A body builder exerts 15 N of force over 3 m. How much work did she do?
3.33 J


5 J


45 J


15 J

Answers

Answer 1
Work done = force x distance

work done = 15 x 3

work done = 45J
Answer 2

Answer:

\(\boxed {\boxed {\sf 45 \ Joules}}\)

Explanation:

Work is the force the causes the movement or displacement of an object. It is the product of force and displacement.

\(W=Fd\)

The force is 15 Newtons and the displacement is 3 meters.

F= 15 N d= 3 m

Substitute the values into the formula.

\(W= 15 \ N * 3 \ m\)

Multiply.

\(W= 45 \ N*m\)

1 Newton meter is equal to 1 Joule, so our answer of 45 Newton meters is equal to 45 Joules.


Related Questions

Mass (kg) Weight (N) 0.05 0.075 0.100 0.125 0.150 0.175 0.200 0.225 0.250 0.275 0.300 Displacement (Ay) 15 cm 23cm 30cm 40cm 48cm 55cm 63cm 71cm 80cm 90cm 97cm 1. Calculate the weight for each mass and fill in the middle column. Show the work for one of these calculations to receive credit. (5 points)

Answers

Here, we need to calculate weight.

Weight is given as the product of mass and gravity. This weight over here can also be denoted by force and it is said to be the force exerted by the bodies on the Earth.

If we take the gravity to be 10 m/s²,

then the weight for each given mass will be,

weight of 0.05 kg = 0.05*10 = 0.5 N

weight of 0.075 kg = 0.075 * 10 = 0.75 N

weight of 0.100 kg = 0.100 * 10 = 1 N

weight of 0.125 kg = 0.125 * 10 = 1.25 N

weight of 0.150 kg =0.150 * 10 = 1.5 N

weight of 0.175 kg = 0.175 * 10 = 1.75 N

weight of 0.200 kg = 0.200 * 10 = 2 N

weight of 0.225 kg = 0.225 * 10 = 2.25 N

weight of 0.250 kg = 0.250 * 10 = 2.5 N

weight of 0.275 kg = 0.275 * 10 = 2.75 N

weight of 0.300 kg = 0.300 * 10 = 3 N

Therefore, through this we got to know that the weight of the body is also the force exerted by the body on the Earth.

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Which of the following best describes the image of a concave mirror when the object is at a distance greater than twice the focal point distance from the mirror?
a. virtual, upright and magnification greater than one
b. real, inverted and magnification less than one
c. virtual, upright and magnification less than one
d. real, inverted and magnification greater than one

Answers

The best describes the image of a concave mirror when the object is at a distance greater than twice the focal point distance from the mirror is (c) virtual, upright, and magnification less than one.

When the object is placed beyond twice the focal length of a concave mirror, the image formed is virtual, meaning it cannot be projected onto a screen. The image is also upright, having the same orientation as the object.

In addition, the magnification of the image is less than one, indicating that the image is smaller in size compared to the object. This is because the concave mirror forms a reduced and virtual image when the object is located beyond the focal point.

The distance between the object and the mirror affects the size and position of the virtual image formed.

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In addition to the anti-VEGF antibody, Marie has decided to also add a VEGFR primary antibody. At which position do you expect the band for VEGFR to appear? Remember that in SDS-PAGE proteins are separated according to their molecular weight. a) VEGFR runs at a lower molecular weight than VEGF b) VEGF and VEGFR run at the same molecular weight c) VEGFR cannot be detected by Western blotting d) VEGFR runs at a higher molecular weight than VEGF

Answers

VEGFR runs at a higher molecular weight than VEGF. In the position,  VEGFR is expected to appear band. Hence, option (c) is correct.

What is VEGFR?

A chemical that binds to vascular endothelial growth factor (VEGF) receptors, which may be present on some cancer cells. This might stop cancers from forming the new blood vessels they require to grow.

Anti-VEGFR monoclonal antibodies of various sorts are being researched for the treatment of cancer. These chemicals fall within the categories of monoclonal antibodies and antiangiogenesis agents.

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TRUE / FALSE. real estate refers to the physical land and improvements constructed on the land.

Answers

True. Real estate refers to the physical land and improvements constructed on the land, such as buildings and structures.

Real estate encompasses both the natural elements (e.g., soil, water, trees) and man-made improvements (e.g., homes, commercial buildings, infrastructure).

Real estate includes all land-related assets, including any physical constructions or enhancements like homes, buildings, or natural resources. Land, homes, apartments, office buildings, retail establishments, and industrial facilities are all included in it. It also includes commercial and residential assets. A movable asset with value, real estate can be purchased, sold, rented, or leased. It plays a significant role in the economy by entailing a variety of tasks like real estate development, investment, brokerage, and property management. Location, supply and demand dynamics, the status of the economy, and regulatory restrictions all have an impact on the value of real estate. Real estate is a substantial investment and a crucial component of commerce, housing, and infrastructure growth.

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According to Newton’s first law, only ___ has the ability to change motion.

Answers

Answer:

A force,

Explanation:

An object will stay in motion unless a the net force is non zero on an object. IE car rolling will slow down due to wheel friction as a force acting on it.

How much heat does it take to raise 0.0438 kg of aluminum from room temperature (20.0°C) to its melting point (660°C)?

HELP​

Answers

Answer:

2.5x10^4 J (scientific notation)

25,000 (Acellus)

Equation:

Q=mcΔT

where:

Q=heat

m = mass

c = specific heat

ΔT=change in temperature

Any rearranging?

Let's see.

No, we need heat.

So no rearranging.

Plug in the numbers and solve

It takes approximately 28,224 joules of heat to raise 0.0438 kg of aluminum from room temperature to its melting point.

To calculate the heat required to raise the temperature of aluminum from room temperature to its melting point, we need to use the specific heat capacity formula: Q = m × c × ΔT

where:

Q = heat (in joules)

m = mass of aluminum (in kilograms)

c = specific heat capacity of aluminum (in joules per kilogram per degree Celsius)

ΔT = change in temperature (in degrees Celsius)

Given:

Mass of aluminum (m) = 0.0438 kg

Specific heat capacity of aluminum (c) = 900 J/kg°C (approximate value for aluminum)

Change in temperature (ΔT) = melting point (660°C) - room temperature (20°C) = 640°C

Now, let's calculate the heat (Q):

Q = 0.0438 kg × 900 J/kg°C × 640°C

Q = 28,224 J (joules)

So, it takes approximately 28,224 joules of heat to raise 0.0438 kg of aluminum from room temperature to its melting point.

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what is the period of a wave that has a wavelength of 1 meter and a speed of 20 hz?

Answers

Answer:

0.05s

Explanation:

frequency = speed / wavelength = 20/1 = 20Hz. Thus period = 1/f = 1/20 = 0.05 s

Frequency = speed / wavelength = 20/1 = 20Hz.

Thus period = 1/f = 1/20 = 0.05 s

What is frequency?

Frequency is the number of waves that pass a fixed point in unit time.

What is time period?

The period of a wave is the time for a particle on a medium to make one complete vibrational cycle.

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is the following sentence true or false? a real image is a copy of anobject formed at the point where light rays actually meet.

Answers

The statement about a real image being formed at the point where light rays meet is accurate, making the sentence true

A real image is indeed a copy of an object formed at the point where light rays actually meet. This is in contrast to a virtual image, where the light rays do not actually meet but only appear to do so when extended backward.

In summary, the statement about a real image being formed at the point where light rays meet is accurate, making the sentence true.

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Please answer these questions. I need them by 11:59pm MST.

Please answer these questions. I need them by 11:59pm MST.
Please answer these questions. I need them by 11:59pm MST.

Answers

The distance traveled by the cart during the first 0.5 seconds is 2 m.

The acceleration of the cart during the first 0.5 seconds is 16 m/s².

The time when the object changes direction is 4 seconds.

The distance travelled by the object between t₁ and t₂ is 16 m.

The total distance travelled while moving up the incline 18 m.

Distance traveled by the cart during the first 0.5 seconds

The distance distance traveled by the cart during the first 0.5 seconds is calculated using formular for area under velocity - time graph.

d₁ = bh

where;

b is the base of the shapeh is height of the shape

d₁ = ¹/₂(0.5 s) x (8 m/s)

d₁ = 2 m

Acceleration of the cart during the first 0.5 seconds

The average acceleration is calculated as follows;

a = Δv/Δt

where;

Δv is change in velocityΔt is change in time

a = (8 m/s - 0 m/s)/(0.5 s)

a = 16 m/s²

Time when the object changes direction

Use the formula for average acceleration as shown below.

a = Δv/Δt

a = (0 - V)/(t₂ - t₁)

-2 = (0 - 8) / (t₂ - 0.5)

t₂ - 0.5 = -8/-2

t₂ - 0.5  = 4

t₂ = 4.5 s

Distance travelled by the object between t₁ and t₂

d₂ = ¹/₂(t₂ - t₁)(v)

where;

t₂ is final timet₁ is initial timev is velocity

d₂ = ¹/₂(4.5- 0.5)(8)

d₂ = 16 m

Total distance travelled while moving up the incline

The total distance travelled while moving up the incline is calculated as follows;

dt = d₁ + d₂

dt = 2 m + 16 m

dt = 18 m

Time at which the carts rolls back to the starting position

v₃ = v₂ + at₃

where;

v₃  is the final velocityv₂ is the initial velocity t₃ is the time when it moves back to the starting position

-8 = 0 + (-2Δt)

-8 = -2Δt

Δt = 8/2

Δt = 4 seconds

t₃ = t₂ + Δt

t₃ = 4.5 s + 4 s = 8.5 s

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charge q1 = 3.00 nc is at x1 = 0 and charge q2 = 7.50 nc is at x2 = 4.00 m. at what point between the two charges is the electric field equal to zero

Answers

The point between the two charges where the electric field equal to zero is calculated to be 1.55 m.

The charge q₁ is given as 3 nc = 3 × 10⁻⁹ c

It is located at x₁ = 0.

The charge q₂ is given as 7.5 nc = 7.5 × 10⁻⁹ c

It is located at x₂ = 4 m.

Let us suppose that, electric field is zero at the point x, it is in between 0 and 4 m.

We know the formula for electric field as,

E = k q /r²

Let us equate the electric field at both the charges.

k q₁/x² = k q₂/(x₂ - x)²

q₁ (x₂ - x)² = q₂ x²

3 × 10⁻⁹× (4 - x)² = 7.5 × 10⁻⁹ × x²

3 × ( 16 + x² - 8x) = 7.5 ×x²

48 + 3x² - 24x = 7.5x²

4.5 x² + 24x - 48 = 0

The two values of x are,

x = 1.55, -6.883

The distance cannot be negative. So, the electric field at x = 1.55 m is said to be zero.

Thus, the required value of x is 1.55 m.

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he speed of waves in a particular guitar string is 425 m/s. determine the fundamental frequency (1st harmonic) of the string if its length is 76.5 cm.

Answers

The fundamental frequency (1st harmonic) of the string is approximately 278.43 Hz.

The fundamental frequency of a sound wave is the lowest frequency present in the wave.

To determine the fundamental frequency (1st harmonic) of the guitar string, we can use the formula:
f = v / (2 * L)
where f is the frequency, v is the speed of waves in the string, and L is the length of the string.
1. Convert the length of the string to meters:
L = 76.5 cm * (1 m / 100 cm) = 0.765 m
2. Substitute the values into the formula:
f = (425 m/s) / (2 * 0.765 m)
3. Calculate the frequency:
f ≈ 278.43 Hz

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example of natural magnet​

Answers

Answer: lodestone

An example of a natural magnet is the lodestone, also called magnetite. Other examples are pyrrhotite, ferrite, and columbite.

Classification of Magnets

Lodestones are a common example of natural magnets. Artificial magnets – Artificial magnets can be produced by man-made means and have a stronger magnetic field. They can also be shaped as required. When an artificial magnet is shaped in the form of a bar, it is called a bar magnet.

Explanation:

Friction is a force that resists the relative motion of two objects in contact.
Why is the speciality of putting the word relative motion without putting motion

Answers

Answer:

Explanation:

Friction is a force that opposes the motion or potential motion of two items that come into contact. The word "relative motion" emphasizes that friction resists the motion of the objects with respect to one other, and it emphasizes that friction specifically operates against the motion or potential motion between two objects in contact.

A wave has a wavelength of 4 m and a frequency of 85 Hz. What is the speed of this wave?

Answers

The speed of wave with a wavelength of 4 m and a frequency of 85 Hz is 340m/s

The speed of a wave is the product of the frequency of the wave and its wavelength. Mathematically, it is expressed as:

\(v = f \lambda\) where:

f is the frequency

\(\lambda\) is the wavelength

Given the following:

f =85Hz

\(\lambda\) = 4 m

Substitute the given parameter into the formula:

v = 85 × 4

v = 340m/s

Hence the speed of wave with a wavelength of 4 m and a frequency of 85 Hz is 340m/s

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a sound wave with a wavelength of 26m passes through glass and then it passes into air where wavelengths changes to 1.6m. if the soundwave has a constant frequency of 220hz, what is it’s approximate speed as it passes through the air?

a, 5,700 m/s
b, 3,500 m/s
c, 350 m/s
d, 570 m/s

Answers

.............The answer is C
Answer : C 350 m/a

Explanation:

1. A capacitor is made of 2 rectangular metal plates with side length of 3cmx6cm separated by a distance of 2. 36cm with water in between the plates. The capacitor has a voltage of 110v and is not connected to a battery. Calculate the capacitance. What is the new capacitance if we replace water with a new dielectric material with a constant of 3. 75 in between the plates? What is the new voltage? What is the charge on each plate?


2. A capacitor of 3. 23µF has an area of 6. 35mm^2. Determine the separation distance between the two plates. If the new capacitance is now 5. 63mF, what is the value of the dielectric inserted to the capacitor? What is the new voltage if the capacitor is connected to a 110 volts source? If the electric field created by two plates 8. 99x10^4 N/C and a working voltage of 63 volts. Will the capacitor experience a dielectric breakdown? Prove your answer.


USE GRESA

Answers

the electric field is more than the threshold value and the capacitor will experience dielectric breakdown.

1. Given values are,
side length of metal plates, a = 3 cm and b = 6 cm
distance between the plates, d = 2.36 cm
voltage, V = 110 V
dielectric constant of water, k = 80.4
dielectric constant of new material, k2 = 3.75
a) To calculate the capacitance of capacitor, the formula is, C=εA/d  ……………… (1)
where A = area of plate, ε = permittivity, and d = separation distance between two plates.
We know that the permittivity of vacuum is given as, ε0 = 8.854 x 10^-12 F/m
The capacitance of capacitor can be expressed as,
C1 = ε0 (kA/d) …………….. (2)
where, ε0 = permittivity of vacuum, k = dielectric constant and A = area of plate.
Substituting the given values in equation (2),
C1 = 8.854 x 10^-12 x 80.4 x (0.03 x 0.06)/0.0236
C1 = 0.000132 F
Therefore, the capacitance of capacitor is 0.000132 F.

b) To calculate the new capacitance, the formula is given as,
C2 = k2ε0A/d ……………… (3)
where k2 is the dielectric constant of new material.
Substituting the given values in equation (3),
C2 = 3.75 x 8.854 x 10^-12 x (0.03 x 0.06)/0.0236
C2 = 0.000263 F
Therefore, the new capacitance is 0.000263 F.

c) The new voltage can be calculated as,
V2 = V1(C1/C2) …………… (4)
Substituting the given values in equation (4),
V2 = 110 (0.000132/0.000263)
V2 = 55 V
Therefore, the new voltage is 55 V.

d) The charge on each plate is given as,
Q = CV ………….. (5)
Substituting the given values in equation (5),
Q = 0.000132 x 110
Q = 0.0145 C
Therefore, the charge on each plate is 0.0145 C.

2. Given values are,
capacitance, C = 3.23 µF
area of plate, A = 6.35 mm^2
separation distance between two plates, d = ?
new capacitance, C2 = 5.63 mF
new dielectric constant, k2 = ?
voltage, V = 110 V
electric field between two plates, E = 8.99 x 10^4 N/C
working voltage, Vw = 63 V

a) The separation distance between two plates can be calculated as,
C1/C2 = d2/d1  …………….. (6)
where d1 and d2 are the initial and final separation distance, respectively.
Substituting the given values in equation (6),
3.23 x 10^-6/5.63 x 10^-3 = d2/d1
d2 = 5.63 x 10^-3 x (d1/3.23 x 10^-6)
Area of plate, A = 6.35 mm^2 = 6.35 x 10^-6 m^2
The capacitance can be expressed as,
C = εA/d
d = εA/C
where ε = permittivity of dielectric material.
Therefore, substituting the given values in above equation,
d1 = ε x 6.35 x 10^-6/3.23 x 10^-6
d1 = 12.50 ε
Substituting the value of d1 in equation (6),
5.63 x 10^-3 = d2/12.50 ε
d2 = 70.38 ε
The separation distance between two plates is 70.38 ε.

b) The new dielectric constant can be calculated as,
C2 = k2ε0A/d2
k2 = C2d2/ε0A
Substituting the given values in above equation,
k2 = 5.63 x 10^-3 x 70.38 ε/(8.854 x 10^-12 x 6.35 x 10^-6)
k2 = 3.95
Therefore, the new dielectric constant is 3.95.

c) The new voltage can be calculated as,
V2 = V1(C1/C2)
Substituting the given values in above equation,
V2 = 110(3.23 x 10^-6/5.63 x 10^-3)
V2 = 0.063 V
Therefore, the new voltage is 0.063 V.

d) The electric field can be expressed as,
E = V/d
d = V/E
Substituting the given values in above equation,
d = 63/8.99 x 10^4
d = 7.01 x 10^-4 m
The voltage, V = 110 V > working voltage, Vw = 63 V

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if i0 = 20.0 w/m2 , θ0 = 25.0 degrees , and θta = 40.0 degrees , what is the transmitted intensity i1 ? express your answer numerically in watts per square meter .

Answers

The transmitted intensity is approximately 12.98 W/m^2.

The intensity of the light transmitted through a surface is given by:

i1 = i0 * cos(θ0) * cos(θta)

where i0 is the intensity of the incident light, θ0 is the angle of incidence (measured from the surface normal), and θta is the angle of transmission (measured from the surface normal).

Substituting the given values, we get:

i1 = 20.0 W/m^2 * cos(25.0°) * cos(40.0°)

i1 = 12.98 W/m^2

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electricity is the blank of electrons, because electrons blank from atom to atom

Answers

Answer:

Electricity is the flow of electrons, because electrons pass from atom to atom.

Plzzzz helpppppppo Near the end of the life cycle of a star why does the star lose its size

Answers

Answer:

Because the energy is waning

Explanation: hope this helps

According to the graph, how much Potassium bromide can be dissolved in 100 g of warer at 40C?

Answers

Answer:

77.8 g potassium bromide can be dissolved in 100 grams of water at 40°C.

Explanation:

In a given a line of KBr is straight.

please convert 3mm to m

Answers

Answer:

Below

Explanation:

To convert mm to m all you need to do is divide the value by 1,000

so : 3 / 1,000 = 0.003 meters

Hope this helped!

The distance of the force from the axis of rotation is called?

Answers

Answer:

explain you qns. briefly

Look at the diagram of the male reproductive system. Name the parts

Answers

The testes are the primary male reproductive organs responsible for producing testosterone.

How to explain the parts

Vas Deferens: Also known as the ductus deferens, it is a muscular tube that carries mature sperm from the epididymis to the ejaculatory ducts.

Seminal Vesicles: These glands produce a fluid rich in fructose and other nutrients, which helps nourish and provide energy to the sperm.

Prostate Gland: It is a walnut-sized gland that produces a milky fluid containing enzymes, proteins, and other substances that contribute to se men formation.

Cowper's Glands: These small glands secrete a clear, alkaline fluid that lubricates the urethra and neutralizes any acidic urine remnants, creating a favorable environment for sperm.

Urethra: This is a tube that runs  serves as a passage for both urine and semen, though not at the same time.

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Look at the diagram of the male reproductive system. Name the parts

A student jumps from a flat surface with an initial velocity of 15ms. If the distance covered is 3m. What is the acceleration due to gravity and the time?

Answers

Answer:

the acceleration due to gravity, g is zero (0)

the time of the motion is 0.2 s

Explanation:

Given;

initial velocity of the student, u = 15 m/s

distance traveled by the student, x = 3 m

The motion of the student is directed towards the horizontal and the acceleration due to gravity, g is zero (0).

The time of the motion is calculated as;

x = ut + ¹/₂gt²

x = ut + ¹/₂(0)t²

x = ut

t = x/u

t = 3 / 15

t = 0.2 s

Therefore, the time of the motion is 0.2 s

given that the moon takes 27.32 days to make a complete circuit around the celestial sphere (360o), what is the approximate angular size of mars?

Answers

Mars exhibits the most range in apparent size and brightness of any planet. Between 25.69" and 3.49", its angular size ranges by a factor of more than seven.

We are aware that it takes the moon 27.32 days to orbit the earth. Thus, we are aware of an orbit's period.

Ratios: 2 days equals 27.32 days, and 1 radian equals 1 second.

Radians per second are equal to (2)/(27.32 days* 24 hours/day * 60 minutes/hr * 60 seconds/minute)

Equation: = 2*pi*(1/T)

Either way, it is clear that we must translate the days into seconds and then divide the resulting number by 2pi.

Mars exhibits the most range in apparent size and brightness of any planet. Between 25.69" and 3.49", its angular size ranges by a factor of more than seven.

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A satellite orbiting Earth at an orbital radius r has a velocity v. What would the velocity be if the satellite is moved to an orbital radius of 6r

Answers

Orbital velocity of satellite

\(v = \sqrt{ \frac{gm}{r} } \)

Radius of new orbit r' =6r

Thus new orbital velocity of satellite:

\(v = \sqrt{ \frac{gm}{6r} } = \frac{v}{ \sqrt{6} } \)

About Orbital speed

For satellites in circular orbits, the relationship between orbital velocity and altitude is strict. The task of a satellite launch rocket is to release the satellite at a suitable place in space, with the appropriate speed and direction of movement to put it in the desired orbit.

How a satellite stays in orbit can be thought of in two equivalent ways, both of which explain the relationship between the satellite's altitude and velocity.

The motion of the satellite can be seen as creating a centrifugal force that opposes the gravitational pull. For example, imagine attaching an object to a string and swinging it in a circle. The object is pulling outward against the string, and that outward force (centrifugal force) becomes greater the faster the object swings. At the right speed, the centrifugal force of the satellite due to motion around the earth just balances the gravitational pull, and the satellite remains in orbit.

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Marine science- question- what is climate change?

Answers

Answer:

Defined below

Explanation:

Climate change is simply the long term change in the average weather patterns that are associated with the local, regional and global climates of the earth. Climate change is usually driven by human activities like burning of fossils; natural processes like cyclic ocean patterns; external factors like volcanic eruptions.

How are engineers creating clothing that can charge your cell phone. Explain the science behind their innovation.

Answers

Answer:

By the use of carbon nanotubes as the clothing material.

Explanation:

Carbon nanotubes is a technology designed by engineers that could make charging of the cell of a phone possible. It has some some required properties like it is strong, conductive and heat-resistant which are suitable for the purpose.

This technology which involves a progressive dipping of a pure cotton material into nafion polymer, then in a chemical solution of carbon nanotubes and finally in polystyrene until it becomes saturated and have a conductive property. The conductive cotton can be used to make such cloths which becomes conductive and produces some electromagnetic waves when there is a contact with sweat or fluid from the body. The waves generated can be used to charge a cell phone through radiation interaction.

Which form of electromagnetic radiation has a wavelength of 10-7 nanometers?
a. Gamma rays
b. Infrared
c. Ultraviolet
d. Radio waves

Answers

The form of electromagnetic radiation that has a wavelength of 10-7 nanometers is known as Ultraviolet. Thus, the correct option for this question is C.

What is Electromagnetic radiation?

Electromagnetic radiation may be defined as a type of radiation that considerably possesses both electric and magnetic fields. Apart from this, these radiations always travel in waves. Electromagnetic radiations include visible light, radio waves, gamma rays, X-rays, etc.

Among all kinds of electromagnetic radiations, gamma rays have the shortest wavelength and high frequency. While microwaves have the longest wavelength and lowest frequency. As the wavelength and frequency are inversely related to one another.

Therefore, ultraviolet radiation is a type of electromagnetic radiation that has a wavelength of 10-7 nanometers. Thus, the correct option for this question is C.

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a stone is thrown horizonttaly from a cliff of a hill with an initial velocity of 30m/s it hits the ground at a horizontal distance of 80m from the foot of the hill how long does a stone travel? what is the height of the hill? (please show the process)​

Answers

Answer:

a) Time = 2.67 s

b) Height = 35.0 m

Explanation:

a) The time of flight can be found using the following equation:

\( x_{f} = x_{0} + v_{0_{x}}t + \frac{1}{2}at^{2} \)   (1)

Where:

\( x_{f}\): is the final position in the horizontal direction = 80 m

\( x_{0}\): is the initial position in the horizontal direction = 0

\(v_{0_{x}}\): is the initial velocity in the horizontal direction = 30 m/s

a: is the acceleration in the horizontal direction = 0 (the stone is only accelerated by gravity)

t: is the time =?  

By entering the above values into equation (1) and solving for "t", we can find the time of flight of the stone:  

\( t = \frac{x_{f}}{v_{0}} = \frac{80 m}{30 m/s} = 2.67 s \)

b) The height of the hill is given by:

\( y_{f} = y_{0} + v_{0_{y}}t - \frac{1}{2}gt^{2} \)

Where:

\( y_{f}\): is the final position in the vertical direction = 0

\( y_{0}\): is the initial position in the vertical direction =?

\(v_{0_{y}}\): is the initial velocity in the vertical direction =0 (the stone is thrown horizontally)            

g: is the acceleration due to gravity = 9.81 m/s²

Hence, the height of the hill is:

\( y_{0} = \frac{1}{2}gt^{2} = \frac{1}{2}9.81 m/s^{2}*(2.67 s)^{2} = 35.0 m \)  

I hope it helps you!

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