A 65.25 kg person holding a steel ball stands motionless on a frozen lake.
The person then throws the ball, which propels the person at 1.25 m/s to the
right and the ball 4.05 m/s to the left. If the initial momentum of the system is
zero, what is the mass of the steel ball?

Answer: you have to divide and multiple fam

Explanation:

Since Two stars M1 and M2 of equal mass make up a binary star system.  their orbital speed is  2.69E4 m/s.

The orbital period of a binary star system is given by the equation:

T = 2 * pi * sqrt(a³ / (G * (M1 + M2)))

where T is the orbital period, a is the semi-major axis of the orbit (half of the distance between the two stars at their closest approach), G is the gravitational constant, and M1 and M2 are the masses of the two stars.

Substituting the given values into this equation, we get:

3.20 days = 2 * pi * sqrt(a³ / (6.67E-11 m³ kg^⁻¹ s^⁻² * (5.45 sm * 1.99E30 kg/sm + 5.45 sm * 1.99E30 kg/sm)))

Solving for the semi-major axis, we find that a = 2.11E11 m.

The speed of each star in the orbit can be found using the equation:

v = sqrt(G * (M1 + M2) / a)

Substituting the values we have calculated, we find that v = 2.69E4 m/s. This is the speed of each star in the orbit.

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Answer:

-17.89 m/s  (or 17.89m/s downward)

edit:

if we round this to the nearest whole number, the answer is -18m/s (or 18m/s downward)

Explanation:

recall that one of the equations of motion can be expressed as:

v² = u² + 2as,

where

v = final velocity = given as 20 m/s

u = initial velocity = given as 7.0 m/s

a = acceleration. Since it is freefalling downwards, the acceleration it would experience would be the acceleration due to gravity = -9.81 m/s²

s = displacement (we are asked to find)

simply substitute the known values into the equation:

v² = u² + 2as

20² = 7² + 2(-9.81)s

400 - 49 = -19.62s

-19.62s = 351

s = 351/-19.62

s = -17.8899

s = -17.89 m/s (or -18 m/s rounded to nearest whole number)

A watermelon is thrown down from a skyscraper with a speed of v7.0 m/s. It lands with an impact velocity of 20 m/s. We can ignore air resistance.

What is the displacement of the watermelon?

Answer: -18

Answer:

0.025 m

Explanation:

From the question,

Applying Hook's law

F = ke................... Equation 1

Where F = Force, k = spring constant of the scale, e = maximum distance at which the spring will compress.

make e the subject of the equation

e = F/k....................... Equation 2

Given: F = 10 N, e = 395 N/m

Substitute these values into equation 2

e = 10/395

e = 0.025 m

Magnetic particle separation is a powerful tool for separating particles based on their velocities in a magnetic field, and it has significant practical applications in various scientific and technological fields.

To separate particles of different velocities moving in a magnetic field, one can utilize a technique called magnetic field separation or magnetic particle separation.

This method takes advantage of the fact that charged particles moving in a magnetic field experience a force called the Lorentz force, which acts perpendicular to both the velocity vector and the magnetic field.

The basic principle behind magnetic particle separation is to apply a magnetic field perpendicular to the motion of the particles. The Lorentz force will then cause the particles to curve in different directions based on their velocities and charges.

By carefully controlling the strength and direction of the magnetic field, particles with different velocities can be steered onto different paths and separated.

One common approach to achieve magnetic particle separation is to use a device called a magnetic separator. This device typically consists of a strong magnet or a series of magnets arranged to create a uniform magnetic field.

The particles to be separated are injected into a chamber or a flow system where the magnetic field is applied. As the particles move through the magnetic field, they experience the Lorentz force and deviate from their original trajectory. The degree of deviation depends on their velocity and charge.

By carefully adjusting the magnetic field strength, particle size, and other parameters, it is possible to optimize the separation process and achieve effective separation of particles with different velocities. This technique has various applications in fields such as biomedical research, environmental monitoring, and materials science.

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a) The value of t u = 140/t`b.

b) The y position of the cannonball at the time t is  55.5 mc.

c) The initial speed of the projectile is 52.4 m/s.

Given that a cannonball is fired horizontally from the top of a cliff. The cannon is at height H = 55.5 m above ground level, and the ball is fired with initial horizontal speed u. The projectile lands at a distance D = 140 m from the cliff. Assume that the cannon is fired at time t = 0 and that the cannonball hits the ground at time t.Now,We have to find the value of t, y position of the cannonball at the time t and the initial speed of the projectile.

a. To find the value of t:Here, we have to use the formula of distance

i.e.,S = ut + (1/2)gt², Where S = 140 m, u = u and g = 9.8 m/s².Hence,140 = u×t ………..(1)We know that, time taken by the cannonball to hit the ground can be calculated as,`(2H)/g`

Since the height of the cannon from the ground is 55.5m, the total height of the cannonball from the ground is

(2H) = 2 × 55.5

= 111 m`2H/g

= 111/9.8`

= 11.32653 s

From equation (1),u×t = 140u = 140/t

Therefore, `u = 140/t`b.

b)To find the y position of the cannonball at the time t:

Here, we have to use the formula of height i.e.,y = u×t – (1/2)gt²,

Where, y = height of the cannonball at time t, u = 140/t, t = time taken by the cannonball to hit the ground and g = 9.8 m/s².

We have already calculated the time taken by the cannonball to hit the ground in the previous step.`

y = 140 - (1/2) × 9.8 × t²`

On substituting the value of t as `t = 11.32653`,

we get,y = 140 - (1/2) × 9.8 × (11.32653)²= 55.5 mc.

c)  To find the initial speed of the projectile:

To calculate the initial speed of the projectile, we need to use the formula of range of projectile

.i.e.,R = u²sin2θ/g

Where R = 140 m, g = 9.8 m/s², θ = 0° (horizontal)

u² = R × g/sin2θ

   = 140 × 9.8/sin0°  

   = 2744m²/s²u  

   = \(\sqrt(2744m^2/s^2)\)

   = 52.4 m/s

Hence, the initial speed of the projectile is 52.4 m/s.

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Answer:

The angle between the electric field lines and the equipotential surface is 90 degree.

Explanation:

The equipotential surfaces are the surface on which the electric potential is same. The work done in moving a charge from one point to another on an equipotential surface is always zero.

The electric field lines are always perpendicular to the equipotential surface.

As

\(dV = \overrightarrow{E} . d\overrightarrow{r}\\\\\)

For equipotential surface, dV = 0 so

\(0 = \overrightarrow{E} . d\overrightarrow{r}\\\\\)

The dot product of two non zero vectors is zero, if they are perpendicular to each other.

Answer:

3380 m

Explanation:

Wind is the stream of air rushing in to fill an area of low pressure. Winds are  generated by the differential distribution of temperature resulting in a pressure difference.

The natural movement of air or other gases in relation to a planet's surface is referred to as wind. There are many different sizes of winds, ranging from thunderstorm flows that last only a few minutes to local breezes.

Large-scale atmospheric circulation is primarily brought on by the planet's rotation and the difference in temperature between the equator and the poles (Coriolis effect).

Thermal low circulations over topography and high plateaus can cause monsoon circulations in the tropics and subtropics. Local winds can be defined in coastal regions by the sea breeze/land breeze cycle; in regions with varying terrain, mountain and valley.

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After 42 minutes, there are 203 x \(10^{20\) atoms remaining of the radioactive substance.

To determine the number of atoms remaining after a certain amount of time has passed, we can use the formula for radioactive decay:

N(t) = N0 * \((1/2)^{(t / T)\),

where:

N(t) = number of atoms remaining at time t,

N0 = initial number of atoms (812 x  \(10^{20\) atoms),

T = half-life of the substance (21 minutes), and

t = time that has passed.

Let's calculate the number of atoms remaining after a given time.

Suppose the time passed is t = 42 minutes (twice the half-life).

N(t) = 812 x  \(10^{20\) * \((1/2)^{(42 / 21)\)

N(t) = 812 x  \(10^{20\) * \((1/2)^2\)

N(t) = 812 x  \(10^{20\) * 1/4

N(t) = 203 x  \(10^{20\) atoms.

So, after 42 minutes, there are approximately 203 x \(10^{20\) atoms remaining of the radioactive substance.

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The change in internal energy of the engine is -50 joule. Hence, option (B) is correct.

Energy cannot be created or destroyed, according to the law of conservation of energy. However, it is capable of change from one form to another. An isolated system's total energy is constant regardless of the types of energy present.

The absorb energy: Q = 600 Joule

Work done: W = 650 Joule.

Let, the change in internal energy of the engine= dU.

According to conservation of energy:

The absorb energy =  change in internal energy  + Work done

Q = dU + W

dU = Q - W

= 600 joule - 650 joule

= - 50 joule.

Hence, the change in internal energy of the engine is -50 joule.

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Answer:

the object's weight changes but its mass stays the same

Answer:

the object's weight changes but its mass stays the same

Explanation:

100% correct

It is not recommended to fire a gun straight up into the air.

When a bullet is fired into the air, it will eventually come down and can pose a danger to people and property below. The bullet can still be lethal when it reaches the ground, especially if it lands on a hard surface or hits someone directly.

Additionally, firing a gun in a residential area can be illegal and can result in legal consequences. In general, guns should only be fired in designated shooting ranges or in self-defense situations where there is an immediate threat to life. It is important to handle firearms responsibly and follow all safety guidelines to prevent accidents and injuries.

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The speed of the artillery shell when it hits its target is 100 m/s.

Given:

Initial vertical displacement (y) = 200 m

Vertical displacement at 100 m in the air (y') = 100 m

Final velocity in the vertical direction (vy') = 0 m/s (at the highest point of the trajectory)

Using the equation for vertical displacement in projectile motion:

y' = vy^2 / (2g),

where g is the acceleration due to gravity (approximately 9.8 m/s^2), we can solve for the initial vertical velocity (vy).

100 m = vy^2 / (2 * 9.8 m/s^2),

vy^2 = 100 m * 2 * 9.8 m/s^2,

vy^2 = 1960 m^2/s^2,

vy = sqrt(1960) m/s,

vy ≈ 44.27 m/s.

Now, since the horizontal motion is independent of the vertical motion, the horizontal speed of the shell remains constant throughout its trajectory. Therefore, the speed of the shell when it hits its target is 100 m/s.

Hence, the speed of the artillery shell when it hits its target is 100 m/s.

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Answer:

option 5

Explanation:

because all u do is have to add them up

Answer:

\(v_1 = 301 Hz\)

\(v_2 = 601 \ \ Hz\)

\(v_3 = 901 \ Hz\)

Explanation:

From the question we are told that

     The  length of the string is  \(l = 90 \ cm = 0.9 \ m\)

     The mass of the string is  \(m_s = 3.5 \ g =0.0035 \ kg\)

     The  distance  from the bridge to the support post \(L = 62 \ c m = 0.62 \ m\)

    The tension is \(T = 540 \ N\)

Generally the frequency is mathematically represented as

        \(v = \frac{n}{2 * L } [\sqrt{ \frac{T}{\mu} } ]\)

Where n is and integer that defines that overtones

i.e  n =   1 is for fundamental frequency

      n =  2   first overtone

       n =3   second overtone

Also  \(\mu\) is the linear density of the string which is mathematically represented as

           \(\mu = \frac{m_s}{l}\)

=>        \(\mu = \frac{0.0035 }{ 0.9 }\)

=>       \(\mu = 0.003889 \ kg/m\)

So for   n = 1

     \(v_1 = \frac{1}{2 * 0.62 } [\sqrt{ \frac{ 540}{0.003889} } ]\)

     \(v_1 = 301 \ Hz\)

So for  n =  2

     \(v_2 = \frac{2}{2 * 0.62 } [\sqrt{ \frac{ 540}{0.003889} } ]\)

     \(v_2 = 601 \ Hz\)

So for  n =  3

     \(v_3 = \frac{3}{2 * 0.62 } [\sqrt{ \frac{ 540}{0.003889} } ]\)

     \(v =901 \ Hz\)

The distance travelled by the vehicle around the circular track is 1,052.4 m.

The distance travelled by the vehicle in one complete cycle is calculated by using the following equation as show below.

d = 2πr

d = πd

Where;

In one complete cycle, the  vehicle will travel the circular track only once.

d = π(335 m)

d = 1,052.4 m

Thus, the distance travelled by the vehicle around the circular track is a function of the diameter of the circular track.

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The complete question is below:

A vehicle, starting from rest, accelerates on a circular track with a 335m diameter. What is the distance travelled by the vehicle when it makes one complete cycle?

Answer: 4.94cm³

Explanation:

Data;

ρ = 1.59g/cm³

mass = 7.85g

volume = ?

density = mass / volume

ρ = m / v

v = m / ρ

v = 7.85 / 1.59

v = 4.94cm³

Answer:

V1 = 5 m/s

t1 = 200 m / 5 m/s = 40 s

Likewise t2 = 70 s

S = 200 m + 280 m = 480 m

T = t1 + t2 = 110 s

Vav = 480 m / 110 s = 4.36 m/s

Given:

Velocity of water waves = 1.8 m/s

Wavelength = 4.4 m

Let's find the frequency the water waves meet th doc.

To find the frequency, apply the formula:

Where:

v is thevelocity = 1.8 m/s

λ is the wavelength = 4.4 m

f is the frequency

Thus, we have:

Therefore, the frequency is 0.409 Hz

ANSWER:

0.409 Hz.

Answer:

m=image distance÷object distance

Answer:

the answer is magnetic

Answer:

The time to achieve a grain diameter of 7.3× 10⁻² mm is 477 minutes

Explanation:

We need to first solve for K

Given that:

grain diameter exponent (n) = 2.2

grain diameter (d) = 7.3 × 10⁻² mm = 7.3× 10⁻⁵ m

d₀ =  2.4 × 10⁻² mm =  2.4 × 10⁻⁵ m

t = 500 min

then from k = \(d^{n} -do^{n} /t\)

= 7.48 × 10⁻¹³ m/min

= \(\frac {(7.3 * 10^{-5} )^{2.2}* (2.4*10^{-5} )^{2.2}}{500}\) = 1.44×10⁻¹²

From K we can determine the time required based on the desired diameter

grain diameter (d) =  7.3 × 10⁻² mm = 7.3× 10⁻⁵ m

so t =\(d^{n} -do^{n} /k\)  = \(\frac {(7.3 * 10^{-5} )^{2.2}* (2.4*10^{-5} )^{2.2}}{1.4*10^{-12} }\) =503.08 = 504 min approximately.

Answer:

a) Connect a series resistance of 8,47 ohms

b)14,16 [A]

c) r = 10,96 ohms

Explanation:

My blower requires 120 (v) then, I have to connect a series resistor to make the nominal 240 (v) of the European voltage outlet drop to 120 (V) but at the same time keep the level of current to operate my blower

In America

P = V*I

1700 (w) = 120*I

I = 1700/120 [A]

I = 14,16 [A]        current needed for the blower

In Europe

120 (v)  (the drop of voltage I need) when a current of 14,16 passes through to series  resistor is

V = I*R          120 = 14,16* R         R = 8,47 ohms

c) P = I*r²

1700 (w) = 14,16 (A) * r²

r² = 120,06

r = 10,96 ohms

Approximately 0.123 kg of liquid water at 26 degrees Celsius would be needed to melt 41 grams of ice.

To calculate the minimum amount of liquid water required to melt 41 grams of ice at 0°C, we need to consider the energy required for the phase change from solid to liquid, which is known as the specific heat of fusion of ice.

The energy required to melt 1 kg of ice is 3.33×105 J/kg.

Therefore, the energy required to melt 41 grams of ice is (3.33×105 J/kg) × (41/1000) kg = 13653 J.

To calculate the amount of liquid water required, we use the specific heat capacity of water, which is 4180 J/kg/°C.

Assuming the initial temperature of water is 26°C, the amount of water needed can be calculated as (13653 J) ÷ (4180 J/kg/°C) ÷ (26°C) = 0.123 kg or approximately 123 ml of water.

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Given that the wavelength is

The speed of rays is

We have to find the frequency.

The formula to calculate frequency is

Substituting the values, the frequency will be

Answer:

300

Explanation Hope I'm not wrong.

The most likely true statement about asynchronous communication is that it is helpful when employees work across multiple time zones.

Asynchronous communication refers to a mode of communication where participants do not need to be present or engaged simultaneously. Instead, they can send and receive messages at their convenience.In today's globalized society, businesses often have teams distributed across different geographical locations and time zones. Asynchronous communication becomes invaluable in such scenarios as it allows team members to collaborate effectively without the constraints of real-time interactions. By utilizing tools like email, project management platforms, or messaging apps, individuals can communicate and exchange information regardless of their location or the time differences.

Asynchronous communication also offers benefits such as flexibility and increased productivity. Team members have the freedom to work at their own pace and prioritize tasks accordingly. It provides opportunities for thoughtful and well-crafted responses, as individuals can take time to gather information or reflect on complex matters before replying.While asynchronous communication is advantageous for teams operating across multiple time zones, it does not rely on all employees working in the same time zone. In fact, it is designed to accommodate diverse schedules and allow individuals to collaborate efficiently despite their varying work hours.

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Answer: 1968 cm3

Explanation: You first need to convert all of your dimensions to the same units.

240 mm = 24 cm

20.5 cm = 20.5 cm

0.04 m = 4 cm

Then volume is Length x width x height = 24 cm x 20.5 cm x 4 cm =