A person is swimming 1.1 m beneath the surface of the water in a swimming pool. A child standing on the diving board drops a ball into the pool directly above the swimmer. The swimmer sees the ball dropped from a height of 4.2 m above the water. From what height was the ball actually dropped?

The magnitude of the vector is approximately 35.85 m.

The angle that this vector makes with the positive x-axis is approximately 32 degrees.

To find the magnitude of the vector with components Ax=29 m and Ay=18 m, we use the Pythagorean theorem:

|A| = √(Ax^2 + Ay^2)

|A| = √(29^2 + 18^2)

|A| = √(841 + 324)

|A| = √1165

|A| =  34.13 m

To find the angle that this vector makes with the positive x-axis, we can use the inverse tangent function:

θ = tan^-1(Ay/Ax)

θ = tan^-1(18/29)

θ = 31.82 degrees

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The linear density of the string is 2.86 x 10^-5 kg/m.

What is linear density?

Linear density, also known as linear mass density, is a measure of the mass of a material per unit length. It is typically used to describe the properties of thin, elongated objects such as strings, wires, and fibers. The unit of measurement for linear density is typically kilograms per meter (kg/m) or grams per centimeter (g/cm). It is calculated by dividing the mass of the material by its length.

To find the linear density of the string, we need to use the relationship between the tension, linear density, and wave properties, which is given by the equation:

Tension = (linear density) * (wave speed)^2

where wave speed is the product of the frequency and wavelength of the wave.

Given the tension, period and wavelength, we can find the linear density using the following steps:

frequency = 1 / period = 1 / 3.82 x 10^-3 s = 261.9 Hz

wave speed = wavelength * frequency = 1.26 m * 261.9 Hz = 331.9 m/s

Tension = (linear density) * (wave speed)^2

944 N = (linear density) * (331.9 m/s)^2

linear density = Tension / (wave speed)^2 = 944 N / (331.9 m/s)^2 = 2.86 x 10^-5 kg/m

Therefore, the linear density of the string is 2.86 x 10^-5 kg/m.

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Answer:

Required energy Q = 231 J

Explanation:

Given:

Specific heat of copper C = 0.385 J/g°C

Mass m = 20 g

ΔT = (50 - 20)°C = 30 °C

Find:

Required energy

Computation:

Q = mCΔT

Q = 20(0.385)(30)

Required energy Q = 231 J

Answer:

is there more?

Explanation:

θ = 39.7º is the angle in degrees that the string makes with respect to the vertical using Newtons law.

In each exercise, we construct the equations at the equilibrium point using Newton's second law for the sphere. We'll assume that plate 1 is on the left for this exercise.

Y Axis

    Y= -W = 0 = W

X axis

       X= - F_{e2} + Tₓ = 0

Let's utilize trigonometry to determine the tension's component parts. We gauge the angle in relation to the vertical

        sin θ = Tₓ / T

        cos θ = T_{y} / t

        Tₓ = T sin θ

        T_{y} = T cos θ

Gauss's law can be used to determine the electric field of each leaf. Since a cylinder forms a Gaussian surface, the component of the field perpendicular to the cylinder's base is the one containing electric flow.

 F = ∫ E. dA

The flow is towards both sides of the plate in this instance, and the scalar product is reduced to the algebraic product.

F = 2E A = q_{int} / ε₀

let's use the concept of surface charge density

       σ = q_{int} / A

we substitute

       2E A = σ A /ε₀

         E = σ / 2ε₀

    T cos θ = mg

         - q σ₁ / 2ε₀  - q σ₂ /2ε₀  + T sinθ = 0

we introduce t in the second equations

         - q /2 ε₀  (σ₁ + σ₂) + (mg / cos θ) sin θ = 0

         mg tan θ = q /2ε₀   (σ₁ + σ₂)

         θ = tan -1 (q / 2ε₀ mg (σ₁ + σ₂)

data indicates the mass of 0.26 g = 0.26 10⁻³ kg

give the charge density on plate 2, suppose ab = 10 10⁻⁶ C / m²

let's calculate

        θ = tan⁻¹ (9.0 10⁻¹⁰ (30 + 10) 10⁻⁶ / (2  (6.25 10⁻¹² *0.26 10⁻³ 9.8))

        θ = tan⁻¹ 8.3 10⁻¹)

        θ = 39.7º

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Answer:

Centre of mass of any body is a point where all mass of a body is supposed to be concentrated

it lies in geometrical centre....

Answer:

Force = Mass × Acceleration

\({ \tt{force = 2250 \times 4.3}} \\ = { \tt{9675 \: newtons}}\)

Answer:

Explanation: 6000z

The minimum time necessary to pull out Margo is 2.64 seconds.

Given the data in the question;

There are two forces acting on Margo, as shown in the image below, the rope Tension acting upward and the force of gravity acting downward.

From Newton's second law of motion:

\(F = m*a\)  

where F is the Force acting on the body, m is the mass and a is the acceleration.

Also, \(F = T - mg\)

So, \(T - mg = ma\)

We know that the value of "g" gravitation due to gravity is \(9.81m/s^2\) and \(1Newton = 1 kg.m/s^2\)

We substitute in our values to find "a"

\(755 kg.m/s^2 - ( 70.0kg*9.81m/s^2) = (70kg * a )\)

\(755 kg.m/s^2 - 686.7 kg.m/s^2 = (70kg * a )\)

\(68.3kg.m/s^2 = (70kg * a )\)

\(a = \frac{68.3kg.m/s^2}{70kg}\)

\(a = 0.9757 m/s^2\)

Now, we set \(v_0 = 0\) to get the minimum time required

From the second equation of motion:

\(s = v_0t + \frac{1}{2} at^2\)

Since \(v_0 = 0\)

\(s = \frac{1}{2} at^2\)

We make time "t", the subject of the formula

\(t = \sqrt{\frac{2s}{a} }\)

We substitute in our values

\(t = \sqrt{\frac{2*3.4m}{0.9757m/s^2} }\)

\(t = 2.63995 s\\\\t = 2.64s\)

Therefore, the minimum time necessary to pull out Margo is 2.64 seconds.

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Answer:

Dams have negative impacts on the environment such as global warming, floods, displacement of local people, etc.

Explanation:

The construction of dams requires space and infrastructure which leads to the displacement of local people from their places.

Fishes cannot migrate from one water body to another due to blockage by the dams.

The construction of dams causes floods in the surrounding areas leading to the loss of habitat of native flora and fauna and causing diseases.

Because of the floods, the river is no longer flowing freely, the water becomes stagnant and the bottom of the reservoir becomes depleted of oxygen reducing the dissolved oxygen in the water and hampering aquatic life.

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The density of a thing is determined by the spacing between its constituent molecules. Less dense materials are those in which their molecules are dispersed and spaced farther apart.

On the reverse hand, items with molecules arranged closely together have higher densities.

The ability to float or sink is caused by this disparity in densities.

Because it has a lower density than liquid B, liquid A will be floating on top of it since it's lighter.

The mass-to-volume ratio is known as density. Due to the fact that they contain less debris, low population materials have a low mass cubic per centi meter.   Density can be defined as a substance's weight for a given quantity. Ground water has a density of 1 gram per millilitre, however this can vary.

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Relationship between Position-time graph and Velocity-time graph:

A positive slope of position corresponds to an increase in velocity.

A constant slope of position corresponds to a constant velocity.

A negative slope of position corresponds to a decrease in velocity.

A zero slope of position corresponds to a zero velocity.

Let us sketch the velocity-time graph as per the above rules.

Relationship between Velocity-time graph and Acceleration-time graph:

A positive slope of velocity corresponds to a positive acceleration.

A constant slope of velocity corresponds to a zero acceleration.

A negative slope of velocity corresponds to negative acceleration.

Let us sketch the acceleration-time graph as per the above rules.

Given data

*The given initial speed of the car is u = 0 m/s

*The given acceleration of the car is a = 1.15 m/s^2

*The given final speed of the car is v = 2.5 m/s

The formula for the distance travelled by the car is given by the kinematic equation of motion as

Substitute the known values in the above expression as

Hence, the distance travelled by the car is s = 2.71 m

Answer:The Moon has a smaller mass than the Earth. If you were to travel to the moon your weight would..

Explanation: It would decrease.

The Moon has a smaller mass than the Earth. If you were to travel to the moon your weight would decrease because the acceleration due by gravity on the moon is less than the acceleration due to gravity on the earth, therefore the correct answer is option C.

It can be defined as the force by which a body attracts another body towards its center as the result of the gravitational pull of one body and another.

In comparison to the Earth, the Moon is less massive. Your weight would drop if you traveled to the moon because the acceleration caused by gravity there is lower than that caused by gravity here on Earth.

As a result of the less gravity on the moon, the weight would decrease.

Thus, the correct answer is option C.

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The P-wave is capable οf traveling apprοximately 5,800 km deep, while the S-wave can travel apprοximately 800 km deep.

An earthquake prοduces a type οf seismic wave knοwn as an S-wave, which is alsο knοwn as a shear wave. It is a wave that carries energy and travels alοng the earth's surface, causing the grοund tο vibrate frοm side tο side.

The S-wave οnly travels thrοugh sοlid material, in cοntrast tο the P-wave (primary wave), which is an energy-carrying wave that travels directly thrοugh the earth. As a result, the S-wave is unable tο traverse gases οr liquids.

B. The fastest wave is the transverse wave, οr S-wave. This is as a result οf the S-wave's greater velοcity than the P-wave's, which is apprοximately 4.6 km/s in cοmparisοn tο the P-wave's apprοximately 7.2 km/s.

C. The mantle is the οnly place where the transverse wave (S-wave) can travel. This is as a result οf the S-wave's significantly lοwer velοcity than the P-wave's, which is apprοximately 4.6 km/s in cοmparisοn tο the P-wave's apprοximately 7.2 km/s.

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Answer:

pregnant

Explanation:

no interest at school

Answer: the final velocity and final velocity velocity can also be written as we It went to one route A. V. Of X. Care plus movie. Why is here? This is a vision number two. And this is a revision number one food equation and one into to get we want to and wrote. We now takes scared plus we not scared away helpless to And by and the horizontal and the vertical component which are we know scare X is equal to we not cost it and we're not scared by going to we not scientific putting these value. Immigration number three. We get we will too. Are we not scared? I got scared to to less. We not scare Science square theater plus two. Why? So this we equal to he went to work and rude. We're not scared people to got scared he to less science security theater Last two. A. Y. Sure we get we s we're not scared into I. Plus to A Y. So we is able to. And road we now scared. Plus two. Am I. So this is a vision number four. And we are given me an artist 14 m purse again. And why he has given us. Uh huh. three m. So we can we find out by putting this value innovation number for the disk 14 scared. Uh huh. Plus To into -9.8 into three. We get to be It will do 11.7. Me did last

Explanation:

Answer:

Use of telemetry and radar astronomy

Explanation:

An astronomical Unit (AU) is a unit of measuring distances in outer space, which is based on the approximate distance between the earth and the Sun.

After several years of trying to approximate the distance between the Sun and the Earth using several methods based on geometry and some other calculations, advancements in technology made available the presence of special motoring equipment, which can be placed in outer space to remotely monitor and measure the position of the sun.

The use of direct radar measurements to the sun (radar astronomy) have also made the determination of the AU more accurate.

A standard radar pulse of known speed is sent to the Sun, and the time with which it takes to return is measured,  once this is recorded, the distance between the Earth and the Sun can be calculated using

distance = speed X time.

However, most of these means have to be corrected for parallax errors

The tension in the strings are 31.47 and 19.25 N respectively.

Mass of the block, m = 3 kg

From the figure, consider the vertical components,

T₁ sin45° + T₂ sin30° = mg

(T₁/√2) + (T₂/2) = 3 x 9.8 = 29.4

Also, consider the horizontal components,

T₁ cos45° = T₂ cos30°

T₁/√2 = T₂ x√3/2

T₁ = T₂ x √3/2 x √2

So,

T₁ = 0.612T₂

Applying in the first equation,

(T₁/√2) + (T₂/2) = 29.4

(0.612T₂/1.414) + 0.5T₂ = 29.4

0.434 T₂ + 0.5 T₂ = 29.4

0.934 T₂ = 29.4

Therefore, the tension,

T₂ = 29.4/0.934

T₂ = 31.47 N

So, the tension,

T₁ = 0.612 T₂

T₁ = 0.612 x 31.47

T₁ = 19.25 N

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Explanation:

Let

T

be the tension of the cable and m

g

be the force of gravity. If the upward direction is positive, then Newton’s second law is T−mg=ma, where a is the acceleration. Thus, the tension is T=m(g+a). We use constant acceleration kinematics (Table 2-1) to find the acceleration (where v=0 is the final velocity, v

0

=−12m/s is the initial velocity, and y=−42m is the coordinate at the stopping point). Consequently, v

2

=v

0

2

+2ay leads to

a=−

2y

v

0

2

=−

2(−42m)

−12m/s

=1.71m/s

2

We now return to calculate the tension:

T=m(g+a)

=(1600kg)(9.8m/s

2

+171m/s

2

)

=1.8×10

4

N

According to the question: the net force on the roof is 8.45 kN.

The vector sum of the forces operating on a particle of object is known as the net force in mechanics. The original forces' impact on the motion of the particle is replaced by the net force, which is a single force. In accordance with Newton's second rule of motion, it causes the particle to accelerate at a rate equal to the sum of all those actual forces.

The net force on the roof is equal to the air pressure multiplied by the surface area of the roof. The air pressure is equal to the density of the air multiplied by the wind speed squared. Therefore, the net force on the roof can be calculated as follows:
Force = (density x wind speed²) x surface area
Force = (1.29 kg/m² x (40 m/s)²) x (250 cm²)
Force = 8.45 kN
Therefore, the net force on the roof is 8.45 kN.

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I don't know if there is other given information that's missing here, so I'll try to fill in the gaps as best I can.

Let m be the mass of the object and v₀ its initial velocity at some distance x up the plane. Then the velocity v of the object at the bottom of the plane can be determined via the equation

v² - v₀² = 2 a x

where a is the acceleration.

At any point during its motion down the plane, the net force acting on the object points in the same direction. If friction is negligible, the only forces acting on the object are due to its weight (magnitude w) and the normal force (mag. n); if there is friction, let f denote its magnitude and let µ denote the coefficient of kinetic friction.

Recall Newton's second law,

∑ F = m a

where the symbols in boldface are vectors.

Split up the forces into their horizontal and vertical components. Then by Newton's second law,

• net horizontal force:

∑ F = n cos(θ + 90º) = m a cos(θ + 180º)

→  - n sin(θ) = - m a cos(θ)

→  n sin(θ) = m a cos(θ) ……… [1]

• net vertical force:

∑ F = n sin(θ + 90º) - w = m a sin(θ + 180º)

→   n cos(θ) - m g = - m a sin(θ)

→   n cos(θ) = m (g - a sin(θ)) ……… [2]

where in both equations, a is the magnitude of acceleration, g = 9.80 m/s², and friction is ignored.

Then by multiplying [1] by cos(θ) and [2] by sin(θ), we have

n sin(θ) cos(θ) = m a cos²(θ)

n cos(θ) sin(θ) = m (g sin(θ) - a sin²(θ))

m a cos²(θ) = m (g sin(θ) - a sin²(θ))

a cos²(θ) + a sin²(θ) = g sin(θ)

a = g sin(θ)

and so the object attains a velocity of

v = √(v₀² + 2 g x sin(θ))

If there is friction to consider, then f = µ n, and Newton's second law instead gives

• net horizontal force:

∑ F = n cos(θ + 90º) + f cos(θ) = m a cos(θ + 180º)

→   - n sin(θ) + µ n cos(θ) = - m a cos(θ)

→   n sin(θ) - µ n cos(θ) = m a cos(θ) ……… [3]

• net vertical force:

∑ F = n sin(θ + 90º) + f sin(θ) - w = m a sin(θ + 180º)

→   n cos(θ) + µ n sin(θ) - m g = - m a sin(θ)

→   n cos(θ) + µ n sin(θ) = m g - m a sin(θ) ……… [4]

Then multiply [3] by cos(θ) and [4] by sin(θ) to get

- n sin(θ) cos(θ) + µ n cos²(θ) = - m a cos²(θ)

n cos(θ) sin(θ) + µ n sin²(θ) = m g sin(θ) - m a sin²(θ)

and adding these together gives

µ n (cos²(θ) + sin²(θ)) = m g sin(θ) - m a (cos²(θ) + sin²(θ))

µ n = m g sin(θ) - m a

m a = m g sin(θ) - µ n

m a = m g sin(θ) - µ m g cos (θ)

a = g (sin(θ) - µ cos (θ))

and so the object would instead attain a velocity of

v = √(v₀² + 2 g x (sin(θ) - µ cos (θ)))

Answer:

whatttttttttttttttttttttttttttt are the items we have to classify into simple machines and compound machine

The electron number cannot be used instead because electrons can be removed from or added to an atom (option C)

The element of an atom is determined by its proton count, while the electron count can exhibit variability. Take, for instance, a sodium atom, which encompasses 11 protons and 11 electrons. However, it has the capacity to relinquish one electron, transforming into a sodium ion housing only 10 electrons.

This occurs due to the relatively loose binding of electrons to the nucleus, enabling their removal through the influence of an electric field or alternative mechanisms.

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Answer:

A

Explanation:

To answer this, we can use process of elimination.

B: This question states that all matter has gravity. This is not correct. All matter is *effected* by gravity, but we do not have gravity inside of us.

C: If this were the case, we would all be floating off into space.

D: Same issue as question B.

I hate to leave you answer less, but there isn't even a question here to answer.

(a) The total displacement is zero

(b) The average velocity from the grocery store to the post office is 11 m/s.

(c) The average speed of the entire trip is 9.71 m/s

The given parameters;

(a) The total displacement is the change in his position;

Displacement = forward position - backward position

Displacement = 510 m - 510 m = 0

(b) The average velocity from the grocery store to the post office;

Displacement = 510 m - 180 m = 330 m

Time of motion from his home to grocery store, = (60 - 45) = 15 s

Time of motion to post office = 45 s - 15 s = 30 s

\(average \ velocity = \frac{330}{30} = 11 \ m/s\)

(c) The average speed of the entire trip;

total distance = 510 m forward + 510 m backward = 1020 m

total time = 45 s + 60 s = 105 s

\(average \ speed = \frac{1020}{105} \\\\average \ speed = 9.71 \ m/s\)

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Answer:

10 m/s

Explanation:

Answer:  Therefore, the change in entropy when 536 g of gold are melted is 0.132 J/K.

Explanation:  To calculate the change in entropy when 536 g of gold are melted, we need to know the entropy of fusion of gold and the temperature at which it melts.

The entropy of fusion of gold is 2.35 J/g·K, and the melting point of gold is 1064 °C or 1337 K.

The change in entropy when gold is melted can be calculated using the formula:

ΔS = Q/T

where ΔS is the change in entropy, Q is the heat absorbed during the process, and T is the temperature at which the process occurs.

The heat absorbed when gold is melted can be calculated using the formula:

Q = m × ΔH_fus

where m is the mass of the gold and ΔH_fus is the enthalpy of fusion of gold, which is 64.9 kJ/mol.

Converting the mass of gold to moles:

536 g / 196.97 g/mol = 2.72 mol

The heat absorbed by the gold when it is melted is:

Q = 2.72 mol × 64.9 kJ/mol = 176.2 kJ

Finally, we can calculate the change in entropy:

ΔS = Q/T = 176.2 kJ / 1337 K = 0.132 J/K

The skater's final angular velocity is approximately 9.86 rad/s.

The skater's final angular velocity can be calculated using the principle of conservation of angular momentum. The equation for angular momentum is given by:

L = Iω

where L is the angular momentum, I is the moment of inertia, and ω is the angular velocity.

Initially, the skater has an angular momentum of:

L_initial = I_initial * ω_initial

Substituting the given values:

L_initial = 2.12 kg m² * 3.25 rad/s

The skater's final angular momentum remains the same, as angular momentum is conserved:

L_final = L_initial

The final moment of inertia is given as 0.699 kg m². Therefore, the final angular velocity can be calculated as:

L_final = I_final * ω_final

0.699 kg m² * ω_final = 2.12 kg m² * 3.25 rad/s

Solving for ω_final:

ω_final = (2.12 kg m² * 3.25 rad/s) / 0.699 kg m²

Hence, the skater's final angular velocity is approximately 9.86 rad/s.

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