A prankster drops a water balloon from the top of a building. If the balloon is traveling at 29.1 m/s when it strikes a window ledge that is 1.5 m above the ground, how tall is the building? Neglect air resistance.

Answer:

a) the factor between the frequencies is      f ’/ f₀ = 9

b) the frequency increases        f ’= 9 f₀

c) So that the frequency is equal to the initial one      k ’= k₀ / 81

d) the torque constant must decrease

Explanation:

This is a simple harmonic motion, like angular velocity

       w = \(\sqrt{\frac{k}{I} }\)

where k is the torsion constant and I the moment of inertia of the flywheel.

Angular velocity and frequency are related

       w = 2π f

we substitute

       \(f= \frac{1}{2\pi } \sqrt{\frac{k}{I} }\)        (1)

We will use the subscript o for the system without change

      f = \(\frac{1}{2\pi }\)  \(\sqrt{\frac{k}{I_{o} } }\)

In the problem they indicate that the torsion constant remains constant, therefore we must analyze the moment of inertia, in general the flywheels are circular discs,

       I = ½ M R²

Let's find the change when reducing the radius r ’= r / 3

Let's use the density

       ρ = m ’/ V’

       m ’= ρ V’

disk volume is

       V = π r² e

suppose that the thickness is small and does not change, substitute

      m ’= ρ π\((\frac{r}{3}) ^{2}\) e = 1/9 m

Moment of inertia

     I ’= ½ m’ r’²

     I ’=\(\frac{1}{2}\) \(\frac{1}{9}\) m (\frac{r}{3}) ^{2} = 1/81 (½ m r²)

     I ’= 1/81 Io

we substitute in equation 1

    f ’= \(\frac{1}{2\pi }\) \sqrt{\frac{k}{I} }

    f ’= \frac{1}{2\pi }   \sqrt{\frac{81k}{Io} }

    f ’= 9 f₀

Let's analyze the questions

a) the factor between the frequencies is

        f ’/ f₀ = 9

b) the frequency increases

        f ’= 9 f₀

c) So that the frequency is equal to the initial one

      k ’= k₀ / 81

d) the torque constant must decrease

The kinetic energy of the truck is approximately 1,964,180 Joules. The kinetic energy of the car is approximately 250,003 Joules.

To calculate the kinetic energy of each vehicle, use the formula:

Kinetic Energy (KE) = 1/2 × mass × velocity²

Given the mass and velocity of each vehicle, plug in the values and calculate the kinetic energy.

For the truck:

Mass = 6,000 kg

Velocity = 92 km/h

= 92,000 m/3600 s

≈ 25.56 m/s

Using the formula:

KE = 1/2 × 6,000 kg × (25.56 m/s)²

Calculating the result:

KE = 1/2 × 6,000 kg × 655.3936 m²/s²

KE ≈ 1,964,180 Joules

Therefore, the kinetic energy of the truck is approximately 1,964,180 Joules.

For the car:

Mass = 1,200 kg

Velocity = 100 km/h

= 100,000 m/3600 s

≈ 27.78 m/s

Using the formula:

KE = 1/2 × 1,200 kg × (27.78 m/s)²

Calculating the result:

KE = 1/2 × 1,200 kg × 771.6884 m²/s²

KE ≈ 250,003 Joules

Therefore, the kinetic energy of the car is approximately 250,003 Joules.

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b) accelerate to the left as much more pressure is pulling it in that direction and on the right however , there is less force .

If the voltage of the battery is doubled, the compass needle would deflect by a greater angle than before.

If the voltage of the battery in the simple circuit is doubled, it would result in a stronger current flowing through the circuit. The increase in current would lead to a stronger magnetic field generated by the circuit.

When the switch is turned on, the flow of current through the wire creates a magnetic field around it. This magnetic field interacts with the magnetic compass, causing the needle to deflect. Doubling the voltage of the battery would increase the current flowing through the wire, thereby increasing the strength of the magnetic field generated by the circuit. As a result, the compass needle would experience a stronger magnetic force, leading to a larger deflection. If the voltage of the battery is doubled, the compass needle would deflect by a greater angle than before. Instead of the previous 5 degrees deflection to the west, the needle may deflect by a larger angle, depending on the exact relationship between the magnetic field strength and the angle of deflection.

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Answer:

6,400

Explanation:

i made sure  the other person was right and i got the same answer

The momentary current drawn by one bulb is 1.5 x 12.5A = 18.75A. we would expect to find a fuse rated at least 60A protecting the lighting system.

To determine the appropriate fuse for the lighting system in the popup camper, we need to calculate the total power dissipated by the 3 bulbs. If one bulb dissipates P watts, then 3 bulbs will dissipate 3P watts.
Given that one bulb dissipates P = 150 watts, then three bulbs will dissipate 3P = 450 watts.
Now, we know that when switching on any of the 3 lights, the bulb draws momentarily 50% more current than its usual dc current draw. This means that the current drawn by each bulb momentarily is 1.5 times its usual dc current draw.

Using the formula for power P=IV, where P is power, I is current, and V is voltage, we can find the momentary current drawn by one bulb as I= P/V. Assuming a voltage of 12V, the usual dc current drawn by one bulb is I=150/12 = 12.5A.  
To find the appropriate fuse, we need to ensure that it can handle the maximum current drawn by the 3 bulbs, which is 3 x 18.75A = 56.25A.  

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We can predict that the car full of riders will reach a speed of 28.0 m/s at the bottom of the first hill based on the principles of conservation of energy.

It is possible to predict the speed that a 2000 kg car full with riders will reach before it's ever placed on the track using the principles of conservation of energy. According to the law of conservation of energy, the total energy in a system remains constant, and it can be converted from one form to another.

To calculate the speed of the car at the bottom of the first hill, we can use the conservation of energy equation, which states that the initial potential energy (PEi) of the car is equal to the final kinetic energy (KEf) of the car.

PEi = KEf

\(mgh = 1/2mv^2\)

Where m is the mass of the car, g is the acceleration due to gravity, h is the height of the hill, and v is the velocity of the car.

Solving for v, we get:

\(v = \sqrt{(2gh)}\)

Using the given values of m = 2000 kg, h = 40 meters, and g = 9.81 m/s², we can calculate the velocity of the car at the bottom of the first hill:

\(v = \sqrt{(2gh)} = \sqrt{(2 \times 9.81 \;m/s^2 \times 40 m)} = 28.0 m/s\)

Therefore, we can predict that the car full of riders will reach a speed of 28.0 m/s at the bottom of the first hill based on the principles of conservation of energy.

In summary, by using the conservation of energy equation, we can predict the speed of the car at the bottom of the first hill based on its mass and the height of the hill. We found that the car full of riders will reach a speed of 28.0 m/s using this method.

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Force, displacement, momentum, velocity and acceleration are  vector quantity among them.

The term "vector quantities" refers to physical quantities that have clearly defined definitions for both magnitude and direction.

As an illustration, consider a boy riding his bike in a north-east direction at a speed of 30 km/h. As a result, we can see that in order to define velocity, we need to know both its magnitude and its direction. As a result, it symbolizes a vector quantity.

To define force, displacement, momentum, velocity and acceleration, we need both magnitude and direction. So, they are vector quantity.

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The molecules of nitrogen are in a sealed container holding 0.020 moles of ideal nitrogen gas, at a pressure of 1.5 atm and a temperature of 290 K is approximately 4.48 x 10^20 molecules of nitrogen.

To answer this question, we need to use the ideal gas law: PV = nRT
where P is the pressure in atmospheres, V is the volume in liters, n is the number of moles, R is the gas constant, and T is the temperature in Kelvin.
First, we need to convert the pressure to kilopascals:
1.5 atm = 1.5 * 101 kPa/atm = 151.5 kPa
Next, we can rearrange the ideal gas law to solve for n:
n = PV/RT
We have all the values we need, so we can plug them in:
n = (151.5 kPa) * (0.020 mol) / ((8.31 J/mol*K) * (290 K))
n = 0.000744 mol
Now that we know the number of moles of N2 gas in the container, we can use Avogadro's number to find the number of molecules:
1 mol N2 = 6.022 x 10^23 molecules N2
0.000744 mol N2 * (6.022 x 10^23 molecules N2/mol) = 4.48 x 10^20 molecules N2
So there are approximately 4.48 x 10^20 molecules of nitrogen in the container.

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Assuming that the box is not sliding off the bus, the forces exerted on it can be represented by the following diagram:

F

F: friction force

The friction force, represented by F in the diagram, acts in the opposite direction of the box's sliding motion. This force is caused by the friction between the box and the bus floor, and it is the only force present in the system. As the bus turns to the left, the box's sliding motion is directed to the right. The direction of the friction force then changes to the left, opposing the motion of the box and slowing it down until it stops.

Answer:

Cutting down trees

Explanation:

The roots of trees often hold settiments in place, thus removing these strong natural barriers makes it easier for erosion to occur.

In order to determine the probability that an electron can be detected in the middle one-third of a well region, we need to take into account the wave function and the boundary conditions.The wave function represents the probability density of finding the electron in a particular location within the well. The boundary conditions are determined by the geometry of the well, which can be rectangular, triangular, or other shapes.

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The bowling ball experiences the greater magnitude impulse during the collision since it is initially at rest and is given the momentum of the small ball which has a speed of 5m/s.

The impulse of the bowling ball can be calculated using the equation impulse = change in momentum = mvf - mvi, where m is the mass of the bowling ball, vf is its final velocity, and vi is its initial velocity.

Since the bowling ball is initially at rest (vi = 0), the impulse can be calculated as mvf = m(5m/s) = 5m^2/s. The impulse of the small ball can be calculated in the same way, giving an impulse of 5m^2/s. Therefore, the bowling ball experiences a greater magnitude impulse during the collision.

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The coefficient of kinetic friction between the pig and the slide is approximately 0.2258.

To solve this problem, we can use the concept of the work-energy theorem, which states that the work done on an object is equal to the change in its kinetic energy.

Let's assume the mass of the pig is 'm' and the coefficient of kinetic friction between the pig and the slide is 'μ'. When the pig slides down the frictionless slide, the work done on the pig is equal to the change in its gravitational potential energy.

When the pig slides down the frictionless slide, the work done is given by:

Work_frictionless = Change in potential energy

                 = m * g * h

where 'g' is the acceleration due to gravity and 'h' is the vertical height of the slide.

When the pig slides down the slide with friction, the work done is given by:

Work_with_friction = Change in kinetic energy + Work against friction

The change in kinetic energy is equal to the final kinetic energy minus the initial kinetic energy. Assuming the pig starts from rest, the initial kinetic energy is zero. Therefore:

Change in kinetic energy = 0.5 * m * v_final^2

where 'v_final' is the final velocity of the pig when it reaches the bottom of the slide.

The work against friction is given by:

Work_against_friction = μ * m * g * d

where 'd' is the distance traveled along the slide. The distance 'd' can be calculated using the trigonometric relationship between the angle of the slide and the distance traveled.

Given that the pig takes four times the time to slide down the frictionless slide, we can assume that the distance traveled on the frictionless slide is four times the distance traveled on the slide with friction.

Therefore, we have:

4 * d_frictionless = d_with_friction

Now, equating the work done on the pig for both cases:

m * g * h = 0.5 * m * v_final^2 + μ * m * g * d_with_friction

Since the angle of the slide is 16°, we can calculate the height 'h' and the distances 'd_frictionless' and 'd_with_friction' using trigonometry:

h = d_frictionless * sin(16°)

d_frictionless = d_with_friction * sin(16°)

Substituting these values into the equation:

d_with_friction * sin(16°) = 0.5 * v_final^2 + μ * g * d_with_friction

Simplifying the equation:

sin(16°) = 0.5 * v_final^2 / (g * (1 + μ))

Now, since we have the ratio of distances, we can also express 'd_with_friction' in terms of 'd_frictionless':

d_with_friction = (1/4) * d_frictionless

Substituting this into the equation:

(1/4) * d_frictionless * sin(16°) = 0.5 * v_final^2 + μ * g * (1/4) * d_frictionless

Now, we have two equations:

1. sin(16°) = 0.5 * v_final^2 / (g * (1 + μ))

2. sin(16°) = 2 * v_final^2 / (g * (1 + 4μ))

Since both equations are equal to sin(16°), we can set them equal to each other:

0.5 * v_final^2 / (g * (1 + μ)) = 2 * v_final^2 / (g * (1 + 4μ))

Simplifying the equation:

1 + μ = 8 + 32μ

Rearranging the equation:

31μ = 7

μ = 7/31

Therefore, the coefficient of kinetic friction between the pig and the slide is approximately 0.2258.

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Answer:

Where is the diagram????

Answer:

reflection

Explanation:

The unknown variables in the model equation for ball's motion include vertical distance traveled by the ball which is 31.86 m and the final velocity of the ball which is 25 m/s.

The given parameter;

The equations that model the motion of the ball is given as follows;

\(h = v_0_y + \frac{1}{2} gt^2\)

\(v_f = v_0_y + gt\)

All the unknown variables in the equations include;

The vertical distance traveled by the ball is calculated as follows;

\(h = \frac{1}{2} gt^2\\\\h = 0.5 \times 9.8 \times 2.55^2\\\\h = 31.86 \ m\)

The final velocity of the ball is calculated as follows;

\(v_f = 0 + 9.8(2.55)\\\\v_f = 25 \ m/s\)

Thus, the unknown variables in the model equation for ball's motion include vertical distance traveled by the ball which is 31.86 m and the final velocity of the ball which is 25 m/s.

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The arrangement of water molecules in Model 2 is characterized by hydrogen bonding. Each water molecule consists of two hydrogen atoms covalently bonded to one oxygen atom. In a covalent bond, the atoms share electrons.

The oxygen atom in a water molecule has a slightly negative charge, while the hydrogen atoms have a slightly positive charge. This polarity creates an attraction between adjacent water molecules. The attraction between water molecules are primarily caused by hydrogen bonding. Hydrogen bonding occurs when the positively charged hydrogen atom in one water molecule is attracted to the negatively charged oxygen atom in a neighbouring water molecule. These hydrogen bonds are relatively weak compared to covalent bonds but play a crucial role in the unique properties of water.

In a hydrogen bond between two adjacent water molecules, the atoms of separate molecules do not share electrons. Instead, the hydrogen bond forms due to the electrostatic attraction between the positively charged hydrogen atom of one water molecule and the negatively charged oxygen atom of another water molecule. This attraction is based on the difference in electronegativity between oxygen and hydrogen, which leads to a partial positive charge on the hydrogen atom and a partial negative charge on the oxygen atom. The hydrogen bonds between water molecules give rise to the high boiling point, surface tension, and cohesive properties of water.

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Answer:

A person that weighs 63.7 kg weighs 63.7 kg

Explanation:

Too complicated to explain.

Answer: 140.4 pounds

Explanation:

The correct answer is option B. It travels up and down. Transverse waves are characterized by the fact that they cause particles in the medium to move perpendicular to the direction of wave propagation.

Transverse waves are a type of wave that causes the particles of the medium to move up and down or side to side as the wave passes through them.

The other options are not right because:

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Answer:

A. freezing water widens the cracks in rocks

Explanation:

chemical weathering (from what i can tell anyways) is when water comes in contact with rocks and over time wears it down.

The time it takes for the cart to move between gate 1 and gate 2 tells you the duration of the impulse, which is the product of the force applied to the cart and the time it takes for the cart to move. This is because impulse is defined as the integral of force over time.

Impulse is the change in momentum of an object, and the amount of impulse depends on the force acting on the object and the amount of time the force is applied. Therefore, if the cart moves between gate 1 and gate 2 in a shorter amount of time, it means that the impulse on the cart is greater. Similarly, if the cart moves between gate 1 and gate 2 in a longer amount of time, it means that the impulse on the cart is less.Impulse is a quantity that describes the change in momentum of an object. It is defined as the force acting on an object multiplied by the time interval over which it acts. The equation for impulse is:I = FΔtwhere I is the impulse, F is the force, and Δt is the time interval.

Therefore, the time that the cart moves between gate 1 and gate 2 tells you about the impulse duration on the cart. If the cart moves between gate 1 and gate 2 in a shorter amount of time, it means that the impulse on the cart is greater. If the cart moves between gate 1 and gate 2 in a longer amount of time, it means that the impulse on the cart is less.

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The distance between the 7th and the tenth second is 29.4 m.

We know that we can have to formulate the information that has been given here so as to obtain a proper progression and this would help us to get the common difference of the progression that we are looking at.

Now we know that the progression would look something like; 4.9, 14.7, 24.5 ....

We can see that this is an arithmetic progression that has a common difference of 9.8.

U7 = a + (n - 1)d

a = first term

n = Number of terms

d = common difference

U7 = 4.9 + (7 - 1) 9.8

= 63.7

U10 = 4.9 + (10 - 1) 9.8

U10 = 93.1

Between the 7th and 10th seconds, we have;

93.1 - 63.7

= 29.4 m

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The dot product is 25, the angle is \(\theta = cos^{-1} \frac{25}{\sqrt{35} \times \sqrt{21}}\), the cross product is 1i + (-6)j + (-7)k, and the area of the parallelogram spanned by vectors A and B is \(\sqrt{86}\).

Given,

A = 5i + 3j + k

B = 4i + j + 2k

i. Dot Product (A · B):

The dot product of two vectors A and B is given by the sum of the products of their corresponding components.

\(A.B = (A_x \times B_x) + (A_y \times B_y) + (A_z \times B_z)\\A.B = (5 \times 4) + (3 \times 1) + (1 \times 2) \\= 20 + 3 + 2 \\= 25\)

ii. Angle between vectors A and B:

The angle between two vectors A and B can be calculated using the dot product and the magnitudes of the vectors.

\(cos\theta = (A.B) / (|A| \times |B|)\\\theta = \frac{1}{cos} ((A.B) / (|A| \times |B|))\\A = \sqrt{(5^2 + 3^2 + 1^2)} =\\ \sqrt{35}\\B = \sqrt{(4^2 + 1^2 + 2^2)} \\= \sqrt{21}cos\theta = \frac{(A.B) / (|A| \times |B|)\\\theta = \frac{1}{cos} \frac{25}{\sqrt{35} \times \sqrt{21}}}\)

iv. Cross Product (A × B):

The cross product of two vectors A and B is a vector that is perpendicular to both A and B and its magnitude is equal to the area of the parallelogram spanned by A and B.

\(A\times B = (A_y \timesB_z - A_z \timesB_y)i + (A_z \timesB_x - A_x \timesB_z)j + (A_x \times B_y - A_y \times B_x)k\\A\times B = ((3 \times 2) - (1 \times 1))i + ((1 \times 4) - (5 \times 2))j + ((5 \times 1) - (3 \times 4))k\\= 1i + (-6)j + (-7)k\)

Area of the parallelogram spanned by vectors A and B:

The magnitude of the cross product A × B gives us the area of the parallelogram spanned by A and B.

Area = |A × B|

Area of the parallelogram spanned by vectors A and B:

Area = |A × B| =

\(\sqrt{(1^2 + (-6)^2 + (-7)^2}\\\sqrt{1+36+49\\\\\sqrt{86}\)

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A tank filled with manure, water, and unused crop plant residues, but with minimal oxygen content, can be used for a process known as anaerobic digestion.

Microorganisms, especially methanogenic bacteria, break down the organic matter into simpler compounds such as fatty acids and sugars through a process called hydrolysis.

Now, let's examine the role of oxygen in anaerobic digestion. Therefore, minimizing the oxygen content in the tank is crucial for the success of the anaerobic digestion process.

To ensure that the tank has minimal oxygen content, it is usually sealed to prevent air from entering. Additionally, the contents of the tank are mixed regularly to promote the growth and activity of the methane-producing microorganisms while ensuring that oxygen levels remain low.

A tank filled with manure, water, and unused crop plant residues but with minimal oxygen content can be used for anaerobic digestion, a process that breaks down organic matter into biogas and digestate.

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Answer:

μ=1/5=0.2

Explanation:

using the formula

Fs=Fn*μ

Where

Fs is the static force

Fn = Normal force

μ= coefficient

so if Fn=25n

and it requires 5 n to start moving, means the max Fs is 5n

5=25μ

μ=5/25

μ=1/5=0.2

64 N force would be required to make a mass of 8 kg accelerate at

8m/s².

The term "force" is defined precisely in science. It is acceptable to refer to a force of this level as a push or a pull. An item does not "have in it" or "contain" a force. Another item applies force to another. The concept of a force does not apply only to living or non-living entities.

The newton (sign N) is the SI unit of force.

The fundamental formula for force is F = ma, where F represents force, m represents mass in kilograms, and a represents acceleration in m×s⁻². It is the second law of motion established by Newton.

Given that,

Acceleration (a) = 8m/s²

Mass (m) = 8 kg

Force (F) = ?

As we know,

Force= mass × acceleration

F = 8 kg × 8 m/sec²

F = 64 N

Therefore, force of 64 N is required to accelerate the body.

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Answer:

The kinetic energy is 16 joules.                        

Explanation:

Kinetic energy (E) is given by:

\( E = \frac{1}{2}mv^{2} \)

Where:

m: is the mass

v: is the speed

When the kinetic energy is 4 joules, the speed of the object is:

\( v_{1}^{2} = \frac{2E_{1}}{m} = \frac{8}{m} \)                         

Now, if the speed is increased twice then we have:

\( E_{2} = \frac{1}{2}mv_{2}^{2} = \frac{1}{2}m(2v_{1})^{2} = \frac{1}{2}m[4(\frac{8}{m})] = 16 J \)

Therefore, the kinetic energy is 4 times the initial value.  

I hope it helps you!                                

Answer:

No

Explanation:

The fastest recorded time for a person to run 100 metres is 9.58 seconds, which is the equivalent of 10.4 metres per second

Answer:

No

Explanation:

Humans can run as fast as 19.3m/s, using their full possible energy.