One end of a horizontal string is attached to a vibrating blade, and the other end passes over a pulley as in Figure (a). A sphere of mass 1.00 kg hangs on the end of the string. The string is vibrating in its second harmonic. A container of water is raised under the sphere so that the sphere is completely submerged. In this configuration, the string vibrates in its second harmonic (or the third normal mode of oscillation) as shown in Figure (b). What is the radius of the sphere?

The gravitational force between two students is 5.336*10^-8 N.

According to universal gravitational law, the force acting on two bodies is given by the formula = F = (G *m1*m2)/r^2

Here mass of one student =m1=75kg,another student m2=54kg

Distance of separation =0.45m, r =0.45/2=0.225m

Force = 6.67*10^-11 (75*54)/(0.225)^2

F=5.336*10^-8 N

The force between two students is 5.336*10^-8 N.

Learn more about gravitational force,

https://brainly.com/question/72250

Answer:

C

Explanation:

C - No heat enters or leaves the gas.

Adiabatic Expansion can be defined be saying, it is an expansion in which no heat is added to or no heat is subtracted from the air. This lack of addition or subtraction, cools during the expansion because of the work that would be done by the air. And as such, we can say that No heat enters the gas, and no heat leaves the gas in the same manner.

I hope that's clear enough

The net force on q1 is 9.94 N.

From Coulomb's Law, the force between two point charges is given by:

where;

All the charges have the same charge and magnitude and are separated by the same distance.

The force between q1 and q2 is:

F12 = (9 * 10⁹ N * m²/C²) * (-2.35 x 10⁻⁶ C)² / (0.100 m)²

F12 = 4.97 N

The positive sign indicates that the force is repulsive

Similarly, the force between q2 and q3 is:

(9 * 10⁹ N * m²/C²) * (-2.35 x 10⁻⁶ C)² / (0.100 m)²

F12 = 4.97 N

The positive sign indicates that the force is repulsive

The net force on q1 will be:

Fnet = F12 + F23

Fnet = 4.97 N + (4.97)

Fnet = 9.94 N

Learn  more about net force at: https://brainly.com/question/14361879

#SPJ1

electromagnetic waves can travel not only through air and solid materials, but also through the vacuum of space.

hope it helps...!!!

The difference in how economic decisions are made in a mixed economy and a market economy is that in a mixed economy both the government and consumers make economic decisions while in a market economy, consumers make all economic decisions.

In a mixed economy, economic decisions are made by both the government and consumers. The government plays a significant role in regulating and influencing economic activities through policies, regulations, and interventions.

In market economy, economic decisions are primarily made by consumers. The market forces of supply and demand dictate the allocation of resources, production levels, and pricing. Consumers have the freedom to choose what to buy and sell, and their purchasing decisions ultimately drive the production and distribution of goods and services.

Read more about Economic Decisions

brainly.com/question/30296708

#SPJ1

Answer:

a

Explanation:

the answer is a because it is feasible

Answer:

conductor

Explanation:

Its easier for electricty to flow through a conductor as it has free electrons

Answer:

1a) The direction to throw the boot is directly away from the closest shore.

2b) The magnitude of the force that the thrown boot exerts on the engineer = 391 N

3c) Time taken to reach shore = 8.414 s

Explanation:

1a) Newton's third law of motion explains that for every action, there is an equal and opposite reaction.

The force generated by throwing the boot in one direction is exerted back on the engineer as recoil in the opposite direction.

Hence, the best direction to throw the boot is opposite the direction that the engineer intends to move towards.

2b) Just as explained in (1a) above, the force exerted in one direction always has a reaction of the same magnitude in the opposite direction.

Hence, the force exerted by the boot on the engineer is equal to the force exerted by the engineer on the boot = 391 N.

3c) For this part, we analyze the total motion of the engineer.

The force exerted by the boot on the engineer initially accelerates the engineer until the engineer reaches a constant velocity dictated the impulse of the initial force (since impulse is equal to change in momentum), this constant velocity then takes the engineer all the way to shore, since the ice surface is frictionless.

The weight of the engineer = W = 588 N

W = mg

Mass of the engineer = (W/g) = (588/9.8) = 60 kg

Force exerted on the engineer by the thrown boot = F = 391 N

F = ma

Initial acceleration of the engineer = (F/m) = (391/60) = 6.52 m/s²

We can then calculate the distance covered during this acceleration

X₁ = ut + ½at₁²

u = initial velocity of the engineer = 0 m/s (the engineer was initially at rest)

t₁ = time during which the force acts = 0.576 s

a = acceleration during this period = 6.52 m/s²

X₁ = 0 + 0.5×6.52×0.576² = 1.08 m

For the second part of the engineer's motion, the velocity becomes constant.

So, we first calculate this constant velocity

Impulse = Change in momentum

F×t = mv - mu

F = Force causing motion = 391 N

t = time during which the force acts = 0.576 s

m = mass of the engineer = 60 kg

v = final constant velocity of the engineer = ?

u = initial velocity of the engineer = 0 m/s

391 × 0.576 = 60v

v = (391×0.576/60) = 3.7536 m/s.

The distance from the engineer's initial position to shore is given as 30.5 m

The engineer covers 1.08 m during the time the force causing motion was acting.

The remaining distance = X₂ = 30.5 - 1.08 = 29.42 m

We can then calculate the time taken to cover the remaining distance, 29.42 m at constant velocity of 3.7536 m/s

X₂ = vt₂

t₂ = (X₂/v) = (29.42/3.7536) = 7.838 s

Time taken to reach shore = t₁ + t₂ = 0.576 + 7.838 = 8.414 s

Hope this Helps!!!

Centimeter is not related to the MKS. Thus, option B is correct.

MKS is refers to meter, kilogram, seconds. It forms the base of international systems of units though SI has since been redefined by different fundamental constants.

There are several derived units from MKS units:-

Frequency, Unit - Hertz

Force, Unit - Newton

Power, Unit - Watt

Energy, Unit - Joule

MKS is refers to meter, kilogram, seconds. It forms the base of international systems of units though SI has since been redefined by different fundamental constants.

Power, Unit - Watt

Energy, Unit - Joule

Therefore, centimeter is not related to the MKS. Thus, option B is correct.

Learn more about centimeter here:

https://brainly.com/question/19098836

#SPJ1

Answer:

A)   θ = 13.1º  , B)  E

Explanation:

A) For this exercise, let's use Newton's second law, let's set a reference frame where the axis ax is in the radial direction and is horizontal, the axis y is vertical.

In this reference system the only force that we must decompose is the Normal one, let's use trigonometry

        sin θ = Nₓ / N

        cos θ = \(N_{y}\) / N

        Nₓ = N sin θ

       Ny = N cos θ

x-axis (radial)

        Nₓ = m a

where the acceleration is centripetal

         a = v² / R

we substitute

        -N sin θ = -m v² / R                   (1)

the negative sign indicates that the force and acceleration towards the center of the circle

y-axis (Vertical)

          Ny - W = 0

           N cos θ = mg

           N = mg / cos θ

we substitute in 1

          mg / cos θ  sin θ = m v² / R

          g tan θ = v² / R

          θ = tan⁻¹ (v² / gR)

we calculate

        θ = tan⁻¹ (25² / 9.8 274)

        θ = 13.1º

B) when comparing the equations the correct one is E

Air can do work when it exerts a force on an object and causes it to undergo displacement. The ability of air to do work is evident in various phenomena, such as wind pushing sails, fans moving objects, and air pressure powering pneumatic systems.

Air can do work through its ability to exert a force over a distance. Work is defined as the transfer of energy that occurs when a force is applied to an object and it undergoes displacement in the direction of the force. When air is in motion, it possesses kinetic energy and can exert a force on objects in its path, thus performing work.

To understand how air can do work, we can consider the example of a moving fan. When a fan is turned on, the blades start to rotate, creating a flow of air. As the air moves, it carries kinetic energy. When the moving air encounters an object, such as a piece of paper, the air molecules collide with the paper's surface and exert a force on it. This force causes the paper to move and displaces it from its initial position.

The work done by the air can be calculated using the equation:

Work = Force * Distance * cos(θ)

Where Force is the magnitude of the force exerted by the air, Distance is the displacement of the object, and θ is the angle between the direction of the force and the displacement.

In the case of air doing work on an object, the force exerted by the air is perpendicular to the direction of motion, resulting in θ = 90 degrees. Since cos(90) = 0, the equation simplifies to:

Work = Force * Distance * 0

Therefore, the work done by the air on the object is zero when the force exerted by the air is perpendicular to the displacement.

However, if the force exerted by the air is not perpendicular to the displacement, such as when blowing air at an angle to move an object, then work is performed. The air exerts a force on the object and causes it to move in the direction of the force, resulting in the transfer of energy.

For more such information on: work

https://brainly.com/question/25573309

#SPJ8

Answer:

If there was no friction it would be impossible to move in any direction other than down.

Explanation:

Friction stops things from sliding apart. If there was no friction everything would slide to the lowest point. It would be impossible to climb up anything. Imagine trying to climb a wall of ice without crampons and an ice pick. It would be impossible.

He would never stop.

Friction rubs one surface against another to generate heat and it slows objects, so if there was no friction, the baseball player would slip and fall and never slow down

Answer:

electron, lightest stable subatomic particle known. It carries a negative charge of 1.602176634 × 10−19 coulomb, which is considered the basic unit of electric charge. The rest mass of the electron is 9.1093837015 × 10−31 kg, which is only 1/1,836the mass of a proton.

Explanation:

I hope this will be helpful for you.

Answer:

Kindly check explanation

Explanation:

Given the following :

Initial Velocity (u) = 10m/s

Angle (θ) = 50°

Horizontal length d1 = 6m

Height d2 = 3.6m

g = acceleration due to gravity = 9.8m/s²

Horizontal component :

X = U× cosΘ = 10 × cos 50 = 10 × 0.6429 = 6.43t

X = 6.43t

Vertical component :

Y = Usinθ - 1/2gt² = 10 ×sin 50 - 1/2(9.8)t² = 7.66t - 4.9t²

From X :

t = X / 6.43

Hence,

Y = 7.66(X/6.43) - 4.9(X/6.43)²

Y = 1.19X - 0.12X²

Slope of ramp Y':

(3.6 ÷ 6)X = 0.6X

Hence,

Y = Y'

1.19X - 0.12X² = 0.6X

-0.12X² = 0.6X - 1.19X

-0.12X² = - 0.59X

X² / X = 0.59 / 0.12

X = 4.92 m

Ball hits the ramp as X is < 6m

In the Roman soldier model for refraction, the first soldier who hits the muddy stream would slow down and turn slightly. Option B is correct.

The Roman soldier model is a simplified model used to explain the behavior of light when it passes from one medium to another. In this model, a group of Roman soldiers is marching across a field towards a muddy stream. The soldiers represent light rays, and the muddy stream represents the boundary between two media with different refractive indices.

When the first soldier hits the muddy stream, they slow down because the speed of light decreases when it passes from a medium with a lower refractive index to a medium with a higher refractive index. Additionally, the soldier turns slightly because the direction of the light ray changes as it passes through the boundary between the two media. This change in direction is called refraction, and it occurs because the speed of light changes when it passes through a medium with a different refractive index.

The amount of refraction that occurs depends on the angle at which the light ray hits the boundary between the two media and the difference in refractive indices between the two media. The Roman soldier model is a useful tool for understanding the basics of refraction, but it has limitations and cannot fully explain all aspects of the phenomenon. Option B is correct.

To know more about the Refraction, here

https://brainly.com/question/16362069

#SPJ1

The approximate centripetal force on an astronaut of mass 80Kg if the centrifuge rotates once every 2s is 3.94 KN

ac = v² / r

v = 2 π r / T

ac = Centripetal acceleration

v = Linear / Tangential velocity

T = Time period

r = Radius

r = 5 m

T = 2 s

v = 2 * 3.14 * 5 / 2

v = 15.7 m / s

ac = 15.7 * 15.7 / 5

ac = 49.298 m / s²

Fc = m ac

m = Mass

m = 80 kg

Fc = 80 * 49.298

Fc = 3943.8 N

Fc = 3.94 KN

Therefore, the approximate centripetal force on the astronaut is 3.94 KN

To know more about centripetal force

https://brainly.com/question/11324711

#SPJ9

The scenario that is an example of the transfer of thermal energy by conduction is D. Warm water ascends inside a tea pot as cooler water sinks.

Conduction is the transfer of heat through a material without the bulk motion of matter. In the case of a tea kettle, the heat source (such as a stove) heats the metal of the kettle, which then conducts the heat to the water inside the kettle.

The hot water molecules transfer their thermal energy to the cooler water molecules through direct contact, which causes the cooler water to become denser and sink while the warmer water becomes less dense and rises.

This creates a convection current, which further distributes the thermal energy within the water.

Option A describes the transfer of thermal energy by radiation, where electromagnetic waves (such as infrared light) transfer energy from the source to the eggs without any direct contact.

Option B describes the transfer of thermal energy by convection, where the cooler water in the pool sinks to the bottom and is replaced by warmer water rising to the surface.

Option C describes the transfer of thermal energy by radiation and convection, where the hot sidewalk radiates heat to the surrounding air, which then rises and is replaced by cooler air.

For more such questions on conduction, click on:

https://brainly.com/question/893656

#SPJ11

Answer:

Power of 5 watts is used

Explanation:

Mechanical Work and Power

Mechanical work is the amount of energy transferred by a force.

Being F the force vector and s the displacement vector, the work is calculated as:

\(W=\vec F\cdot \vec s\)

If both the force and displacement are parallel, then we can use the equivalent scalar formula:

W=F.s

Power is the amount of energy converted per unit of time. The SI unit of power is the watt, equal to one joule per second.

The power can be calculated as:

\(\displaystyle P=\frac {W}{t}\)

Where W is the work and t is the time.

It's required to calculate the power used in t=30 seconds when W=150 Joules of work are completed. Substitute in the formula:

\(\displaystyle P=\frac {150}{30}\)

P = 5 Watt

Power of 5 watts is used

Answer: Here you go, i hope this kinda helps.

Explanation:Disambiguation is just a fancy way of saying "asking clarifying questions".

Watson Assistant replies to user's questions based on a confidence score.

Sometimes the customer's question could be interpreted in two or three different ways.

For example, if you say you'd like to "book a table for 8", the assistant is able to ask a clarifying question:

Did you mean booking a table for 8PM, 8AM, or booking a table for 8 guests?

Watson Assistant will ask the question when its confidence score is divided between a few options to ensure that your customers get exactly the right service they need.

Answer:

A

Explanation:

The lift force is the force that opposes the weight of an object, so A, the upward force is the correct answer.

Answer:

a protective and waxy or hard layer covering the epidermis of a plant, invertebrate, or shell.

Answer:

The cuticles for animals are a thin layer of clear dead skin around the nail bed on fingers and toes. As the nail grows, it naturally pushes and damages the underside of the skin around the base of the nails, called the eponychium. The space between the eponychium and the bottom of the nail is where the cuticle is located.  

The cuticle definition related to plants is a protective and waxy or hard layer covering the epidermis. The plant cuticle is an extracellular hydrophobic layer that covers the aerial epidermis.

Explanation:

Answer: either 3.20s or 1.18s

Explanation:

The experimental value of the expression due to gravity through the experiment will come out to be 8.41u, the error in the value has Accord because of air friction.

Acceleration due to gravity is a form of acceleration that is exercised by the gravitational pull of the earth its value is fixed at the surface n is equal to 9.8u.

Aries composed of molecules and their food when an object passes through air strikes the a molecules they are molecules according to Newton's third law strike back at the object therefore reducing its speed. This force by the molecule is known as air friction.

The setup of the given experiment consists of:

A bob of mass m

A stopwatch with high accuracy

An inch tape

A speedometer

Experiment is conducted in the following manner:

Using Newton's first law of motion

i.e. v = u + a × t  

Where,

u is initial velocity

v is final velocity

a is acceleration due to gravity

t is time taken to cover distance

From the data given v = 16.82m/s

t is 2 seconds

Substituting value in Newton's first law of motion we get

Value of acceleration due to the gravity = 8.41

Therefore, The experimental value of the expression due to gravity through the experiment will come out to be 8.41u, the error in the value has Accord because of air friction.

Learn more about Newton's law of motion here:

https://brainly.com/question/974124

#SPJ1

Answer:the branch of science concerned with the nature and properties of matter and energy. The subject matter of physics, distinguished from that of chemistry and biology, includes mechanics, heat, light and other radiation, sound, electricity, magnetism, and the structure of atoms.

Explanation:

Answer:

What Electricity questions?

Explanation:

The total weight in Newtown is 21.56 N.

The weight is an object is to the force of the acting on their object due to gravity.

Weight is a force described by the   physics which is due  to the gravitation pull of  earth mercury is the

It's magnitude can be the  calculated by multiplying the mass with the by the  acceleration due to gravity but to the

And direction is always to the the centre of earth has

the weight of an object is to the  force acting on their object by the  due to gravity. Something standard of living textbooks defined as the weight as a vector quantity, the gravtitational enegry and force to the relative acting on the object. Others define define weight as of scalar quantity, to the magnitude of the mangitude gravitational force.

Here earth acceleration due to gravity is g= 9.8 ms^-2

And mass is 2+0.2 = 2.2  kg

So weight is 2.2(9.8)

= 21.56 N

To know more about weight click-

https://brainly.com/question/229459

#SPJ1

At point B, the ball is moving at a speed of around 2.05 m/s. At point C, the ball is moving at a speed of roughly 3.67 m/s.

Speed is the rate at which an object travels along a path over time, whereas velocity is the speed and direction of an item's motion.

(a) The ball has plummeted to a height at point B of h = r(1 - cos), where r is the hemisphere's radius and is the angle formed by the vertical and the line connecting A and B.

The ball loses as much potential energy as it gains in kinetic energy:

mgh = (1/2)mv² + (1/2)Iω²

Since the ball is rolling without slipping, we have v = rω. Also, for a solid sphere or ball, I = (2/5)mr^2.

By simplifying and substituting these formulas, we obtain:

mgh = (7/10)mv²

Solving for v, we get:

v = √((10/7)gh)

Substituting the given values, we get:

v = √((10/7) x 9.8 m/s² x 0.5 m x (1 - cos(30°)))

≈ 2.05 m/s

(b) The ball has dropped through a height of h = 2r at point C. Applying the same simplifications and conservation of energy equation as before, we arrive at:

mgh = (7/5)mv²

Solving for v, we get:

v = √((5/7)gh)

By simplifying and substituting these formulas, we obtain:

v = √((5/7) x 9.8 m/s² x 1.0 m)

≈ 3.67 m/s.

To know more about speed visit:-

https://brainly.com/question/29100366

#SPJ1

The minimum coefficient of static friction required for this claim to be made possible is 0.7

In an inclined plane system, the coefficient of static friction is the angle at which an object slide over another.  

The gravitational force component exceeds the static friction force when the angle rises. Hence, the object begins to slide.

According to Newton second law;

\(\sum F_x = \sum F_y = 0\)

\(\mathbf{mg sin \theta -f_s= N-mgcos \theta = 0 }\)

\(\mathbf{mg sin \theta =f_s}\)

\(\mathbf{mg sin \theta =\mu_s N}\)

N = mg cos θ

Equating both force components on the L.H.S and R.H.S, we have the following

\(\mathbf{mg sin \theta =\mu_s \ mg \ cos \theta}\)

\(\mathbf{sin \theta =\mu_s \ \ cos \theta}\)

\(\mathbf{\mu_s = \dfrac{sin \theta }{ cos \theta}}\)

According to the trigonometry rule:

\(\mathbf{tan \theta= \dfrac{sin \theta }{ cos \theta}}\)

∴

\(\mathbf{\mu_s =\tan \theta}}\)

\(\mathbf{\mu_s =\tan 35^0}}\)

\(\mathbf{\mu_s = 0.700}}\)

Therefore, we can conclude that the minimum coefficient of static friction needed for this claim to be possible is 0.7

Learn more about static friction here:

https://brainly.com/question/13000653?referrer=searchResults

Answer:

Refer to the step-by-step Explanation.

Step-by-step Explanation:

Simplify the equation with given substitutions,

Given Equation:

\(mgh+(1/2)mv^2+(1/2)I \omega^2=(1/2)mv_{_{0}}^2+(1/2)I \omega_{_{0}}^2\)

Given Substitutions:

\(\omega=v/R\\\\ \omega_{_{0}}=v_{_{0}}/R\\\\\ I=(2/5)mR^2\)\(\hrulefill\)

Start by substituting in the appropriate values: \(mgh+(1/2)mv^2+(1/2)I \omega^2=(1/2)mv_{_{0}}^2+(1/2)I \omega_{_{0}}^2 \\\\\\\\\Longrightarrow mgh+(1/2)mv^2+(1/2)\bold{[(2/5)mR^2]} \bold{[v/R]}^2=(1/2)mv_{_{0}}^2+(1/2)\bold{[(2/5)mR^2]}\bold{[v_{_{0}}/R]}^2\)

Adjusting the equation so it easier to work with.\(\Longrightarrow mgh+\dfrac{1}{2} mv^2+\dfrac{1}{2} \Big[\dfrac{2}{5} mR^2\Big]\Big[\dfrac{v}{R} \Big]^2=\dfrac12mv_{_{0}}^2+\dfrac12\Big[\dfrac25mR^2\Big]\Big[\dfrac{v_{_{0}}}{R}\Big]^2\)

\(\hrulefill\)

Simplifying the left-hand side of the equation:

\(mgh+\dfrac{1}{2} mv^2+\dfrac{1}{2} \Big[\dfrac{2}{5} mR^2\Big]\Big[\dfrac{v}{R} \Big]^2\)

Simplifying the third term.

\(\Longrightarrow mgh+\dfrac{1}{2} mv^2+\dfrac{1}{2} \Big[\dfrac{2}{5} mR^2\Big]\Big[\dfrac{v}{R} \Big]^2\\\\\\\\\Longrightarrow mgh+\dfrac{1}{2} mv^2+\dfrac{1}{2}\cdot \dfrac{2}{5} \Big[mR^2\Big]\Big[\dfrac{v}{R} \Big]^2\\\\\\\\\Longrightarrow mgh+\dfrac{1}{2} mv^2+\dfrac{1}{5} \Big[mR^2\Big]\Big[\dfrac{v}{R} \Big]^2\)

\(\\ \boxed{\left\begin{array}{ccc}\text{\Underline{Power of a Fraction Rule:}}\\\\\Big(\dfrac{a}{b}\Big)^2=\dfrac{a^2}{b^2} \end{array}\right }\)

\(\Longrightarrow mgh+\dfrac{1}{2} mv^2+\dfrac{1}{5} \Big[mR^2\Big]\Big[\dfrac{v^2}{R^2} \Big]\\\\\\\\\Longrightarrow mgh+\dfrac{1}{2} mv^2+\dfrac{1}{5} \Big[mR^2 \cdot\dfrac{v^2}{R^2} \Big]\)

"R²'s" cancel, we are left with:

\(\Longrightarrow mgh+\dfrac{1}{2} mv^2+\dfrac{1}{5} \Big[mR^2\Big]\Big[\dfrac{v^2}{R^2} \Big]\\\\\\\\\Longrightarrow mgh+\dfrac{1}{2} mv^2+\dfrac{1}{5}mv^2\)

We have like terms, combine them.

\(\Longrightarrow mgh+\dfrac{1}{2} mv^2+\dfrac{1}{5} \Big[mR^2\Big]\Big[\dfrac{v^2}{R^2} \Big]\\\\\\\\\Longrightarrow mgh+\dfrac{7}{10} mv^2\)

Each term has an "m" in common, factor it out.

\(\Longrightarrow m(gh+\dfrac{7}{10}v^2)\)

Now we have the following equation:

\(\Longrightarrow m(gh+\dfrac{7}{10}v^2)=\dfrac12mv_{_{0}}^2+\dfrac12\Big[\dfrac25mR^2\Big]\Big[\dfrac{v_{_{0}}}{R}\Big]^2\)

\(\hrulefill\)

Simplifying the right-hand side of the equation:

\(\Longrightarrow \dfrac12mv_{_{0}}^2+\dfrac12\cdot\dfrac25\Big[mR^2\Big]\Big[\dfrac{v_{_{0}}}{R}\Big]^2\\\\\\\\\Longrightarrow \dfrac12mv_{_{0}}^2+\dfrac15\Big[mR^2\Big]\Big[\dfrac{v_{_{0}}}{R}\Big]^2\\\\\\\\\Longrightarrow \dfrac12mv_{_{0}}^2+\dfrac15\Big[mR^2\Big]\Big[\dfrac{v_{_{0}}^2}{R^2}\Big]\\\\\\\\\Longrightarrow \dfrac12mv_{_{0}}^2+\dfrac15\Big[mR^2\cdot\dfrac{v_{_{0}}^2}{R^2}\Big]\\\\\\\\\Longrightarrow \dfrac12mv_{_{0}}^2+\dfrac15mv_{_{0}}^2\Big\\\\\\\\\)

\(\Longrightarrow \dfrac{7}{10}mv_{_{0}}^2\)

Now we have the equation:

\(\Longrightarrow m(gh+\dfrac{7}{10}v^2)=\dfrac{7}{10}mv_{_{0}}^2\)

\(\hrulefill\)

Now solving the equation for the variable "v":

\(m(gh+\dfrac{7}{10}v^2)=\dfrac{7}{10}mv_{_{0}}^2\)

Dividing each side by "m," this will cancel the "m" variable on each side.

\(\Longrightarrow gh+\dfrac{7}{10}v^2=\dfrac{7}{10}v_{_{0}}^2\)

Subtract the term "gh" from either side of the equation.

\(\Longrightarrow \dfrac{7}{10}v^2=\dfrac{7}{10}v_{_{0}}^2-gh\)

Multiply each side of the equation by "10/7."

\(\Longrightarrow v^2=\dfrac{10}{7}\cdot\dfrac{7}{10}v_{_{0}}^2-\dfrac{10}{7}gh\\\\\\\\\Longrightarrow v^2=v_{_{0}}^2-\dfrac{10}{7}gh\)

Now squaring both sides.

\(\Longrightarrow \boxed{\boxed{v=\sqrt{v_{_{0}}^2-\dfrac{10}{7}gh}}}\)

Thus, the simplified equation above matches the simplified equation that was given.