8. The horizontal and vertical components of a velocity are 46.1 m/s and 62.5 m/s respectively. What is the magnitude and direction of the velocity? Answer: 77.7 m/s, 53.6°​

Answer:

the correct answer is C   v = 60 cm / s

Explanation:

The speed of a wave is related to the frequency and the wavelength

         v = λ f

They indicate that the object performs 20 oscillations every second, this is the frequency

         f = 20 Hz

the wavelength is the distance until the wave repeats, the distance between two consecutive peaks corresponds to the wavelength

         λ = 3 cm = 0.03 m

let's calculate

       v = 20 0.03

       v = 0.6 m / s

       v = 60 cm / s

the correct answer is C

The vehicle has a 2000kg mass.

Take a mass's acceleration into account. Use the formula F = m a to determine the force's value. Kilogram-meter/second-squared will be used as the unit of force. The short name for this unit, which is made up of the three basic SI units, is newton.

F= ma

m= F/a

m= 50000/25

m= 2000 kg

According to Newton's Second Law of Motion, acceleration (gaining speed) occurs whenever a force acts on a mass (object). This law of motion is best demonstrated by riding a bicycle. The mass is your bicycle. The force that propels you forward on your bicycle comes from your leg muscles.

To know more about Newtons visit:-

https://brainly.com/question/16889018

#SPJ1

The speed of blood through the aorta is 0.265 m/s .Blood travels through the aorta at a speed of around 40 cm/s and has a radius of about 1.2 cm.

In the supine position of a ascending aorta, males and females, respectively, experienced maximum velocities at 120 and 108 cm. s-1, whereas the corresponding acceleration was 2254 and 2148 cm. s-2.

volumetric flow rate, Q = 5.0L/min = 0.005 m³/min x 1min/60s = 8.333 x 10⁻⁵ m³/s

radius of the aorta, r = 1.0 cm = 0.01 m

Area of the aorta = πr²

Area of the aorta = π(0.01)² = 3.142 x 10⁻⁴ m²

Volumetric flow rate is given by;

Q = Av

where;

v is the speed of blood through the aorta

v = Q /A

v = (8.333 x 10⁻⁵ ) / (3.142 x 10⁻⁴)

v = 0.265 m/s

The following equation mathematically expresses this: V = Q/A in which Blood flow is measured in millilitres per second (ml/s). • A = area cross-sectionale (cm2) 5 mPas is the average viscosity. The barrier to blood flow is known as blood viscosity.

To know more about speed visit:

https://brainly.com/question/28224010

#SPJ1

It is advisable that Jeff should begin to save about 5% of his income to serve as his retirement plan.

Retirement refers to such a time when one is no longer involved in actual work. It is important that a person ought to save up some money for use via a retirement plan.

It is advisable that Jeff should begin to save about 5% of his income to serve as his retirement plan since he still has many years of work ahead of him.

Learn more about retirement:https://brainly.com/question/20751552?

#SPJ1

If the cup is perfectly insulated, no heat can flow in or out of the system. Therefore, the temperature of the system will remain constant at 0°C until all the ice has melted.

What amount of heat is needed to melt the ice?

To calculate the amount of heat required to melt the ice, we can use the formula:

Q = m * L

Where Q is the amount of heat required, m is the mass of ice, and L is the latent heat of fusion of water, which is 334 J/g.

The mass of ice is 50 grams, so:

Q = 50 g * 334 J/g = 16,700 J

Therefore, it will require 16,700 Joules of heat to melt the ice.

Once all the ice has melted, the temperature of the water will start to increase. We can use the specific heat capacity of water to calculate the amount of heat required to raise the temperature of the water.

The specific heat capacity of water is 4.18 J/g°C.

The temperature of the water needs to increase by 0°C to reach the melting point of ice (0°C), and then it needs to increase by another 1000°C to reach boiling point of water (100°C). So, the total temperature change is 100°C.

The mass of the water is 50 grams, so:

Q = m * c * ΔT

Q = 50 g * 4.18 J/g°C * 100°C

Q = 20,900 J

Therefore, it will require 20,900 Joules of heat to raise the temperature of the water from 0°C to 100°C.

In total, the amount of heat required to melt the ice and raise the temperature of the water to boiling point is:

Total Q = Q_ice + Q_water

Total Q = 16,700 J + 20,900 J

Total Q = 37,600 J

Therefore, it will require 37,600 Joules of heat to melt the ice and raise the temperature of the water to boiling point in the perfectly insulated cup.

Learn more about melting from

https://brainly.com/question/29464401

#SPJ1

The answer to the first part of the question is 24 V and the answer to the second part of the question is 48 V.

The formula which relates Charge, Capacitance and Voltage is

Charge = Capacitance × Voltage

Q = CV

where Q denotes the charge, C denotes the capacitance and V denote the voltage.

Using the above formula the charge on the capacitance will be

Q = CV

C = 10 mF

V = 24 V

Q = 240 mC

Charge on capacitance is 240 mC.

Now after we disconnect the battery

C = 10 mF (will remain same)

Q = 240 mC

V = Q/C

V = 240/10 V

V = 24 V

So after we removed the battery, The voltage will remain same.

Now we know that parallel plate capacitor formula is

C = ε(A/d)

from here

C ∝ 1/d, and as there is no loss of charge we can say that V ∝ 1/d

Form C ∝ 1/d and V ∝ 1/C we can state that

V ∝ d   {where d is the measurement of separation between the plates}

so if we double the distance between the plates then, the voltage will also get double.

Previously our voltage was 24 V, now if we double the distance between the plates the voltage will also get double, and it will become 48 V.

So, the voltmeter will take a reading of 24 V if voltmeter is connected across the two plates without discharging them, and if we double the plate separation then it will take 48 V as reading.

Learn more about Capacitors here:

https://brainly.com/question/13578522

#SPJ10

The statement that describes the transformation of the graph of function f onto the graph of function g is: The graph shifts 2 units right and 7 units down.

To determine the transformation of the graph of function f onto the graph of function g, we compare the two functions f(x) and g(x) and observe the changes in the equations.

The function f(x) = (1/x - 3) + 1 represents a reciprocal function that is shifted vertically 1 unit up and horizontally 3 units to the right. The reciprocal function is reflected about the line y = x.

The function g(x) = (1/(1 + 4)) + 3 simplifies to g(x) = 4 + 3 = 7, which is a constant function representing a horizontal line at y = 7.

By comparing the equations, we can see that the transformation from f(x) to g(x) involves the following changes:

The term 1/x in f(x) is replaced by the constant 1/(1 + 4) in g(x), resulting in a vertical shift of 7 units up.

The term -3 in f(x) is replaced by 3 in g(x), resulting in a vertical shift of 3 units up.

The +1 in f(x) is replaced by +3 in g(x), resulting in an additional vertical shift of 2 units up.

Therefore, the overall transformation is a shift of 2 units to the right and 7 units down.

Hence, the correct statement is: The graph shifts 2 units right and 7 units down.

For more such questions on graph, click on:

https://brainly.com/question/26865

#SPJ8

Answer:

Hello your question is incomplete hence I will give you a general answer as regards rotation of vector matrix assuming angle of rotation  = \(\frac{\pi }{4}\)

answer :

angle of rotation = \(\frac{\pi }{4}\)

vector matrix produced = attached below

Explanation:

lets assume the vector matrix [ 6, -2 ] is rotated clockwise by an angle of \(\frac{\pi }{4}\)

The resultant matrix = attached below

Result of the rotation =  attached below

attached below is the detailed solution

Answer: I got it right on Edmentum

Explanation: Answers attached below

Answer:

the answer is B, stability

Explanation:

A traditional economy is a system that is based on honorable customs, history, and beliefs. Tradition guides economic decisions, such as production and distribution. Traditional economies depend on agriculture, fishing, hunting, gathering or some combination above. They use exchange instead of money. Most traditional economies operate in emerging markets and developing countries. They are often in Africa, Asia, Latin America and the Middle East. But you can find scholarships from traditional economies scattered all over the world. Economists and anthropologists believe that all other economies started out as traditional economies. Thus, they expect the remaining traditional economies to evolve into market, command or mixed economies over time.

Answer:

d

Explanation:

(a) The average speed must you have for the second half of the trip to meet your goal is 8 km/h.

(b) The value obtained (8 km/h) is not reasonable for the second half of the distance since the first half is 48km/h.

Average velocity is defined as the change in position or displacement (∆x) divided by the time intervals (∆t) in which the displacement occurs.

average velocity = total distance / total time

v = (d)/(0.5d/v₁ + 0.5d/v₂)

where;

90 km/h = (d) / (0.5d/48 + 0.5d/v₂)

90(0.5d/48 + 0.5d/v₂) = d

0.9375d + 0.5d/v₂ = d

d(0.9375 + 0.5/v₂) = d

0.9375 + 0.5/v₂ = 1

0.5/v₂ = 0.0625

v₂ = 0.5/0.0625

v₂ = 8 km/h

Thus, the average speed must you have for the second half of the trip to meet your goal is 8 km/h.

The value obtained (8 km/h) is not reasonable for the second half of the distance since the first half is 48km/h.

Learn more about average velocity here: https://brainly.com/question/24739297

#SPJ1

In order to find the solid, you would want the object in which sound travels the fastest

In this case, since in object C, the speed of sound is the fastest, it is the most likely to be a solid

So object C is most likely to be a solid

Answer:

c. speed

Explanation:

In a distant-time graph the x value is usually the time and the y value is usually the distance.

If slope is the change in y over the change in x, on a distant time graph the slope would be the change in time over the change in distance

Or time / distance.

Time / distance happens to calculate speed.

Thus, the slope of a line on a distant-time graph is speed.

\(\huge\textbf{Hey there!}\)

\(\large\textbf{The formula for Slope of a line is: }\mathbf{m = \dfrac{rise}{run}}\large\textbf{ whereas it is}\\\large\textbf{equal to/equivalent to }\mathbf{ \dfrac{y_2 - y_1}{x_2- x_1} \ .}\\\\\large\textbf{Basically, the slope of the line is measured with its }\\\large\textbf{\underline{steepness}. The word steepness simply means a}\\\lage\textbf{very sharp slope.}\)

\(\large\textbf{On slope of a line on distant-time graph is basically how }\\\large\textbf{ \boxed{\bf FAST} a particular object is.}\)

\(\large\textbf{Now, that we got that information out of the way we}\\\large\textbf{can find out our answer.}\)

\(\large\textbf{The formula for distance is: }\mathbf{d= \sqrt{(x_2 - x_1)^2 + (y_2 +y_1)^2}}}\)

\(\large\textsf{We cannot say that OPTION A isn't your answer because you}\\\large\textsf{cannot calculate slope of a line on a distant-time graph. You}\\\large\textsf{cannot calculate the speed of the object by using that formula.}\\\large\textsf{So, this eliminates Option A. as your answer.}\)

\(\large\textbf{The formula of time is: }\mathbf{time = \dfrac{distance}{speed}}\)

\(\large\textsf{Yes, it calculates the distance but it doesn't calculate how fast a(n)}\\\large\textsf{object is going. So this eliminates Option B. as your answer.}\)

\(\large\textsf{The formula for speed is: }\mathbf{s = \dfrac{d}{t}}\large\textbf{ whereas s = \underline{speed}, }\\\large\textsf{d = \underline{distance} you have \underline{traveled}, \& t = \underline{time} that has}\\\large\textsf{been \underline{elapsed}.}\\\large\textsf{Option C. could possibly be your answer}\)

\(\large\textbf{Option C. seems to be the closes to your result than the}\\\large\textbf{to your answer.}\)

\(\large\boxed{\text{Therefore, your answer should be: \boxed{\textbf{Option C. Speed}}}}\huge\checkmark\)

\(\huge\textbf{Good luck on your assignment \&}\\\huge\textbf{enjoy your day!}\)

~\(\frak{Amphitrite1040:)}\)

the scientific method is described as self-correcting and cyclical therefore it ain't linear but cyclic.

Hope this helped you- have a good day bro cya)

Answer:

Explanation:

f N is the number of forces acting on a body, the net force formula is given by,

FNet = F1 + F2 + F3…. + FN.

FNet = Fa + Fg.

FNet = Fa + Fg + Ff + FN.

The total distance covered by the car is 4 kilometers, this is because we are taking into account displacement and not just distance.

Displacement is defined as the change in the position of an object while distance is an object's overall movement in a directionless fashion.

There are many different units that can be used to measure distance (inches, feet, miles, kilometers, and centimeters), but the meter is the SI unit. It is a scalar amount because it does not consider

On the number line, we can see the movement as follows

1 0 -1 -2 -3= 4km

Distance is always positive and never gets smaller as you move. Displacement can be negative, positive, or zero because it refers to the change in the position of an object with respect to its original location.

Learn more about displacement here:

https://brainly.com/question/14422259

#SPJ!

Answer:

Just like a solid ,the density of a liquid equals the mass of the liquid by its volume;D=m/v. The density of the water is 1 gram per cubic centimeter. The density of a substance is the same regardless of the size of the sample.

To convert one system of unit to another  of derived quantities is not a use of dimensional analysis.

Checking for consistency in the dimensions on both sides of an equation entails looking at the dimensions of the physical quantities involved in a problem, such as length, mass, time, electric charge, and temperature.

The core tenet of dimensional analysis is that physical quantities, such as length, mass, and time, may be described in terms of their basic dimensions.

Learn more about dimensions:https://brainly.com/question/1769579

#SPJ1

All of the options listed are included in the uses of dimensional analysis.

Dimensional analysis is a powerful tool used in physics to:

The dimensional analysis involves analyzing the dimensions of physical quantities and using them to establish relationships between them.

By using the principles of dimensional analysis, we can simplify complex physical problems and gain insights into the behavior of physical systems.

More on dimensional analysis can be found here: https://brainly.com/question/13156854

#SPJ1

Answer:

4000j

Explanation:

0.5 × 10^2 × 80 = 4kJ = 4000Joules

The first harmonic of the standing wave on a string with a loose end represents half a wavelength.

The fraction of a wavelength represented by the first harmonic is 1/2.

The higher harmonics of a standing wave on a string with a loose end are odd-number multiples of the first harmonic.

1. The first harmonic of a standing wave on a string with a loose end occurs when there is a node near the driver end and an antinode at the loose end. To measure the frequency of the first harmonic, we need to determine the fraction of a wavelength represented by this standing wave.

The first harmonic of the standing wave on a string with a loose end represents half a wavelength.

The first harmonic of a standing wave on a string with a loose end consists of a node near the driver end and an antinode at the loose end. This configuration creates the simplest standing wave pattern.

In a standing wave, a node is a point where the amplitude of the wave is always zero, representing a point of minimum displacement. An antinode, on the other hand, is a point of maximum displacement, where the amplitude is at its highest.

Since the loose end does not invert the phase of the wave upon reflection, the reflected wave and the original wave constructively interfere at the loose end, resulting in an antinode.

In the first harmonic, there is exactly half a wavelength between the node near the driver end and the antinode at the loose end.

Therefore, the fraction of a wavelength represented by the first harmonic is 1/2.

2. To predict the frequencies of higher harmonics, we can use the relationship that the frequency of each harmonic is a multiple of the frequency of the first harmonic. The higher harmonics can be calculated as follows:

Second Harmonic: The second harmonic consists of two nodes and one additional antinode compared to the first harmonic. The fraction of a wavelength for the second harmonic is 1/2 * 2 = 1. Thus, the second harmonic has a frequency that is twice that of the first harmonic.

Third Harmonic: The third harmonic consists of three nodes and two additional antinodes compared to the first harmonic. The fraction of a wavelength for the third harmonic is 1/2 * 3 = 1.5. Thus, the third harmonic has a frequency that is three times that of the first harmonic.

Fourth Harmonic: The fourth harmonic consists of four nodes and three additional antinodes compared to the first harmonic. The fraction of a wavelength for the fourth harmonic is 1/2 * 4 = 2. Thus, the fourth harmonic has a frequency that is four times that of the first harmonic.

In general, the higher harmonics of a standing wave on a string with a loose end are odd-number multiples of the first harmonic.

For more such questions on wavelength, click on:

https://brainly.com/question/10728818

#SPJ8

If a 1.5 kg ball has a momentum of 4.5 kg*m/s, the velocity of the ball is  3 m/s.

According to the question, the given quantity is,

Mass of the ball = 1.5 kg

The momentum of the ball =  4.5 kg. m/s

The momentum is defined as the product of the mass of the object and the velocity of the object, so p = mv.

p = momentum of an object

m = mass of an object

v = velocity of an object

According to question the given value outs in the formulae,

p= mv

4.50 = 1.50 × v

v = 4.50/ 1.50

v = 3 m/s.

Therefore, the velocity of the ball is  3 m/s.

Learn more about velocity, here:

https://brainly.com/question/2451846

#SPJ9

Answer:

Explanation:

It's graph A because the pressure in the tire is increasing as the amount of air going into it increases. B says the pressure drops exponentially as air goes in, and C says that the pressure stays the same as air goes in. Pressure in a tire increases proportionally to the amount of air in it.

The object with a mass of 2.3 kg that is the rock will have a weight of 22.5 N.

W = m * g

W = Weight

m = Mass

g = Acceleration due to gravity

g = 9.8 m / s²

For the book,

m = 1.1 kg

W = 1.1 * 9.8

W = 10.78 N

For the Box,

m = 4.5 kg

W = 4.5 * 9.8

W = 44.1 N

For the Rock,

m = 2.3 kg

W = 2.3 * 9.8

W = 22.5 N

Therefore, the object that has a weight of about 22.5 N is the rock

To know more about Weight

https://brainly.com/question/13040516

#SPJ1

Answer:

The truck will undergo the largest change in momentum if it has a greater mass than the small car.

Explanation:

The change in momentum of an object can be calculated using the equation:

Δp = m * Δv

where Δp represents the change in momentum, m represents the mass of the object, and Δv represents the change in velocity.

Since we are comparing the change in momentum of the car and the truck, we need to consider the masses of both vehicles.

Let's assume the mass of the car is represented by m_car, and the mass of the truck is represented by m_truck.

Since both vehicles collide head-on, the change in velocity (Δv) will be the difference between their initial velocities, considering that they are moving in opposite directions:

Δv = v_truck - v_car

Now, let's compare the change in momentum for the car and the truck:

For the car:

Δp_car = m_car * Δv

For the truck:

Δp_truck = m_truck * Δv

Comparing the magnitudes of the change in momentum, we can neglect the negative sign:

|Δp_car| = |m_car * Δv|

|Δp_truck| = |m_truck * Δv|

Since both Δv and Δp are positive values, we can conclude that the vehicle with the greater mass will undergo the largest change in its momentum.

Therefore, if the mass of the truck (m_truck) is greater than the mass of the car (m_car), then the truck will undergo the largest change in its momentum. Conversely, if the mass of the car is greater, then the car will undergo the largest change in its momentum.

The distance of the image formed by the lens is at 10.7 cm on the ruler.

option C.

The distance of the image is calculated by applying lens formula as shown below;

1/f = -1/u + 1/v'

where;

From the diagram, the focal length of the lens = 8.5 cm

the object distance = 3 cm

The image distance is calculated as follows;

1/v' = 1/f + 1/u

1/v' = 1/8.5 + 1/3

1/v' = 0.45

v' = 1/0.45

v' = 2.21 cm

The position of the image on the rule is calculated as follows;

v = v'  +  8.5 cm

v = 2.21 cm + 8.5 cm

v = 10.71 cm

Thus, the ray - diagram shows the position or distance of the image formed.

Learn more about ray diagram here: https://brainly.com/question/15506795

#SPJ1

Answer: evaporation

Explanation:

Refrigerators work by causing the refrigerant circulating inside them to change from a liquid into a gas. This process, called evaporation, cools the surrounding area and produces the desired effect.

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.  

Answer:

A. 450 N

B. 3240 J

C. 0.77 KW

Explanation:

From the question given above, the following data were obtained:

Height of one step = 20 cm

Number of steps = 36

Mass of runner = 45 kg

Time taken = 4.2 s

Next, we shall convert 20 cm to metre (m). This can be obtained as follow:

100 cm = 1 m

Therefore,

20 cm = 20 cm × 1 m /100 cm

20 cm = 0.2 m

Next, we shall determine the total height. This can be obtained as follow:

Height of one step = 0.2 m

Number of steps = 36

Total height =?

Total height = 36 × 0.2

Total height = 7.2 m

A. Determination of the runner's weight.

Mass of runner (m) = 45 kg

Acceleration due to gravity (g) = 10 m/s²

Weight (W) =?

W = m × g

W = 45 × 10

W = 450 N

B. Determination of the increase in the potential energy.

At the ground level, the potential energy (PE₁) is 0 J.

Next, we shall determine the potential energy at 7.2 m. This can be obtained as follow:

Mass of runner (m) = 45 kg

Acceleration due to gravity (g) = 10 m/s²

Total height (h) = 7.2 m

Potential energy at height 7.2 m (PE₂) = ?

PE₂ = mgh

PE₂ = 45 × 10 × 7.2

PE₂ = 3240 J

Final, we shall determine the increase in potential energy. This can be obtained as follow:

Potential energy at ground (PE₁) = 0 J

Potential energy at height 7.2 m (PE₂) = 3240 J

Increase in potential energy =?

Increase in potential energy = PE₂ – PE₁

Increase in potential energy = 3240 – 0

Increase in potential energy = 3240 J

C. Determination of the power.

Energy (E) = 3240 J

Time (t) = 4.2 s

Power (P) =?

P = E/t

P = 3240 / 4.2

P = 771.43 W

Finally, we shall convert 771.43 W to kilowatt (KW). This can be obtained as follow:

1000 W = 1 KW

Therefore,

771.43 W = 771.43 W × 1 KW / 1000 W

771.43 W = 0.77 KW

Therefore, her power is 0.77 KW

Answer:

The acceleration of an object as produced by a net force is directly proportional to the magnitude of the net force, in the same direction as the net force, and inversely proportional to the mass of the object

Explanation:

it's newton's second law