 100 feet (h = 100 ft).

Therefore, we can write: P_p + rhogh = P_n. where rho is the density of the fluid (water), which is approximately 1000 kg/m^3.

To convert the height from feet to meters, we multiply by 0.3048 m/ft, which gives: h = 100 ft * 0.3048 m/ft = 30.48 m

To convert the pump pressure from psi to Pa, we multiply by 6894.76 Pa/psi, which gives: P_p = 86 psi * 6894.76 Pa/psi = 593089 Pa

Substituting these values into the equation, we get:

P_n = P_p + rhogh

P_n = 593089 Pa + 1000 kg/m^3 * 9.81 m/s^2 * 30.48 m

P_n = 893892 Pa

Therefore, the nozzle pressure is approximately 893892 Pa, or about 129.6 psi.

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The values into the acceleration equation, we get: a = (24.9 N - 44.1 N) / 9 kg = -2.3 m/s^2. Therefore, the mass is decelerating along the incline.

The speed at which velocity varies with regard to time. Since acceleration has both a magnitude and a direction, it is a vector number.

Let's first determine the mass's potential energy at the summit of the incline:

PE = mgh = 9 kg * 9.8 m/s² * 0.5 m = 44.1 J

PE = (1/2)kx² = (1/2) * 2.3 N/cm * (32 cm / 100)²

= 11.8 J

KE = (1/2)mv²

The work done by friction is given by:

W = f * d * cosθ

Therefore, the kinetic energy of the mass just as it reaches the bottom of the incline is:

KE = PE(spring) - W(friction) = 11.8 J - 2.4 J = 9.4 J

Substituting the given values into the kinetic energy equation and solving for v, we get:

9.4 J = (1/2) * 9 kg * v²

v = √(9.4 J / (4.5 kg)) = 1.84 m/s

Finally, we can calculate the acceleration of the mass along the incline using the equation:

a = (f_net - f_friction) / m

f_friction = μ_k * m * g = 0.5 * 9 kg * 9.8 m/s²= 44.1 N

The net force acting on the mass along the incline is given by:

f_net = m * g * sinθ = 9 kg * 9.8 m/s² * sin(15°) = 24.9 N

Substituting the values into the acceleration equation, we get:

a = (24.9 N - 44.1 N) / 9 kg

= -2.3 m/s².

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The power dissipated in the 3.0 resistor is 3.0 watts when the resistors are connected to the given circuit and connected across a 12-volt battery.

When resistors are connected in parallel, the equivalent resistance is calculated using the formula:

1/Req = 1/R1 + 1/R2 + ... + 1/Rn

where Req is the equivalent resistance, and R1, R2, ..., Rn are the individual resistances. Once the equivalent resistance is known, we can calculate the total current in the circuit using Ohm's law, I = V/Req, where V is the voltage across the circuit.

In this problem, the 3.0 and 6.0 resistors are connected in parallel, so their equivalent resistance is:

1/Req = 1/3 + 1/6 = 1/2

Req = 2 ohms

The equivalent resistance of the parallel combination is then connected in series with the 4.0 resistor, giving a total resistance of:

Rtot = Req + R3 = 2 + 4 = 6 ohms

The total current in the circuit is given by Ohm's law as:

I = V / Rtot = 12 / 6 = 2 amps

Now, we can calculate the power dissipated in the 3.0 resistor using the formula for power, P = I^2 * R. Since the 3.0 resistor is in parallel with the 6.0 resistor, it carries half of the total current or 1 amp. Thus, the power dissipated in the 3.0 resistor is:

P = I^2 * R = 1^2 * 3.0 = 3.0 watts

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The stomp rocket's rate of ascent at pi/4 radians is approximately 110.9 meters per second, given a horizontal distance of 400 meters and a rate of change of 0.4 radians per second.

We know that the tangent of the angle of elevation of the stomp rocket at time t is equal to h(t)/400 (where 400 is the horizontal distance between the students and the rocket). So, when the angle of elevation is pi/4, we can solve for h(t) and find that h(t) = 400 * tan(pi/4) = 400 meters. Next, we can use the chain rule of calculus to find the rate of change of the height of the rocket with respect to time. Since the angle of elevation is increasing at a rate of 0.4 radians per second, we can find that dh/dt = dh/d(theta) * d(theta)/dt = (400 / cos(pi/4)) * 0.4 = approximately 110.9 meters per second.

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The total mass of the two objects is 5.10 kg, the heavier mass of each object is 3.40 kg, while the lighter mass of each object is 1.70 kg.

The expression for the force of gravity F between two objects of mass m1 and m2 separated by a distance r is:

F = (Gm1m2)/r²

where G is the gravitational constant

[tex]m1 = (Fr²)/(Gm2)\\Substitute F = 1.02 × 10^-8 N, r = 19.3 cm = 0.193 m, and G = 6.67 × 10^-11 Nm²/kg²:\\m1 = (1.02 × 10^-8 N × (0.193 m)²)/(6.67 × 10^-11 Nm²/kg² × 5.10 kg)m1 = 3.40 kg[/tex]

Thus, the heavier mass of each object is 3.40 kg, while the lighter mass of each object is 1.70 kg.

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Answer:

To solve this problem, we can use the formula:

time = distance/speed

Distance is the distance traveled, and speed is the car's speed.

Substituting the given values, we get:

time = 300 km / 60 km/h = 5 hours

Therefore, it would take the car 5 hours to travel 300 km at 60 km/h. Rounded to the nearest whole number, the answer is 5 hours.

One of the strongest arguments for the Big Bang theory is the Cosmic Microwave Background Radiation (CMB). It is believed that the CMB, a faint electromagnetic glow that permeates the entire cosmos, is the radiation left over from the actual Big Bang.

Arno Penzias and Robert Wilson made the first finding of radiation in 1964; they were awarded the 1978 Nobel Prize in Physics for it. Strong proof from the CMB supports the theory that the universe originated with a Big Bang by showing that it was once much hotter and denser than it is today.

A scientific hypothesis that explains the universe's beginning is the Big Bang theory. The universe originated as a hot, dense, and infinitely tiny point, known as a singularity, around 13.8 billion years ago, claims this hypothesis. The vast and intricate universe we see today was ultimately created as a result of the rapid expansion and cooling of this singularity over time.

Cosmic Microwave Background Radiation is one of the most important pieces of proof for the Big Bang hypothesis. (CMB). It is believed that the CMB, a form of electromagnetic radiation that permeates the entire universe, is the radiation that was left over after the Big Bang. Using a radio observatory, Penzias and Wilson made the initial discovery in 1964.

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The velocity of car A after the collision is 1.72 m/s in the opposite direction of its initial velocity.

We can use the conservation of momentum to solve for the velocity of car A after the collision.

The initial momentum of the system is:

p_initial = m_A * v_A + m_B * v_B

= 281 kg * 2.82 m/s + 281 kg * (-1.72 m/s)

= 0 kg m/s

Since momentum is conserved, the final momentum of the system is also zero:

p_final = m_A * v_A' + m_B * v_B'

= 0 kg m/s

Where

Solving for v_A', we get:

v_A' = -(m_B / m_A) * v_B

Substituting the given values, we get:

v_A' = -(281 kg / 281 kg) * (-1.72 m/s)

= 1.72 m/s

Therefore, the velocity of car A after the collision is 1.72 m/s in the opposite direction of its initial velocity.

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The constant angular acceleration of the wheel is approximately 32.56 rad/s².

The formula for angular acceleration is:

α = (ωf - ωi) / t

where α is the angular acceleration, ωf is the final angular velocity, ωi is the initial angular velocity, and t is the time interval.

We are given ωi = 0 and ωf = 98.2 rad/s. We are also given the time interval t = 3.01 s. To find the angular acceleration α, we just need to substitute the given values into the formula:

α = (98.2 - 0) / 3.01
α ≈ 32.56 rad/s²

Therefore, the constant angular acceleration of the wheel is approximately 32.56 rad/s².

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Answer:

[tex]1 \: {m}^{2} \: has \: 10000 \: {cm}^{2} [/tex]

Explanation:

Since 1 m has 100 cm, we can find how many cm2 does 1m2 have:

1m^2 = 1 m × 1 m (1 m has 100 cm)

1m^2 = 100 cm × 100 cm= 10000 cm^2

On July 5th, the moon was in its waxing gibbous phase.

The illumination of the moon increases during the waxing phases, from the new moon to the full moon. Based on the given information, we know that:
1. On July 4th, the moon was 55% illuminated.
2. On July 5th, the moon was 68% illuminated.
3. On July 6th, the moon was 83% illuminated.

Since the illumination percentage is increasing each day, the moon is in its waxing phase. When the illumination is between 51% and 99%, it is considered a waxing gibbous phase.

The illumination of the moon increased from 55% to 68% between July 4th and July 5th. This is an increase of 13%. Based on the standard terminology for lunar phases, a waxing phase where the moon is between half-full and full is called a "waxing gibbous" phase. A waxing gibbous phase is characterized by illumination between 51% and 99%. Since the moon was 68% illuminated on July 5th, it was in a waxing gibbous phase at that time.

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Both straight and circular antennas can pick up magnetic oscillations, but they have different polarization properties.

A straight antenna is sensitive to electric field polarizations while a circular antenna is sensitive to magnetic field polarizations.

Therefore, a circular antenna is better suited for picking up circularly polarized electromagnetic waves while a straight antenna is better suited for picking up linearly polarized electromagnetic waves.

In general, the choice of antenna depends on the polarization of the signal being received.

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The region of very bright colors embedded within a hook echo on a radar screen indicating damage being produced by a tornado is called a debris ball.

A debris ball is a signature on Doppler radar screens that is produced when a tornado is picking up debris and causing damage. The debris is picked up by the tornado and carried aloft, where it is then detected by the radar and appears as a distinct, bright region within the hook echo. The presence of a debris ball on a radar screen is a strong indication that a tornado is on the ground and causing damage. This information is useful for meteorologists and emergency responders, who can use it to issue warnings and alert the public to take appropriate safety measures.

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39.21 NTension in the cord The tension in the cord can be calculated as follows; Mass of sphere = 4.7 kg Density of water = 1000 kg/m³Density of the sphere = 4000 kg/m³Now, the density of the sphere will tell us the volume of the sphere.

The density of the solid sphere is 4000 kg/m³. It weighs 4.7 kg. When the sphere is immersed in water, the tension in the cord can be calculated as follows: So, we have the Volume of sphere = Mass/Density= 4.7/4000= 0.001175 m³The volume of water displaced by the sphere is equal to the volume of the sphere. The volume of water = Volume of sphere = 0.001175 m³Now, let's use the density of water to find the mass of the water that was displaced. The density of water is 1000 kg/m³. So, Mass of water displaced = Density of water × Volume of water= 1000 × 0.001175= 1.175 kgNow we can calculate the weight of the sphere. The weight is equal to the mass of the sphere × the acceleration due to gravity (g). We can assume g to be 9.8 m/s².Weight of sphere = Mass of sphere × g= 4.7 × 9.8= 46.06 NTension in the cord = Weight of sphere - Buoyant force= 46.06 - (mass of water displaced × g)= 46.06 - (1.175 × 9.8)= 39.21 N.

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Answer:

The correct option is D. Air resistance slows the ball's fall as it approaches Earth.

Explanation:

Potential difference of the EMF labeled "h" in the circuit is 5 V.

Current entering  junction between 4 Ω resistor and EMF labeled "h" is 1.0 A, and the current leaving  junction through  6 Ω resistor is also 1.0 A. Kirchhoff's second law, also known as  law of conservation of energy, states that  sum of  potential differences around any closed loop is equal to zero. We encounter a potential difference of 9 V due to EMF, a potential difference of 4 V due to 4 Ω resistor, and a potential difference of 6 V due to  6 Ω resistor. The total potential difference is therefore:

[tex]9 V - 4 V - 6 V = -1 V[/tex]

According to Kirchhoff's second law . Therefore,  potential difference of  EMF labeled "h" must be:

[tex]V_h = 9 V - 4 V = 5 V[/tex]

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Temperature is a crucial factor in sericulture, which is the process of rearing silkworms for the production of silk. The optimal temperature range for silkworm growth and development is between 25°C and 30°C, with a relative humidity of 70-80%.

If the temperature is too low for silkworms, they grow more slowly, and their development may be delayed, resulting in lower silk production. This is because silkworms are cold-blooded creatures that rely on their environment to regulate their body temperature.

Temperature control is crucial in sericulture because it affects the growth, development, and survival of silkworms, which in turn affects the quality and quantity of silk production.

Maintaining the optimal temperature range helps to ensure that silkworms develop and mature quickly, produce high-quality silk, and have a low mortality rate. Temperature control also helps to prevent disease outbreaks and reduces the risk of silkworms becoming stressed and dying.

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Answer:

W = 1/2 K x^2        work in stretching spring x meters

W2 / W1 = 10^2 / 5^2           1/2 and K's cancel

W2 = 4 W1

W2 = 100 N

It takes a force of 25 n to stretch a spring 5 m beyond its natural length. " the work done in stretching the spring 10 m from its natural length is 250 Joules."

To calculate the work done in stretching the spring, we will use Hooke's Law and the work-energy principle. Hooke's Law states that the force needed to stretch or compress a spring is proportional to the displacement from its natural length:
F = k * x
where F is the force, k is the spring constant, and x is the displacement from the natural length. We are given that it takes a force of 25 N to stretch the spring 5 m beyond its natural length, so:
25 N = k * 5 m
Now, solve for the spring constant k:
k = 25 N / 5 m = 5 N/m
Next, we need to calculate the work done in stretching the spring 10 m from its natural length. The work-energy principle states that the work done on an object is equal to the change in its potential energy:
W = (1/2) * k * x^2
where W is the work done, k is the spring constant, and x is the displacement from the natural length. We found the spring constant k to be 5 N/m, and we are given that the displacement x is 10 m, so:
W = (1/2) * 5 N/m * (10 m)^2
Now, calculate the work done:
W = (1/2) * 5 N/m * 100 m^2 = 250 J
Therefore, the work done in stretching the spring 10 m from its natural length is 250 Joules.

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To an observer on the Moon, the illuminated part of the Earth would appear to be in the shape of a crescent, with the points of the crescent facing towards the Moon, which is why it would be in the waxing crescent phase.

We need to understand that the phases of the Moon are determined by its position relative to the Earth and the Sun. The New Moon phase occurs when the Moon is directly overhead of Earth and Sun. When the Earth is between the Moon and the Sun, it is in the Full Moon phase. And when the Moon is at a right angle to the Earth and the Sun, it is in one of the intermediate phases, such as the waning gibbous phase.

So, if an observer on Earth views the Moon in the waning gibbous phase, it means that the Moon is positioned at a right angle to the Earth and the Sun. To an observer on the Moon, the Earth would appear to be in the opposite phase, which is the waxing crescent phase.

To visualize this, imagine drawing a straight line connecting the Earth and the Sun, and another straight line connecting the Moon and the Earth. When the Moon is at a right angle to the Earth and the Sun, these two lines form a right triangle. The side of the triangle that connects the Earth and the Moon will be illuminated by the Sun, while the side of the triangle that faces away from the Sun will be dark.

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Horizontal distance traveled by the rocket is x = 0 yards.

The angle of launch θ = 0.98 radians.

The distance traveled by the rocket s = 415 yards.

We need to find horizontal distance traveled by the rocket (x).

Horizontal velocity ([tex]v_{x}[/tex]) = initial velocity ([tex]v_{0}[/tex]) × cos(θ)

Distance traveled horizontally (x) = horizontal velocity ([tex]v_{x}[/tex]) × time (t)

We don't know initial velocity or the time.

Distance traveled (s) = initial velocity ([tex]v_{0}[/tex]) × sin(θ) × time (t) + (1/2) × acceleration (a) × time²

Rocket is fired vertically upward and lands back on the ground. We can assume the final velocity is zero.

time (t) = √(2s/a)

a here is the acceleration due to gravity. If we assume the rocket is fired on Earth,  a = 9.8 m/s².

time (t) = √(2 × 415 / 9.8) = 9.37 seconds

Use the horizontal velocity equation,

Horizontal velocity ([tex]v_{x}[/tex]) = initial velocity ([tex]v_{0}[/tex]) × cos(θ)

We don't know [tex]v_{0}[/tex], but we do know the vertical velocity at the highest point of the trajectory is zero.

Vertical velocity ([tex]v_{y}[/tex]) = initial velocity ([tex]v_{0}[/tex]) × sin(θ) - acceleration (a) × time (t)

At the highest point, [tex]v_{y}[/tex] = 0

[tex]v_{0}[/tex] = [tex]v_{y}[/tex] / sin(θ) = 0 / sin(0.98) = 0

Therefore, the initial velocity is zero and the horizontal velocity is also zero. The rocket is launched vertically and lands back on the ground vertically. So horizontal distance traveled by the rocket is x = 0 yards.

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The total charge that went through the 60-watt, 120-volt study lamp between 2:00 pm and 2:00 am is 216,000 coulombs.

To find the charge, follow these steps:

1. Calculate the time the lamp was on: The lamp was on for 12 hours (from 2:00 pm to 2:00 am).

2. Convert the wattage and voltage to amperes (current): Power (W) = Voltage (V) × Current (A). So, Current (A) = Power (W) / Voltage (V) = 60 W / 120 V = 0.5 A.

3. Convert the time to seconds: 12 hours × 60 minutes/hour × 60 seconds/minute = 43,200 seconds.

4. Calculate the charge: Charge (Q) = Current (I) × Time (t) = 0.5 A × 43,200 s = 216,000 coulombs.

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When a green light illuminates a purple costume on a theatrical stage, the color of the costume will appear as a darker shade of green. This is due to the subtractive color model, which states that colors are created when light is reflected off of an object and absorbed by the object.

In this case, the purple costume is reflecting green light and absorbing all other colors, resulting in a darker shade of green. This effect is even more dramatic when the light is brighter, resulting in a nearly black color.

The color of a costume is also affected by the lighting equipment used, such as the color and power of the light. This means that the costume’s color can be changed based on the lighting used on the stage.

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If the gravitational force between two massive spheres is 10 n and if the distance between the spheres is cut in half, the force between the masses is 40 N.

The gravitational force between two massive spheres can be calculated using the formula:

F = G *[tex](m_1 * m_2) / r^2[/tex]

where F is the gravitational force between the spheres, G is the gravitational constant, [tex]m_1[/tex] and [tex]m_2[/tex] are the masses of the two spheres, and r is the distance between the centers of the two spheres.

If the distance between the two spheres is halved, the new distance between them is r/2.

Using the formula above, the new gravitational force between the spheres is:

F' = G * [tex](m_1 * m_2) / (r/2)^2[/tex]

F' = G *[tex](m_1 * m_2) / (1/4)r^2[/tex]

F' = 4 * G * [tex](m_1 * m_2) / r^2[/tex]

Therefore, if the distance between the two massive spheres is cut in half, the gravitational force between the spheres increases by a factor of 4.

In this case, the new gravitational force between the spheres is 40 N.

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The bullet and rifle both gain the same magnitude of momentum. The correct answer is option A.

In this case, the rifle and bullet are initially at rest and after firing, they move in opposite directions with equal magnitudes of momentum. Therefore, the momentum gained by the bullet is equal in magnitude and opposite in direction to that gained by the rifle, and hence the total momentum of the system remains constant.

The average force acting on the bullet and rifle during the firing is not necessarily the same, as it depends on factors such as the mass and acceleration of the bullet and rifle, and the duration of the firing. Similarly, the acceleration of the bullet and rifle can be different, depending on their masses and the forces acting on them during the firing. Finally, the kinetic energy gained by the bullet and rifle is not necessarily the same, as it depends on their masses and velocities after the firing. Hence, the correct answer is option A.

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