The horizontal and vertical components of the initial velocity of a football are 24 m/s and 7 m/s respectively. what is the initial velocity of the football?

2.5 × 10⁻⁷ atoms will occupy 3.51 mm.

Firstly converting the radius of a tungsten atom from picometer to millimeter.

As per the known fact, 1 pm = 10⁻⁹ mm

Radius in mm = 137 × 10⁻⁹ mm

Radius in mm = 1.37 × 10⁻⁷ mm  

Now, if atoms are laid side by side, then the distance occupied by each atom will be equal to it's diameter.

Now, 1.37 × 10⁻⁷ mm space is occupied by : 1 atom

Space occupied by 3.51 mm = (1÷ 1.37 × 10⁻⁷)×3.51

Performing multiplication and division

Space occupied by 3.51 mm = 2.5× 10⁻⁷ atoms

Hence, 2.5× 10⁻⁷ atoms will occupy 3.51 mm.

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[tex]\frac{-2}{15} \\radians per secondExplanation:Denoting the distance in feet between the wall and the base of the ladder by x and the angle in radians between the ladder and the ground by y, it is notedcos(y)=x/10which impliesy=arccos(x/10)Denoting time in seconds by t, it is further noted that[/tex]

[tex]\frac{dy}{dt}= \frac{dy}{dx}\frac{dx}{dt} (chain rule)\\ Noting (using standard table of derivatives for convenience)\\\frac{dy}{dx} = -\frac{0.1}{\sqrt{1-0.01x^{2} } } \\\frac{dx}{dt} =0.8 f/sec\\so,\\\frac{dy}{dt}(8)=\frac{dy}{dx}\frac{dx}{dt} = -\frac{0.08}{\sqrt{1-0.01(64)} } \\ = -\frac{0..8}{\sqrt{0.36} } =\frac{8}{60} = \frac{-2}{15 } radian/sec[/tex]

The radian is a term of angular measurement established so that an arc with an arc length of 1 is produced by an angle over one radian area enclosed from the center of a unit circle.

When measuring angles, the radian is frequently employed in physics. For instance, angular velocity is frequently expressed in terms of radians per second (rad/s). The reciprocal of one revolution per second is two radians per second.

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According to potential energy, the energy released is 78.4 kJ.

We need to know about potential energy to solve this problem. The potential energy is the object's energy caused by its position. Potential energy can be determined as

PE = m . g . h

where PE is potential energy, m is mass, g is the gravitational acceleration (9.8 m/s²) and h is height.

From the question above, we know that

m = 80 kg

h = 100 m

By substituting the given parameters, we can calculate the height

PE = m . g . h

PE = 80 . 9.8 . 100

PE = 78400 joules

PE = 78.4 kJ

Hence, the energy released is 78.4 kJ.

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The rockets average acceleration during these first 5 minutes is 33.33 m/s².

The average acceleration of an object refers to the rate at which the velocity changes with time of motion of the object.

a = Δv/Δt

where;

The given parameters include;

v = 10 km/s = 10 km/s x 1000 m/1km = 10,000 m/s

t = 5 minutes = 5 x 60 s = 300 seconds

a = 10,000 / 300

a = 33.33 m/s²

Thus, the rockets average acceleration during these first 5 minutes is 33.33 m/s².

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By using the blackbody radiation formula, the temperature of the filament inside the bulb is changed by a factor of 10⁰'²⁵.

To tackle this issue, we need to understand black body radiation. A black body object's energy emission is inversely proportional to its area and the temperature to the fourth power. It may be established that

P = A . e . σ . T⁴

where P (power), A (surface area), e (emissivity), ( 5.67 x 10¯⁸ W/m²K⁴), and T (temperature) are all variables.

From the question above, we know that

P1 = 10 watt

P2 = 100 watt

T1 = T1

By using the black body radiation formula, the ratio of temperature is

T1⁴ / T2⁴ = P1 / P2

Hence,

T1⁴ / T2⁴ = P1 / P2

T1⁴ / T2⁴ = 10 / 100

T1⁴ / T2⁴ = 1 / 10

T2⁴ = 10T1⁴

T2 = ⁴√(10T1⁴)

T2 = T1 x 10⁰'²⁵

Thus, the temperature of the filament inside the bulb is changed by a factor of 10⁰'²⁵.

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A light-rail commuter train accelerates at a rate of 1.40 m/s2, it take 15.17s to reach its top speed of 76.5 km/h, starting from rest.

When describing the motion of the objects in terms of distance, time, and direction, physicists use the basic quantities of speed and velocity. Two terms and two distinct meanings. Yet, not uncommonly, we hear these terms used in interchangeably. So, what is the difference? Why is it incorrect to use terms speed and velocity interchangeably?

The reason is very simple. Speed is time rate at which an object is moving along a path, while velocity is the rate and direction of an object’s movement. Put another way, the speed is a scalar value, while velocity is a vector.

The mathematical calculation for speed is relatively straightforward, wherein the average speed of an object is calculated by dividing the distance traveled by the time it took the object to travel distance. Velocity, on the other hand, is more complicated mathematically and can be calculated in different ways, depending on what information is available about object’s motion. In its simplest form, average velocity is calculated by dividing change in position (Δr) by change in the time (Δt).

The formula to find the acceleration is:

[tex]a=\frac{v-u}{t}\\ t=\frac{v-u}{a}\\\\ =\frac{21.25-0}{1.40} \\\\ =15.17[/tex]

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Answer:

0.003 meters

Explanation:

[tex]d=3mm(\frac{1m}{1000mm} )=\frac{(3)(1)}{1000} =\frac{3}{1000} =0.003m[/tex]

Hope this helps

Answer:

3× 10^ {-3}m  

Explanation:

3mm=0.003m

0.003= 3× 10^ {-3}

If the mass of squirrel is 0.40g and the force by which boat pulls the squirrel is 2N, then the acceleration of squirrel is 5 m/s²

Given,

Force = 2N

Mass = 0.4kg

According to Newton's second law of motion, the rate of change of momentum is directly proportional to the force.

F = ma ----(1)

where,

m is the mass of the body

a is the acceleration by which body move

F is the force

From 1 equation,

a = F/ m

By substituting all the values, we get

a = 2/0.4

a = 5

Thus, we concluded that if the mass of squirrel is 0.40g and the force by which boat pulls the squirrel is 2N, then the acceleration of squirrel is 5 m/s².

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By using uniform motion, the car displacement is 225 meters.

We need to know about the uniform motion to solve this problem. The uniform motion is an object's motion under acceleration. It should follow the rule

vt = vo + a . t

vt² = vo² + 2a . s

s = vo . t + 1/2 . a . t²

where vt is final velocity, vo is initial velocity, a is acceleration, t is time and s is displacement.

From the question above, we know that

a = 2 m/s²

vo = 0 m/s

t = 15 s

Use the third equation to calculate the displacement

s = vo . t + 1/2 . a . t²

s = 0 . 15 + 1/2 . 2 . 15²

s = 0 + 225

s = 225 m

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The difference between the solar system, the galaxy, and the universe is as  follows:

A solar system consists of a star and objects that are affected by its gravity revolve around it. The objects that revolve around the star are planets, moons, asteroids, and comets. Take an example of our solar system, the Sun is the star, and all the planets including Earth and moons are revolving around it.

A Galaxy consists of billions of stars and Solar systems. Despite billions of stars, most of a galaxy is empty. This tells a lot about the size of a galaxy. The galaxy that we are in is known as Milky Way.

The universe is all matter and space that there is. It consists of all the galaxies, the solar systems, and everything known to mankind.

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A piano string having a mass per unit length equal to 5.20 10^-3 kg/m is under a tension of 1 250 n, then speed with which the wave travels is 490.29 m/sec

Wavelength x Frequency equals speed. When the wavelength and frequency values are known, this equation can be used to determine the wave speed.

If the wave speed and the other value are known, the equation for wave speed can be written to solve for wavelength or frequency. Unit = meters/second

The distance a wave shape travels divided by the time it takes to cover that distance is its velocity. Also known as wave velocity V. Symbol meters/second are the units (ms-1).

The speed of the wave's doubles when the frequency of a wave source is doubled.

V= sqrt T/u = sqrt [1250/5.20 x 10^-3]

= 490.29 m/sec

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The mass of objects such as books, sandwiches, phones, pictures can be measured using a weighing balance scale.

The mass of an object is defined as the scalar quantity of that object that shows the amount of matter that makes up the object.

Mass is called a scalar quantity as it doesn't require the direction of an object but only it's magnitude to be measured.

it is measured in Kilograms or Kg using a weighing balance scale.

The volume of an object is the relationship that exists between its height, length and width. That is, L×W×H.

The volume of the ten rectangular shaped objects given above can be measured once the height, length and width of the objects are known.

The density of the objects is the relationship that exists between the mass and the volume of the object. That is,

Density= mass/volume.

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They are 1 meter apart.

The definition of force in physics is that it is a push or pull on a massed object that helps change its velocity.

An external force is a kind of agent that has the power to alter any type of resting or moving condition of a body. It has got its own direction and a magnitude.

One thing experiences a force from another. There are both living things and non-living objects in the concept of a force.

All objects, living and non-living, have the ability to exert a force on or against another item, as well as have their actions affected by forces.

The newton, abbreviated N, is the SI unit of force. The meter and unit are the foundation units that pertain to force.

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We have looked at generational cohorts (e.g., gen x, millennials and gen z) in class. these are helpful to marketers, since all consumers within a generational cohort share the same lifestyle preferences

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If you drop the same rock from half the height, the acceleration will be 4.9 m/s².

The acceleration of the object dropped from half of the given height is calculated as follows;

h = vt + ¹/₂at²

where;

h = 0 +  ¹/₂at²

h =  ¹/₂at²

2h =  at²

a = 2h/t²

a = (2 x 0.5h)/t²

a = (h)/(t²)

a = (17 m) / (1.86263²)

a = 4.9 m/s²

Thus,  if you drop the same rock from half the height, the acceleration will be 4.9 m/s².

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The refractive index, n of glass is 1.53.

The critical angle of a refracting medium such as glass is the angle at  no refracted ray is obtained for light passing through the medium between the boundary or interface of the medium and a less dense medium, rather an emergent ray which is per perpendicular to the normal is obtained.

Beyond the critical angle, total internal reflection occurs.

The refractive index of a medium is the ration of the velocity of light in the less dense medium to that in a denser medium.

Given that the critical angle of a medium is C;

Refractive index, n of the medium = 1/ sin C

The critical angle from glass to air is 40.5°

The refractive index of glass = 1/sin 40.5°

Refractive index, n of glass = 1.53

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The s sublevel can only hold two electrons because it has one orbital. The p sublevel has three orbitals and a maximum capacity of six electrons.

The d sublevel may hold a maximum of 10 electrons due to its five orbitals. Additionally, the 4 sublevel has 7 orbitals and a maximum of 14 electrons.

The third energy level has nine orbitals.

N is the number of orbits, while n2 is the number of orbitals (s).

How many orbitals can each set of quantum numbers identify at their greatest capacity?

As a result, the provided quantum number can only identify a maximum of one orbital, or 3pz.

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The velocity components of an electron moving between two charged parallel plates are[tex]v_y + Eed/m_ex v_x[/tex].

Any vector's magnitude, represented by its unit and pointing in the direction of the vector, is its length. As a result, the acceleration's magnitude is equal to the length of the acceleration vector and it is pointed in the same direction.

let the magnitude charge of the electron =[tex]e = 1.6 \times10^{-19} C[/tex]

me= mass of electron = 9.11 x 10^-31

force on the electron = Ee

Magnitude of acceleration [tex]a= Ee/m_e[/tex]

In x direction there is no field --> no force---> no acceleration

[tex]d = v_xt[/tex]

[tex]t = d/v_x[/tex]

the y-component of electron's velocity when its x coordinate has changed by a distance [tex]d v_y' = v_y + at = v_y + Eed/m_ex v_x[/tex]

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True

Capacitance is the ability of a component or circuit to collect and store energy in the form of an electrical charge.

Electric Charge is the property of subatomic particles that causes them to experience a force when put in an electric and magnetic field.  Electric charges are of two sorts: Positive and Negative, commonly carried by charge carriers protons and electrons.

Electric charge is a scalar quantity. Apart from having a magnitude and direction, a quantity to be named a vector ought to too comply the laws of vector addition, such as triangle law of vector addition and parallelogram law of vector addition; as it were at that point the amount is said to be a vector quantity. When two currents meet at a intersection, within the case of an electric current, the resultant current of these will be an algebraic sum and not the vector whole. Subsequently, an electric current may be a scalar quantity, in spite of the fact that it has magnitude and direction.

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Answer:

None of the choices is appropriate.

Explanation:

The boat will eventually stops and then speeds up in the reverse direction.

Because the object has an initial positive (northward) velocity and a negative (southward) acceleration; so, a graph of velocity versus time slopes down steadily from an original positive velocity. Eventually, the graph cuts through zero and goes through increasing-magnitude negative values.

Acceleration is the name we give to any process where the velocity changes. Since velocity is a speed and a direction, there are only two ways for you to accelerate: change your speed or change your direction—or change both.

Magnitude is defined as the maximum extent of size and the direction of an object. Magnitude is used as a common factor in vector and scalar quantities. By definition, we know that scalar quantities are those quantities that have magnitude only. Whereas vector quantities are those quantities that have both magnitude and direction.

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   The electrical charge of the metal sphere is ∈ = 2.78×10⁻⁷C  

   The value of the load or strength of the paint droplet is ∈ = 2×10⁻¹⁰ C

   Forces are the definition of Newton's second law, which is stated under the relation:

∑ Force = mass × acceleration.

  In other words, force is the origin of motion since it generates acceleration in a system.

Completamos el enunciado:

"An electrostatic paint sprayer has a 0.200-m-diameter metal sphere at a potential of 25.0 kV that repels paint droplets onto a grounded object. (a) What charge is on the sphere? (b) What charge must a 0.100-mg drop of paint have to arrive at the object with a speed of 10.0 m/s?"

We must determine the charge on the sphere initially.

a)  We determine the radius of the sphere:

r = 0.2m/2

∈ = rV/k

∈ = (0.1m)(25000V) / (9×10⁹Nm²/C²)

∈ = 2.78×10⁻⁷C

b)     If the mass of the paint drop is 0.1mg, and it moves with a velocity of 10m/s, we determine the kinetic energy.

Ke = mV²/2

Ke = 0.1×10⁻⁶kg (10m/s)² / 2

Ke = 5×10⁻⁶J = ΔE

∈ = ΔE/ ΔV

∈ =5×10⁻⁶J / 25000V

∈ = 2×10⁻¹⁰ C

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Answer: 16 meters; -4 meters

Explanation:

For this question, you can ignore the times that were given to you.

a.) Let's start with distance. Distance is a total sum, regardless of direction. This student walked 6 meters, stands still (0 meters), 3 meters, and 7 meters. Sum up these values: 6+0+3+7 = 16 meters

b.) Displacement adds direction. The student walks 6 meters away. We will give this the +x-direction. They then walk 3 meters back towards the origin (-x-direction) and pause for a second. They continue to walk 7 more meters toward the origin (-x-direction). This time when we sum these values we must include the signs: 6+(-3)+(-7) = -4 meters. We can test this by referring to the sentence where it says they passed their starting point. This means they are now in the -x-direction and we have a negative displacement.

Hope this helps!

The vehicle that is traveling  at a 13 m/s has a velocity expressed in miles per hour of: 29.016 miles/h

To solve this problem the we have to do the conversion of units with the given information.

Information about the problem:

By converting the velocity units from  (m/s) to miles per hour (miles/h) we have:

v = 13 m/s * 1 km/1000 m * 0.62 miles/ 1 km * 3600 s/1 h

v = 29.016 miles/h

It is the transformation of a value expressed in one unit of measurement into an equivalent value expressed in another unit of measurement of the same nature.

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Answer:

SYRINGE B PLUNGER FORCE=3*2=6

Force produced by plunger B is 6 Newtons

Answer:

Doesn't matter how fast it was going, all that matters now is that little ducky went splat and he is living no more

Explanation:

There is not enough information

There is no ground.

There is no ducky.

And it is not moving.

The car will travel 69.3m while accelerating, using the equation of motion.

Using the equation of motion:

[tex]v^{2}- u^{2} = 2as[/tex]

[tex]s = \frac{v^{2}-u^{2} }{2a}[/tex]

where, s = displacement

u = initial velocity

v = final velocity

a = acceleration

Plugging in the values we get,

[tex]s = \frac{21^{2} - 5^{2} }{2*3.0}[/tex]

s = 69.3meters

Therefore, the car will travel 69.3m while accelerating, using the equation of motion.

The complete question is: A car accelerates from 5.0 m/s to 21 m/s at a constant rate of 3.0 m/s2, How far does it travel while accelerating?

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Based on the calculations, the radius of a tantalum (Ta) atom is equal to 0.143 nm.

Given the following data:

Density of tantalum (Ta) = 16.6 g/cm³.

Atomic weight of tantalum (Ta) = 180.9 g/mol.

Density can be defined as a ratio of mass to the volume of a physical object such as a tennis ball. Mathematically, the density of a physical object can be calculated by using this formula:

Density = Mass/Volume

For the mass of this unit cell, we have:

Mass = 2 atoms/unit-cell  × 180.9 g/mol × 1  mol /6.022 x 10²³ atoms/mol

Mass = 6.01  x 10⁻²² g/unit-cell

Next, we would determine the volume and edge length of the cube:

Volume, V = 6.01 x 10⁻²²/16.6

Volume, V = 3.62 x 10⁻²³ cm³

For the edge length, we have:

V = a³

a = ∛V

a = ∛3.62 x 10⁻²³ cm

Edge length, a = 3.31 x 10⁻⁸ cm

Mathematically, the edge length of a body-centered cubic unit cell is given by this formula:

a = 4r/√3

r = a × √3/4

r =  3.31 x 10⁻⁸ × √3/4

Radius, r = 1.43 × 10⁻⁸ cm

Lastly, we would convert the value in cm to nm:

Radius, r = 1.43 × 10⁻⁸ × 1/100 × 1 × 10⁹

Radius, r = 0.143 nm.

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The furanose form of the fructose is generated by formation of a hemiketal involving the attack of the hydroxyl group on carbon 5 with carbon 2.

Furanose can be drawn in the different structures such as Haworth structures and Fischer projections. But arrangement of atoms in the plane of the ring and Ch2Oh groups outside the plane of the ring can be clearly understood from Haworth structures. By looking at the Haworth furanose ring, one can observe that the −OH group on the second carbon is placed in two different ways on the plane of the ring. If hydroxyl group −OH is placed below the ring then it can be called as alpha form. If the −OH group is placed above ring, then it is named as beta furanose. These two forms are similar in all the respects except in stereo-geneticity. Furanose can form pyranose rings also by hemiketal formation of carbonyl of second carbon and hydroxyl of sixth carbon. This results in the formation of pyranose form of fructose. But predominant form of fructose among both is furanose rings. In both these form anomers are possible.

The furanose form of the fructose is generated by formation of a hemiketal involving the attack of the hydroxyl group on carbon 5 with carbon 2.

(This generates five-member furanose ring typical of fructose.)

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The number of significant figures in the product is 2.7537 x 10¹.

The term significant figures refers to the number of important single digits  in the coefficient of an expression in scientific notation.

(3.52 x 10^-11) x (7.823 x 10^11)

= (3.52 x 7.823) x (10⁻¹¹ ⁺ ¹¹)

= 27.53696 x 10⁰

= 27.53696

= 2.7537 x 10¹

Thus, the number of significant figures in the product is 2.7537 x 10¹.

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