A 4.0 kg model rocket is launched, shooting 50.0 g of burned fuel from its exhaust at an average velocity of 625 m/s. What is the velocity of the rocket after the fuel has burned?

Answer: Workdone293.02KJ

Explanation: The equation to use to calculate Workdone = Change in KE + Change in PE

Assuming velocity is constant,KE becomes 0

Workdone= Change in PE=mg

W=92×9.8×325=293.02KJ

Answer:

P = 7.28 N.s

Explanation:

given,

initial momentum of cue ball in x- direction,P₁ = 9 N.s

momentum of nine ball in  x-  direction, P₂ = 2 N.s

momentum in perpendicular direction i.e. y - direction,P'₂ = 2 N.s

momentum of the cue after collision = ?

using conservation of momentum

in x- direction

P₁ + p = x  + P₂

p is the initial momentum of the nine balls which is equal to zero.

9 + 0  = x  + 2

x = 7 N.s

momentum in x-direction.

equating along y-direction

P'₁ + p = y + P'₂

0 + 0 = y + 2

y = -2 N.s

the momentum of the cue ball after collision is equal to resultant of the momentum .

[tex]P = \sqrt{x^2+y^2}[/tex]

[tex]P = \sqrt{7^2+(-2)^2}[/tex]

      P = 7.28 N.s

the momentum of the cue ball after collision is equal to P = 7.28 N.s

The momentum of the cue ball after the collision is calculated to be 6.2 N·s in based on the conservation of momentum.

This physics problem involves the principle of conservation of momentum. Initially, the cue ball has a momentum of 9.0 N·s. After the collision, the nine-ball has a momentum of 2.0 N·s in the original direction and another 2.0 N·s in a perpendicular direction. To find the momentum of the cue ball after the collision, we need to take into account that the total momentum of the system is conserved before and after the collision.

In this case, the total initial momentum is the momentum of the cue ball, which is 9.0 N·s. After the collision, the total momentum should still be 9.0 N·s. The sum of the momenta of the nine-ball (which is the square root of the sum of the squares of the two momentum components, due to the Pythagorean theorem) is 2.8 N·s. Therefore, the momentum of the cue ball after the collision will be the total initial momentum minus the momentum of the nine-ball after the collision, which gives us 9.0 N·s - 2.8 N·s = 6.2 N·s.

To solve this problem, we can use the principle of conservation of momentum. Before the collision, we have the momentum of the cue ball which is 9.0 N·s. After the collision, we have the momentum of the nine-ball which is 2.0 N·s in the original direction of the cue ball and 2.0 N·s perpendicular to that direction. Since momentum is conserved, the total momentum before the collision is equal to the total momentum after the collision. Therefore, the momentum of the cue ball after the collision is the difference between the total momentum before the collision and the momentum of the nine-ball after the collision.

To calculate the momentum of the cue ball after the collision, we subtract the momenta of the nine-ball from the initial momentum of the cue ball. The momentum of the cue ball after the collision is therefore 9.0 N·s - (2.0 N·s + 2.0 N·s) = 5.0 N·s in the original direction of the cue ball.

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Answer:

kinetic energy in each pulse = 9.5J

Explanation:

Conventionally, overall energy = kinetic + potential

Hence kinetic energy in each pulse = half of the total energy = 0.5 x 19

energy = 9.5J

The kinetic energy is in each pulse is 19J.

The Power delivered is defined at the rate of work done, if P be the power, W be the work done and t be the time for which the work is done then:

P = W/t

W = Pt

given that P = 10w and t = 1.9s

W = 10×1.9 J

W = 19J

Now, the work done is equal to the change in Kinetic energy (KE)

ΔKE = W = 19J

Hence, the kinetic energy is 19J.

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Answer:

spring constant of the spring will be equal to 317.33 N/m

Explanation:

We have given mass of the child m = 6.80 kg

Spring is stretched by length of 0.210 m . so x = 0.210 m

Acceleration due to gravity [tex]g=9.8m/sec^2[/tex]

Force on the child will be equal to [tex]W=mg[/tex]

This force will be balanced by spring force

And spring force is equal to F = Kx

So kx = mg

[tex]k\times 0.210=6.80\times 9.8[/tex]

k = 317.33 N /m

So spring constant of the spring will be equal to 317.33 N/m

Answer:

"Scientists used them to create new theories"

Explanation:

The Scientific Revolution was a sequence of actions that manifest the development of contemporary science through the early contemporary period, when advances in mathematics, physics, astronomy, biology and chemistry altered the opinions of civilization around nature. The scientific revolution denotes to the quick developments in European scientific, mathematical, and political assumed, grounded on a new philosophy of experimentation and a belief in growth that defined Europe in the 16th and 17th centuries.

Final answer:

The telescope and Pascal's Law played a significant role in laying the foundation of the Scientific Revolution. The telescope allowed for groundbreaking observations of the solar system and the universe, while Pascal's Law led to advancements in fluid mechanics and hydraulic engineering.

Explanation:

The new technology, such as the telescope, and new theories, such as Pascal's Law, played a significant role in laying the foundation of the Scientific Revolution.

Firstly, the invention of the telescope in 1608 allowed astronomers like Galileo Galilei to make groundbreaking observations of the solar system and the universe, leading to the development of new theories and understandings of celestial bodies.

Secondly, Pascal's Law, formulated by Blaise Pascal, established the principle that pressure exerted on a fluid is transmitted uniformly in all directions, which laid the foundation for the field of fluid mechanics and led to advancements in hydraulic engineering and other areas.

Answer:

0.59 cm

Explanation:

height of cup (h) = 10 cm

radius of cup (r) = 10 cm

rate of change of water level (V') = 16π/3 [tex]cm^{3} /sec[/tex]

rate of change of height (h) = 3 cm

the ratio of the height to radius (h:r) = 10:10

h/r = 10/10

h/r = 1

r=h

formula for volume of a volume (v) = [tex]\frac{1}{3}[/tex].π[tex]r^{2}[/tex]h

substituting r=h into the formula above we have

v = [tex]\frac{1}{3}[/tex].π[tex]h^{2}[/tex]. h = [tex]\frac{1}{3}[/tex].π[tex]h^{3}[/tex]

differentiating the above we have

v' = 3([tex]\frac{1}{3}[/tex]π[tex]h^{2}[/tex])h' = π[tex]h^{2}[/tex].h'

rearranging the above we have

h' = v' / (π[tex]h^{2}[/tex])

where

h' = ((16 x π) / 3) ÷ ( π x [tex]3^{2}[/tex])

h' = ((16 x 3.142) / 3) ÷ ( 3.142 x [tex]3^{2}[/tex])

h' = 16.76 / 28.28

h' = 0.59 cm

The formula U = mgy is not accurate for calculating the gravitational potential energy of a satellite orbiting at a significant height because g is not constant at such distances. Instead, the formula U = -GMm/r should be used. This reflects the gravitational potential becoming more negative at larger distances, which means orbits at those distances are bound due to the total energy remaining negative.

It's inaccurate to use the simple formula U = mgy to calculate the gravitational potential energy of a satellite orbiting Earth at a significant height because this formula assumes that the gravitational acceleration (g) is constant. However, g varies with altitude and is less at higher altitudes. For satellites in orbit, especially at a height of one Earth radius above the surface, we need to use a more general expression that accounts for the change in g with distance from the center of Earth.

The correct formula for calculating the gravitational potential energy (GPE) of a satellite at a distance r from the center of Earth (where r is significantly greater than the Earth's radius) is derived from the law of universal gravitation and is U = -GMm/r, where G is the gravitational constant, M is the mass of Earth, and m is the mass of the satellite.

This more general expression shows that at large distances, GPE becomes increasingly negative, approaching zero as r becomes infinitely large. A satellite with negative total energy is in a bound orbit because the kinetic energy (which is always positive) is not enough to overcome the magnitude of the negative GPE, hence the satellite remains gravitationally bound to Earth. As for the trend in the ratio of kinetic energy to the change in potential energy as the size of the orbit increases, it generally decreases, indicating that for larger orbits, the kinetic energy constitutes a larger fraction of the total energy needed to maintain the orbit.

The assumption made in this derivation is that the satellite orbits around the center of the astronomical body (such as Earth), and not around a common center of mass, which is not exact but works well since Earth is much more massive compared to the satellite, as in the case of the Moon orbiting the Earth.

Part A. The initial speed of the egg is 17.7 m/s.

Part B. The maximum height of the egg is 15.98 m.

Part C. The magnitude of the velocity at its highest point is 0 m/s.

Part E. The magnitude and direction of the acceleration in the upward direction is 9.8 m/s2.

Given that the distance traveled by the egg is 34 m in time 5 seconds.

The distance at its initial point will be zero.

The initial speed of the egg can be calculated by the position equation of the egg.

[tex]x = x_0 + v_0t + \dfrac {1}{2}at^2[/tex]

Where x is the initial position of the egg that is 0 m, x_0 is the final position that is 34 m in time t = 5 s, v_0 is the initial speed and a is the acceleration. Since the egg is thrown vertically, hence the acceleration of the egg is similar to the gravitational acceleration.

[tex]0 = 34 + v\times 5 + \dfrac {1}{2}\times(- 9.8)\times 5^2[/tex]

[tex]v = \dfrac {122.5 - 34}{5}[/tex]

[tex]v = 17.7 \;\rm m/s[/tex]

The initial speed of the egg is 17.7 m/s.

The maximum height for the egg can be calculated by the equation given below.

[tex]v^2 = v_0^2 + 2gh[/tex]

For the highest point, the final speed v will be zero and the initial speed v_0 is 17.7 m/s. Hence,

[tex]0 = (17.7)^2 + 2\times (-9.8)\times h[/tex]

[tex]19.6 h = 313.29[/tex]

[tex]h = 15.98 \;\rm m[/tex]

The maximum height of the egg will be 15.98 m.

The velocity of the object thrown at a height will be zero at its highest point. Hence the velocity of the egg will be zero at its highest point.

Velocity [tex]v_h[/tex] = 0 m/s

The egg is thrown vertically upward, hence its acceleration is similar to the gravitational acceleration.

Acceleration a = 9.8 m/s2

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Answer:

Spring constant of the spring will be 68.6 N/m

Explanation:

It is given mass which is vertically hung m = 6.80 kg

Spring is stretched by length of 0.1 m , so x = 0.210 m

Acceleration due to gravity will be equal to [tex]g=9.8m/sec^2[/tex]

Force on the mass which is vertically hung will be equal to mg

This force will be balanced by spring force acting on the mass

And spring force is equal to F = Kx

So kx = mg

[tex]k\times 0.1=0.7\times 9.8[/tex]

k = 68.6 N /m

So spring constant of the spring will be equal to 68.6 N/m

Answer:

It's an ORDINAL Level of measurement.

The level of measurement for data collected on a Always/Sometimes/Never scale is ordinal.

The level of measurement for data collected on a Always/Sometimes/Never scale is ordinal. In an ordinal scale, data can be categorized and ordered, but the intervals between data points may not necessarily be equal or meaningful. In this case, the habit categories would have a natural order (Always, Sometimes, Never), but the difference between Always and Sometimes may not be the same as the difference between Sometimes and Never.

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Answer:

d) business intelligence

Explanation:

 Business intelligence refers to applications and technologies that are used to gather, provide access to, and analyze data and information to support decision-making efforts. Business Intelligence uses technologies for the data analysis of business information to make strategic decision for enterprises. Common functions of business intelligence technologies include reporting, online analytical processing, analytics, data mining, process mining, complex event processing, business performance management, benchmarking, text mining, predictive analytics and prescriptive analytics.

The technologies that support decision-making by collecting and analyzing data are known as business intelligence. Transforming data into information is achieved through asking relevant questions and using information systems. Information technology advancements have greatly improved this process.

The application and technologies used to gather, provide access to, and analyze data and information to support decision-making efforts are referred to as business intelligence. The process of transforming data into information involves collecting raw data, which are simply facts, measurements, or characteristics, and then analyzing these data to gain valuable insights or knowledge. Clearly, to obtain information, one must ask the right questions and use information systems to process the raw data. Due to advancements in information technology, such as computerized databases and database management systems, data can be stored, retrieved, manipulated, and analyzed more efficiently than ever, contributing significantly to the Information Age we live in today.

Answer: Option (1) is the correct answer.

Explanation:

Formula to calculate correlation coefficient is as follows.

           Correlation coefficient = [tex]\sqrt{R^{2}}[/tex]

As the slope for given equation is positive so, it means that the correlation will also be positive in nature.

Therefore, we will calculate the value of correlation coefficient as follows.

         Correlation coefficient = [tex]\sqrt{R^{2}}[/tex]

                                               = [tex]\sqrt{(0.288)^{2}}[/tex]  

                                               = 0.54

Thus, we can conclude that the correlation coefficient, r is 0.54.          

Answer: The oscilloscope is not a plotting machine.

Explanation: The Oscilloscope is not a plotting machine is a device which is use to measure the frequency,period, peak to peak Voltage Vpp or any signal. That is alternating.

So, if you're such you wired your circuit whose output signal you want to measure very well and all connections and settings are done accurately, then you can reduce the volt/div below 0.2. You not seeing any signal at 0.2v/div shows that the amplitude of the signal coming into the Oscilloscope is not up to that.

The x-axis on an oscilloscope represents time, while the y-axis represents voltage. To view a 6 volt signal when the 'volts/div' is set at 0.2, you should adjust it to 2 volts/div or higher, as the current setting is too low to display the signal's amplitude correctly.

On an oscilloscope, the horizontal axis (or x-axis) typically represents time, allowing you to see how a signal changes over time. The vertical axis (or y-axis) represents voltage, displaying the amplitude of the signal. If you are attempting to view a 6 volt signal with the "volts/div" setting at 0.2 volts per division, the signal will be off-scale, because each division will represent only 0.2 volts, and a 6 volt signal would require 30 divisions to be fully displayed, which is beyond the scope of a standard oscilloscope screen.

To properly view the 6 volt signal, you should turn the dial to 2 volts/div or higher. This adjustment will ensure that the signal occupies fewer divisions on the screen, making it visible. If you set it to 0.02 volts/div, the signal would be even less visible because the signal would then require 300 divisions, which is impractical to display.

Answer:

[tex]\displaystyle CD=BE\ \frac{CA}{BA}[/tex]

Explanation:

Thales Theorem

It applies when a line is drawn parallel to one side of a triangle and it intersects the other two sides. The theorem states that line divides the two sides in the same ratio or proportion.

We have drawn the triangle that describes the situation stated in the question, where we want to know the value of CD, knowing the values of BE, BA, and CA. The red line BE is parallel to the line CD, so the Tales theorem must stand meaning that the sides AC and AB are proportionally divided at the same ratio as CD and BA, thus

[tex]\displaystyle \frac{CD}{BE}=\frac{CA}{BA}[/tex]

We can solve for CD (the height of the flagpole)

[tex]\boxed{\displaystyle CD=BE\ \frac{CA}{BA}}[/tex]

Answer:If we want to find the height of an object like a flagpole, we can use right triangles. In the graphic above, triangle ABE is similar to triangle ACD. In the graphic line segment DC is the height of the flagpole. Using the length of BE (your height), AB (your shadow), and AC (the shadow of flagpole), we can use a proportion to determine the height of the flagpole.

Explanation: fill in the blank

Answer:

[tex]\dfrac{F}{L}=\dfrac{\mu_oI^2}{2\pi d}[/tex]

Explanation:

If the current flowing in two wires is I and they are separated by a distance of d. We know that the magnetic field due to a wire is given by :

[tex]B=\dfrac{\mu_oI}{2\pi d}[/tex]

Where

d is the separation between wires

The magnetic force between the wires is given by :

[tex]F=BIL[/tex]

I is the current in wire

L is the length of the wires

[tex]F=\dfrac{\mu_oI^2L}{2\pi d}[/tex]

The magnetic force per unit length is given by :

[tex]\dfrac{F}{L}=\dfrac{\mu_oI^2}{2\pi d}[/tex]

So, the force per unit length F/L between the two wires is [tex]\dfrac{\mu_oI^2}{2\pi d}[/tex]. Hence, this is the required solution.

Answer:

Explanation:

According to Boyle's law  for constant temperature of gas Pressure is inversely proportional to the volume of gas.

[tex]PV=nRT[/tex]

[tex]PV=constant[/tex]

[tex]P\propto \frac{1}{V}[/tex]

if Pressure is tripled then

[tex]P\times V_1=3P\times V_2[/tex]

[tex]V_2=\frac{V_1}{3}[/tex]

Volume becomes one-third of original volume          

Final answer:

According to Boyle's Law, tripling the pressure on a gas at constant temperature will reduce its volume to one third of the original volume.

Explanation:

The question is based on Boyle's Law which states that for a given mass of an ideal gas at constant temperature, the volume of the gas is inversely proportional to its pressure. Therefore, if the pressure acting on a gas is tripled (pressure is proportional to 3), the volume will be reduced to one third of its original value (volume is proportional to 1/3), assuming that the temperature and the amount of gas remain constant.

To find the vector sum of the electric forces exerted on particle 3, calculate the electric forces exerted by particle 1 and particle 2 and add them as vectors. Use Coulomb's law to find the electric forces. Add the x and y components of the forces to get the vector sum.

To find the vector sum of the electric forces exerted on particle 3, we need to calculate the electric forces exerted on particle 3 by particle 1 and particle 2 and then add them together as vectors. The electric force exerted on particle 3 by particle 1 can be found using Coulomb's law, which states that electric force between two charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them.

By substituting the given values into the equations, you can calculate the x and y components of the vector sum of the electric forces exerted on particle 3.

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Final answer:

To find the vector sum of the electric forces exerted on particle 3, we need to calculate the electric force between particle 3 and both particle 1 and particle 2. The electric force between two charges is given by Coulomb's Law. By plugging in the charges and distances, we can calculate the electric forces and find the vector sum.

Explanation:

To find the vector sum of the electric forces exerted on particle 3, we need to calculate the electric force between particle 3 and both particle 1 and particle 2. The electric force between two charges is given by Coulomb's Law:

F = k * (|q1| * |q2|) / r^2

Where F is the electric force, k is the electrostatic constant, q1 and q2 are the charges, and r is the distance between the charges. Since particle 1 is fixed at the origin, the distance between particle 3 and particle 1 is |-4.0 m| = 4.0 m. Similarly, the distance between particle 3 and particle 2 is |4.0 m - (-4.0 m)| = 8.0 m. Plugging in the values, we can calculate the electric forces between particle 3 and both particle 1 and particle 2.

Let's calculate:

F3-1 = (9 * 10^9 N.m^2/C^2) * (|-4.0 μC| * |8.0 μC|) / (4.0 m)^2

F3-2 = (9 * 10^9 N.m^2/C^2) * (|-4.0 μC| * |8.0 μC|) / (8.0 m)^2

Now, we can find the vector sum of the electric forces by adding the x-components and the y-components of both forces.

Explanation:

Iron has tiny magnetic domains inside it. Each domain acts like a tiny magnet with its own magnetic field. These domains are randomly distributed thus resulting in zero magnetic field and iron doesn't behave like a magnet.

When a copper wire is wound around the nail and current is passed through the coil, magnetic field is generated. This magnetic field penetrates through the nail. Due to this the magnetic domains of the nail align in the same direction thus having a net magnetic field. The nail behaves like a magnet till the time current flows through the coil.

Answer:

convection

Explanation:

Convective heat transfer, often referred to simply as convection, is the transfer of heat from one place to another by the movement of fluids. this time fluid is out atmosphere.

Answer:

9 Km

Explanation:

given,

distance of the river = 4 Km = 4000 m

speed of the boy = 2 m/s

speed of the dog back and forth = 4.5 m/s

distance ran by the dog = ?

time taken by the boy to cover the distance

we know,

distance = speed x time

[tex]t = \dfrac{4000}{2}[/tex]

t = 2000 s.

now, distance travel by the dog.

d= 4.5 x 2000

d = 9000 m

d = 9 Km

distance covered by the dog is equal to 9 Km.

The acceleration of the proton is 6.7×10¹⁰ m/s² in the direction of the electric field.

Electrostatic force:

The force on a charged particle due to an electric field is given by:

F = qE

where q is the charge = 1.6×10⁻¹⁹C

and E is the electric field = 700N/C

Also, from Newton's laws of motion;

F = ma

where m is mass = 1.67×10⁻²⁷kg and a is acceleration

ma = qE

a = qE/m

[tex]a=\frac{1.6\times10^{-19}\times700}{1.67\times10^{-27}}\;m/s^2\\\\a=6.7\times10^{10}\;m/s^2[/tex]towards the direction of the electric field.

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Answer:

8.29 * 10^{13} N

Explanation:

Weigth is the force of gravity a body of mass experiences due to the gravity of another mass.

Force=mass*acceleration (to calculate the mass of the object);

675=m*9.8; Mass = 68.88 kg

Force= [tex]\frac{GMm}{r^{2} }[/tex]; M is the mass of the bigger object, m is the mass of the smaller object, r is the seperation in between (radius in this case) and G is the Gravitational constant.

Mass of the sun = 1.989 × 10^30 kg

G = 6.67 × 10-11 m3 kg-1 s-2

mass of the object = 68.88 kg;

Applying the formula:

Force=[tex]\frac{(6.67 * 10^{-11} ) * (68.88) * (1.989 * 10^{30} )}{(((21 *10^{3} ))/2)^{2} }[/tex]

Force = 8.29 * 10^{13} N

The weight on the surface of a neutron star that has the same mass as our Sun and a diameter of 21.0 km will be 8.29 × 10¹³ N

Given that the weight of the person on the earth is 675N.

mg = 675N

where m is the mass of the person.

m = 675/g

m = 675/9.8

m = 68.87 kg

The gravitational force on the surface of a celestial body is given by:

F = GMm/R²

where G is the gravitational constant

M is the mass of the body

m is the mass of the person

and, R is the radius of the body

F = (6.67 × 10⁻¹¹)( 2 × 10³⁰)(68.87) / (21/2 × 10³)²

F = 8.29 × 10¹³ N

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Explanation:

Kirchhoffs Voltage Rule, or KVL, explains that "the overall voltage throughout the circuit in any closed loop network is equal to the sum of all voltage decreases inside the same loop" which is equivalent to zero. In other words, the mathematical sum of all within the loop voltages must be equal to zero.

Answer: A. Vb1 = -6m/s , Vb2 = 9m/s.

B. Vb1 = 4.5m/s , Vb2 = 4.5m/s

Explanation: A. In a perfectly elastic collision the objects involved moved with a different velocity after collision. Also kenitic energy is conserved. In other to get the different velocity of ball 1 (Vb1) and ball 2 (Vb2) after collision, we apply the following formula

Vb1 = {{m1 - m2}*V1}/{m1 +m2}

Vb2 = {{2m1}*V1}/{m1 + m2}

Where V1 = velocity of ball 1 before collision=15m/s

m1 = mass of ball 1

m2 = mass of ball 2.

Substituting in the above equation:

Vb1 = {{0.15kg - 0.35kg}*15}/{0.15 + 0.35}

= {{-0.2}*15}/0.5

= -3/0.5

= -6m/s

Also,

Vb2 = {{2*0.15kg}*15m/s}/{0.15kg + 0.35kg}

={0.3kg*15m/s}/0.5kg

=4.5/0.5

=9m/s

B. In a perfectly inelastic collision the object involved move with a common velocity after collision.

We have that ,

m1*V1 + m2*v2 = {m1 + m2} V¹

Where V¹ is the final velocity of both balls after a perfectly inelastic collision.

NOTE: v2 here is 0m/s since ball 2 was at rest before collision.

So we have,

0.15kg*15m/s + 0.35kg*0m/s = {0.15kg + 0.35kg}*V¹

2.25 kgm/s = 0.5kg* V¹

Making V¹ subject of formula we have,

V¹ = 2.25kgm per sec/0.5kg

=4.5m/s. vb1 = Vb2 = V¹

NOTE also that the mass of the balls from the question were given in gram hence we converted to kilogram the standard unit for mass by dividing by 1000.

Answer:

For both ball 1 and ball 2, the change in velocity is less in an inelastic collision.

Explanation:

a short simple answer

Explanation:

In both cases the conversion of one chemical element into another is obtained, modifying the number of protons in the nucleus. The difference is that artificial transmutation needs an outside cause, since an outside particle reacts with the nucleus, while in nuclear  decay not cause outside is needed.

Explanation:

A wave on a string is described is given by :

[tex]D(x,t)=2\ cm\ sin[(12.57\ rad/m)-(638\ rad/s)t][/tex]

The linear density of the string is 5 g/m.

Where

x is in meters and t is in seconds

The general equation of a wave is given by :

[tex]y=A\ sin(kx-\omega t)[/tex]

(2) The speed of the wave in terms of tension is given by :

[tex]v=\sqrt{\dfrac{T}{\mu}}[/tex]

Also, [tex]v=\dfrac{\omega}{k}[/tex]

So, [tex]\dfrac{\omega}{k}=\sqrt{\dfrac{T}{\mu}}[/tex]

[tex]T=\dfrac{\mu \omega^2}{k^2}[/tex]

[tex]T=\dfrac{5\times 10^{-3}\times (638)^2}{(12.57)^2}[/tex]

T = 12.88 N

(3) The maximum displacement of a point on the string is equal to the amplitude of the wave. So, the maximum displacement is 2 cm.

(4) The maximum speed of a point on the string is given by :

[tex]v=A\omega[/tex]

[tex]v=0.02\times 638[/tex]

v = 12.76 m/s

Hence, this is the required solution.

Answer:

1- Surface water

2- Groundwater

3- Lake

4- River

5- Watershed/Catchment basin

6- Wetland

Explanation:

The questions are defining concepts involved in the study of Geography, specifically hydrology. These concepts include surface water, groundwater, a lake, a river, a watershed, and a wetland.

The series of questions relates to the nature and characteristics of different water bodies and water-related geographical phenomena.

1. Surface water refers to all liquid fresh water located above ground.
2. Precipitation that infiltrates Earth's surface and percolates downward becomes groundwater.
3. A lake is a large body of water that has extensive areas of open water, some of which is too deep for photosynthetic life.
4. A river meanders across land and structures the landscape.
5. A watershed is the entire land area that supplies a river or stream with water from precipitation.
6. A wetland has water-saturated soil, shallow standing water, and ample vegetation.

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Answer:

3.735×10⁻⁶ N

Explanation:

From newton' s law of universal gravitation,

F = Gmm'/r² .............................. Equation 1

Where F = Gravitational force between the person and the refrigerator, m = mass of the person, m' = mass of the refrigerator, r = distance between the person and the refrigerator. G = gravitational universal constant.

Given: m = 70 kg, m' = 200 kg, r = 0.5 m

Constant: G = 6.67×10⁻¹¹ Nm²/kg².

F = (6.67×10⁻¹¹×70×200)/0.5²

F = 93380×10⁻¹¹/0.25

F = 373520×10⁻¹¹

F = 3.735×10⁻⁶ N

Hence the force between the person and the refrigerator =  3.735×10⁻⁶ N

Answer: [tex]1.000\times 10^2m^2[/tex]

Explanation:

Significant figures : The figures in a number which express the value -the magnitude of a quantity to a specific degree of accuracy is known as significant digits.

The rule apply for the multiplication and division  is :

The least precise number present determines the number of significant figures in the answer.  

The rule apply for the addition and subtraction is :

The least precise number present after the decimal point determines the number of significant figures in the answer.

Area of square collector 1 =

Area of square collector 1 =[tex]6.00m\times 6.00m=36.0m^2[/tex]

Area of square collector 2 =[tex]length\times breadth[/tex]

Area of square collector 2 =[tex]8.000m\times 8.000m=64.00m^2[/tex]

Combined area of both collectors = Area of square collector 1 + Area of square collector 2 = [tex]36.0m^2+64.00m^2=100.0m^2=1.0\times 10^2m^2[/tex]

The combined area of both collectors is [tex]1.000\times 10^2m^2[/tex]

The combined area of both solar collectors is 1.0 × 10² m².

To find the combined area of both solar collectors, simply add the areas of the two squares. The formula for the area of a square is length multiplied by width. For the first solar collector measuring 6.00 m by 6.00 m, the area is 6.00 m x 6.00 m = 36.00 m². To find the combined area of both solar collectors, simply add the areas of the two squares. The formula for the area of a square is length multiplied by width. For the first solar collector measuring 6.00 m by 6.00 m, the area is 6.00 m x 6.00 m = 36.00 m². For the second solar collector measuring 8.000 m by 8.000 m, the area is 8.000 m x 8.000 m = 64.00 m². Adding the areas, we get 36.00 m² + 64.00 m² = 100.00 m².The correct answer, using the correct number of significant figures, is therefore 1.0 × 10² m². This answer is represented by option b.For the second solar collector measuring 8.000 m by 8.000 m, the area is 8.000 m x 8.000 m = 64.00 m². Adding the areas, we get 36.00 m² + 64.00 m² = 100.00 m².

The correct answer, using the correct number of significant figures, is therefore 1.0 × 10² m². This answer is represented by option b.