The main greenhouse gases in the atmospheres of the terrestrial planets are

Answer:The universe sprang into existence as singularity around 13.7 billion years ago.

Explanation:

Answer:

Explanation:

a ) Let the height achieved be h .

We shall apply law  of conservation of mechanical energy.

1 /2 mv² = mgh

h = v² / 2g

v = 110 km/h

= 30.55 m /s

h = [tex]\frac{30.55\times30.55}{2\times9.8}[/tex]

h = 47.61 m

b )

Kinetic energy of car in the beginning

= 1/2 x 750 x (30.55)²

= 349988.43 J

Potential energy at 22 m height

= 750 x 9.8 x 22

= 161700 J

Energy lost due to frictional force

= 349988.43 - 161700

= 188288.43 J

c )

Distance covered along the slope

d = 22 / sin2.5

= 22 / 0.043619

d = 504.36 m

If F be average frictional force

work done by friction

F x d

= F x 504.36

so

F x 504.36 = 188288.43

F = 188288.43 / 504.36

= 373.32 N

Final answer:

Using the conservation of energy principle, the car's initial kinetic energy is converted into potential energy as it ascends the hill. The potential energy at the given height can be used to determine the thermal energy generated by friction. Calculating the average force of friction requires knowing this thermal energy and the distance traveled, considering the slope angle.

Explanation:

To calculate the height a car can coast up with negligible work done by friction, we can use the principle of conservation of energy. Specifically, the car's initial kinetic energy (due to its initial speed) will be converted into potential energy (due to gaining height) as it coasts uphill until it comes to a stop.

(a) The Height a Car Can Coast Up

Initial kinetic energy (KE) is given by the equation KE = \(\frac{1}{2}mv^2\), where m is the mass of the car and v is its speed. If we convert 110 km/h to meters per second (30.56 m/s), we can calculate the available kinetic energy. The potential energy (PE) at the height h is given by PE = mgh, where g is the acceleration due to gravity (9.81 m/s^2) and h is the height. Setting KE equal to PE, we can solve for h.

(b) Thermal Energy Generated by Friction

If the car actually reaches a height of 22.0 m, we can calculate the difference in the theoretical and actual potential energy to find the thermal energy due to friction. Subtracting the actual potential energy from the total initial kinetic energy gives us the energy lost to friction.

(c) Average Force of Friction

To calculate the average force of friction on a slope of 2.5°, we will use the energy lost to friction divided by the distance traveled along the slope and correct for the slope angle. This gives the component of the friction force that acts parallel to the hill's surface.

1) The electrostatic force between the two pieces of paper is [tex]2.16\cdot 10^{13} N[/tex]

2)

Explanation:

1)

The electrostatic force between two charged objects is given by Coulomb's law:

[tex]F=k\frac{q_1 q_2}{r^2}[/tex]

where:

[tex]k=8.99\cdot 10^9 Nm^{-2}C^{-2}[/tex] is the Coulomb's constant

[tex]q_1, q_2[/tex] are the two charges

r is the separation between the two charges

In this problem, we have the following situation:

[tex]q_1 = 0.2 C[/tex] is the charge on the first piece of paper

[tex]q_2 = 0.3 C[/tex] is the charge on the second piece of paper

[tex]r=0.005 m[/tex] is their separation

Substituting into the equation, we find the magnitude of the electrostatic force between them:

[tex]F=k\frac{q_1 q_2}{r^2}=(8.99\cdot 10^9) \frac{(0.2)(0.3)}{(0.005)^2}=2.16\cdot 10^{13} N[/tex]

2)

The electrostatic force can be either attractive of repulsive, depending on the relative sign of the charges of the objects involved.

In particular, we have:

Therefore, in this case:

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Answer

given,

number of dog = 8

mass of each dog= 19 Kg

mass of sled = 210 Kg

average force = 185 Nss

a) writing all the horizontal force

   force acting by dog - friction force = (M + 8m) a

   8 F_d - μ m g = (M + 8m) a

assuming coefficient of friction of snow be μ = 0.14

    8 x 185 - 0.14 x 210 x 9.8 = (210 + 8 x 19 ) x a

               a = 3.29 m/s²

b)  the kinetic friction of coefficient is less than static friction

 hence, we can suggest that acceleration of the sled will increase once the sled start to move.

                a > 3.29 m/s²

Answer:

v₂ = 7.6 x 10⁴ m/s

Explanation:

given,

speed of comet(v₁) = 1.6 x 10⁴ m/s

distance (d₁)= 2.7 x 10¹¹ m

to find the speed when he is at distance of(d₂) 4.8 × 10¹⁰ m

v₂ = ?

speed of planet can be determine using conservation of energy

K.E₁ + P.E₁ = K.E₂ + P.E₂

[tex]\dfrac{1}{2}mv_1^2-\dfrac{GMm}{r_1} = \dfrac{1}{2}mv_2^2-\dfrac{GMm}{r_2}[/tex]

[tex]\dfrac{1}{2}v_1^2-\dfrac{GM}{r_1} = \dfrac{1}{2}v_2^2-\dfrac{GM}{r_2}[/tex]

[tex]v_2^2= v_1^2 + \dfrac{2GM}{r_2}-\dfrac{2GM}{r_1}[/tex]

[tex]v_2= \sqrt{v_1^2 +2GM(\dfrac{1}{r_2}-\dfrac{1}{r_1})}[/tex]

[tex]v_2= \sqrt{(1.6\times 10^4)^2 +2\times 6.67 \times 10^{-11}\times 1.99 \times 10^{30}(\dfrac{1}{4.8\times 10^{10}}-\dfrac{1}{2.7\times 10^{11}})}[/tex]

v₂ = 7.6 x 10⁴ m/s

The speed when at a distance of [tex]4.8*10^{10} m[/tex] is mathematically given as

vf = 6.92 * 10^(4) m/s

Generally, the equation for the conservation of energy is mathematically given as

E = (1/2)mv^2 - GmM/r

Where

E_i = E_f

Hence

(1/2)mv_i^2 - [tex]\frac{GmM}{(r_i)}[/tex] = (1/2)mv_f^2 - [tex]\frac{GmM}{(r_f)}[/tex]

[tex]v_f = \sqrt{[(v_i)^2 + 2MG((1/r_f) - (1/r_i))]}[/tex]

Therefore

[tex]v_f = \sqrt{(2.1*10^4)^2 + 2(1.9891 * 10^{31})*(6.67 * 10^{-11})(\frac{1}{4.9} * 10^{10}) - (\frac{1}{2.5} * 10^{11}))} *20.408 *10^{12}[/tex]

[tex]v_f = \sqrt{(441000000) + 435.38 * 10^{7}}[/tex]

vf = 6.92 * 10^(4) m/s

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Answer:

The angular momentum in this case is [tex] \mathbf{24\,\frac{kg\,m^{2}}{s}} [/tex]

Explanation:

The angular momentum of a point mass moving around an axis of rotation is the cross product between the distance of the object to the axis (r) of rotation and the linear momentum (p) of the particle:

[tex] \overrightarrow{L}=\overrightarrow{r}\times\overrightarrow{p} [/tex] (1)

But linear momentum is defined as mv, so (1) is:

[tex]\overrightarrow{L}=\overrightarrow{r}\times m\overrightarrow{v} [/tex](2)

And its magnitude is:

[tex]L=rmv*\sin\theta=(4)(2)(3)\sin(90)=\mathbf{24\,\frac{kg\,m^{2}}{s}} [/tex] (3)

It is important to note that [tex] \theta [/tex] is the angle between the radius vector and the velocity vector, because the axis of rotation is perpendicular to the circle and through its center this angle is equal to 90° and [tex] \sin(90) = 1 [/tex]

Answer:

B. Color perception is achieved by activation of various combinations between the tree cone types.

Explanation:

Human eye have only three photo receptor ( three wavelength) but they can see several thousands of shades of color because color perception is gained by combination of these three wave length cone types ( RED, BLUE AND GREEN) into various combinations. Our retina have two types of cell:- cone cells and cylindrical cells. Cone cells are responsible for the identification of color.

Answer:

The force of impact of the water bottle is F = 13,475 N

Explanation:

Given data,

The height of the antenna, h = 275 m

The mass of the 1 L water bottle, m = 1 kg

Let the bottle moves distance immediately after the impact is, d = 0.2 m

The force exerted by the bottle on the bushes at the ground is given by the formula,

                                   F = mgh / d

Substituting the values

                                   F = 1 x 9.8 x 275 / 0.2

                                      = 13,475 N

The value of the force of impact can be reduced by increasing the value of d, it is like the lowering the hand along with the motion of the ball to catch it thereby reduce the force of impact.

The force of impact of the water bottle is F = 13,475 N

Answer:(1) Pre-solar nebula

(2). Planet formation

Explanation:

Nebular hypothesis says that the Solar System formed from the gravitational collapse of a fragment of a giant molecular cloud.

One of the collapsing fragments called the pre-solar nebula formed what became the Solar System.

The planet can also be formed by accretion. Accretion is a process in which planets began as dust grains in orbit around the central protostar.

When the terrestrial planets were forming, they remained immersed in a disk of gas and dust.

Answer: c is true

Explanation: the boy choirstars sang the soprano and alto. Although Palestrina choir is made up of six voice part of soprano, alto, tenor, baritone and bass and the choir sings without instruments.

In the case of Giovanni Pierluigi da Palestrina’s Pope Marcellus Mass, the correct statement is that all the parts were originally sung by men and boys. It was not written in Italian, does not represent Protestant music tactics and was not banned by the Council of Trent.

Out of the provided options, the statement that is true of Giovanni Pierluigi da Palestrina’s Pope Marcellus Mass is that all the parts were originally sung by men and boys (option c). The work is a significant one in the history of polyphonic choral music and it marked a departure from the complex style of the early Renaissance period. Instead of Italian, the mass is actually written in Latin, which was the language conventionally used in the liturgy of the Catholic Church (thus discrediting option b). Unlike Protestant music of the time (which negates option a), it does not emphasize congregational singing but instead focuses on the choir. It was also never banned by the Council of Trent. (disproving option d)

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The initial speed of the mountain biker can be determined using principles of projectile motion, by first calculating the time of flight from the vertical displacement and then substitifying this into the equation for horizontal displacement.

This problem can be solved using principles of projectile motion, where motion is analysed separately along the vertical and horizontal axes.

The time of flight can be determined by considering the vertical displacement and using the equation y = V0y*t - 0.5*g*t^2, where y is the vertical displacement, V0y is the initial vertical velocity, t is the total time, and g is the acceleration due to gravity. Solving for t, we can substitute this into the equation for horizontal displacement x = V0x*t, where x is the horizontal displacement and V0x is the initial horizontal velocity. This allows us to solve for the initial speed.

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The mountain biker's initial speed is found using the principles of projectile motion by resolving into horizontal and vertical components and solving a quadratic equation. The initial speed needed to achieve the jump is approximately 13.65 m/s.

Determining the Initial Speed of the Mountain Biker

To find the initial speed of the mountain biker, we'll use the principles of projectile motion. We'll perform a step-by-step analysis considering horizontal and vertical components separately.

Given data:

Step-by-Step Solution

Step 1: Separate the initial speed into horizontal (Vx) and vertical (Vy) components:

[tex]V_x = V_0 \cos(35.2^o) \\V_y = V_0 \sin(35.2^o)[/tex]

Step 2: Use the horizontal motion formula to express time (t):

[tex]x=V_xt[/tex]

[tex]$\begin{equation}t = \frac{x}{Vx} = \frac{30.1}{V_0 \cos(35.2^o)}\end{equation}$[/tex]

Step 3: Use the vertical motion formula considering the displacement:

[tex]$\begin{equation}y = V_y t + \frac{1}{2} a t^2\end{equation}$[/tex]

Substituting known values and simplifying, we have:

[tex]$\begin{equation} -14.7 = (V_0 \sin(35.2^o)) \times \frac{30.1}{V_0 \cos(35.2^o)} + \frac{1}{2}(-9.8) \left( \frac{30.1}{V_0 \cos(35.2^o)}\right)^2\end{equation}$[/tex]

[tex]or, -14.7=V_0\times0.57\times \frac{30.1}{V_0\times 0.817} -4.9\times (\frac{30.1}{V_0\times 0.817})^2 \\or,-14.7=20.99-4.9\times\frac{906.01}{V_0^2\times0.66} \\or, 6650.9/V_0^2=20.99+14.7\\or,V_0^2=6650.9/35.69\\or, V_0=13.65m/sec[/tex]

The initial speed is 13.65 m/sec.

Answer:

the final temperature is T f = 64.977 ° C≈ 65°C

Explanation:

Since the thermus is insulated, the heat absorbed by the ice is the heat released by the coffee. Thus:

Q coffee + Q ice = Q surroundings =0 (insulated)

We also know that the ice at its melting point , that is 0 °C ( assuming that the thermus is at atmospheric pressure= 1 atm , and has an insignificant amount of impurities ).

The heat released by coffee is sensible heat : Q = m * c * (T final - T initial)

The heat absorbed by ice is latent heat and sensible heat : Q = m * L + m * c * (T final - T initial)

therefore

m co * c co * (T fco - T ico) + m ice * L + m ice * c wat  * (T fwa - T iwa) = 0

assuming specific heat capacity of coffee is approximately the one of water c co = c wa = 4.186 J/g°C and the density of coffee is the same as water

d co = dw = 1 gr/cm³

therefore m co = d co * V co = 1 gr / cm³ * 106 cm³ = 106 gr

m co * c wat * (T f  - T ico) + m ice * L + m ice * c wat  * (T f - T iwa) = 0

m co * c wat * T f+ m ice * c wat  * T f  = m ice * c wat  * T iwa  + m co * c wat * Tico -m ice * L

T f  = (m ice * c wat  * T iwa  + m co * c wat * Tico -m ice * L ) /( m co * c wat * + m ice * c wat )

replacing values

T f = (11 g * 4.186 J/g°C * 0°C +  106 g * 4.186 J/g°C*80°C - 11 g * 334 J/gr) / ( 11 g * 4.186 J/g°C +  106 g * 4.186 J/g°C* ) = 64,977 ° C

T f = 64.977 ° C

Answer:

T = 812.8414 N

Explanation:

Using the law of newton we found the vertical(y) and horizontal(x) forces as:

∑[tex]F_x[/tex] = T - [tex]F_k[/tex] = ma

Where T is the tension, [tex]F_k[/tex] is the friction force, m is the mass of the stuntman and a is the aceleration of the stuntman.

but a is equal to 0 because he is moving at a constant velocity, so:

T - [tex]F_k[/tex] = 0

T = [tex]F_k[/tex]

Also,

[tex]F_k[/tex] = [tex]U_kN[/tex]

where [tex]U_k[/tex] is the coefficient of kinetic friction and N is the normal force.

For find N we use:

∑[tex]F_y =[/tex] N - mg = 0

N = mg

N = (119)(9.8)

N = 1166.2

Finally we solve for T as:

T = [tex]U_kN[/tex]

T = (0.697)(1166.2)

T = 812.8414 N

Answer:

See attachment

Explanation:

Answer:

Explanation:

This generator is called Vande Graff generator.

It collects the charge from the belts and accumulate on a large sphere.

It is used to accelerate the charge particles and based on the principle of corona discharge and charge resides on the outer surface.

Answer:

See explanation below

Explanation:

To do this, we need the relation between a fermi and angstrom. We know the relation between the angstrom and meters, and fermi and meters, so, we can actually solve this by doing the conversion of meters.

1 A = 1x10^-10 m

1 m = 1 A / 1x10^-10 m

1 m = 1x10^10 A

Now if we do the same thing with the fermi:

1 f = 1x10^-15 m

1 m = 1 f / 1x10^-15 m

1 m = 1x10^15 f

then:

1x10^10 A = 1x10^15 f

A/f = 1x10^10 / 1x10^15

A/f = 1x10^-5

Answer:

v₃ = 28.2842 m/s

∅ = 45°

Explanation:

Given info

vi = 0 m/s

m₁ = m₂ = m

m₃ = 3m

mi = m₁ + m₂ + m₃ = m + m + 3m = 5m

v₁x= - 60 m/s

v₁y= 0 m/s

v₂x= 0 m/s

v₂y= - 60 m/s

We can apply the Principle of Conservation of Momentum as follows

pix = pfx   ⇒   mi*vix = m₁*v₁x + m₂v₂x + m₃*v₃x

⇒  5m*(0) = m*(-60) + m*(0) + 3m*v₃x

⇒  0 = -60*m + 3m*v₃x     ⇒    v₃x = 20 m/s (→)     (I)

piy = pfy   ⇒   mi*viy = m₁*v₁y + m₂v₂y + m₃*v₃y

⇒  5m*(0) = m*(0) + m*(-60) + 3m*v₃y

⇒  0 = -60*m + 3m*v₃y    ⇒    v₃y = 20 m/s (↑)     (II)

then

v₃ = √(v₃x² + v₃y²)

⇒  v₃ = √((20 m/s)² + (20 m/s)²) = 20√2 m/s = 28.2842 m/s

is the magnitude of its velocity immediately after the explosion

∅ = tan⁻¹(v₃y / v₃x)

⇒ ∅ = tan⁻¹(20 m/s / 20 m/s) = tan⁻¹(1) = 45°

is the direction of its velocity immediately after the explosion (the angle with respect to the x-axis)

The third piece of the exploding vessel moves along the positive x and y axes due to the conservation of momentum. The magnitude of its velocity can be derived by applying the Pythagorean theorem to its momentum components and its angle with respect to the x-axis is 45 degrees.

This question involves concepts from physics specifically dealing with the conservation of momentum in two-dimensional motion. As the vessel explodes, the total initial momentum of the vessel (at rest) should be equal to the total final momentum, given that no external force is acting on the system.

Since the two pieces with equal mass fly off perpendicular to each other at the same speed, the x and y-components of their momentum will cancel each other out as they are equal in magnitude but opposite in direction. Consequently, the third piece with thrice the mass must account for the total momentum. Therefore, its direction of motion will be along the positive x and y axes.

To figure out the magnitude of velocity, we use the Pythagorean theorem on the x and y momentum components (which are equal in this scenario). We then derive the velocity of the last piece by the ratio of its momentum to its mass. The angle with respect to the x-axis would be 45 degrees as it is moving equally along the positive x and y axes.

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Answer:

C. undulating displacement of air molecules caused by pressure changes.

Explanation:

Sound is a mechanical wave arising from the movement back and forth of the media objects through which the sound wave travels.If a sound wave moves through air from left to right, then particles of air will move both to the right and to the left as the sound wave's energy passes through it.

The sound wave is formed by air molecules that are displaced due to pressure changes.

Therefore the answer is C.

Sound waves are caused by the undulating displacement of air molecules due to pressure changes. Hence, option(c) is correct.

1. When an object like a speaker cone vibrates, it alternately compresses and expands the air around it.

2. The regions where air molecules are pushed together are called compressions, and the regions where they are spread apart are called rarefactions.

3. Sound waves travel through the air as longitudinal waves, consisting of alternating high-pressure (compression) and low-pressure (rarefaction) regions.

4. These pressure changes propagate at a speed of approximately 340 m/s in air, creating the disturbance known as a sound wave.

Answer:

λ=589nm

Explanation:

The wavelength of the sodium light can be calculated using the next equation:

[tex] \lambda = \frac{\Lambda D}{L} [/tex]  

where Λ: is the distance between the adjacent bright regions, λ: is the wavelength of the sodium light, L: is the distance between slits and screen, and D: is the distance between slits.  

[tex] \lambda = \frac{7.32mm \cdot 0.12mm}{1490mm} = 5.89\cdot 10^{-4}mm = 589nm [/tex]

Therefore, the λ of the sodium light is 589 nm.  

I hope it helps you!

Answer:

5 N

Explanation:

The bucket is moving at a constant speed of 2m/s Therefore F=ma is 0 N for this to be correct the magnitude of the force exerted by the rope must be equal to the weight of the bucket which is 5 N

Answer:

Magnitude of force on the rope=5N

Explanation:

The bucket is lowered by a constant speed,therefore the tension on the rope must be equal to the weight of the bucket.

The energy [tex]6.311 \times 10^{7} \mathrm{J}[/tex] is transferred to the surroundings from water in order to freeze completely.

Explanation:

Water will transfer to surrounding will come from cooling energy from 22.3°C  to 0°C and then freezing energy is

[tex]\mathrm{E}_{\mathrm{t}}=\mathrm{E}_{\text {cooling }}+\mathrm{E}_{\text {freezing }}[/tex]

[tex]\mathrm{E}_{\mathrm{t}}=\mathrm{M}\left(\mathrm{C}_{\mathrm{w}} \Delta \mathrm{t}+\mathrm{L}_{\mathrm{f}}\right)[/tex]

We know that,

\mathrm{C}_{\mathrm{W}}=4190 \mathrm{J} / \mathrm{kgk}

[tex]\mathrm{L}_{\mathrm{f}}=333 \times 10^{3} \mathrm{J} / \mathrm{kg}[/tex]

As per given question,

M = 148 kg

[tex]\Delta \mathrm{t}=22.3^{\circ} \mathrm{C}[/tex]

Substitute the values in the above formula,

[tex]\mathrm{E}_{\mathrm{t}}=148\left(4190 \times 22.3+333 \times 10^{3}\right)[/tex]

[tex]E_{t}=148\left(93437+333 \times 10^{3}\right)[/tex]

[tex]E_{t}=148 \times 426437[/tex]

[tex]\mathrm{E}_{\mathrm{t}}=6.311 \times 10^{7} \mathrm{J}[/tex]

The energy [tex]6.311 \times 10^{7} \mathrm{J}[/tex] is transferred to the surroundings from water in order to freeze completely.

To calculate the energy required to freeze a tub of water completely, we need to account for the energy needed to both cool the water to its freezing point and then to convert it to ice. This involves the specific heat capacity of water and the latent heat of fusion.

We use the formula Q = mc extDelta T to calculate the energy to change the temperature of water to 0°C, where:

Then, we calculate the energy needed for the phase change (freezing) using the formula Q = mLf, where:

The total energy is the sum of the energy to cool the water and the energy to freeze it.

Calculations:

Answer:

x = 0.6034 m

Explanation:

Given

L = 5 m

Wplank = 225 N

Wman = 522 N

d = 1.1 m

x = ?

We have to take sum of torques about the right support point.  If the board is just about to tip, the normal force from the left support will be going to zero.  So the only torques come from the weight of the plank and the weight of the man.

∑τ = 0  ⇒     τ₁ + τ₂ = 0  

Torque come from the weight of the plank = τ₁

Torque come from the weight of the man = τ₂

⇒  τ₁ = + (5 - 1.1)*(225/5)*((5 - 1.1)/2) - (1.1)*(225/5)*((1.1)/2) = 315 N-m (counterclockwise)

⇒  τ₂ = Wman*x = 522 N*x   (clockwise)

then

τ₁ + τ₂ = (315 N-m) + (- 522 N*x) = 0

⇒  x = 0.6034 m

Answer:

0.0971

Explanation:

we know that

[tex]f max = kn[/tex]

that fmax is maximum of static friction , k is coefficient of friction and n is surface reaction force

so we know that from newtons second law

mg=n

so

kmg = 102

k = 102/mg = 102/(10*105) = 0.0971

Final answer:

The coefficient of static friction (μs) between the sofa and carpet is calculated by dividing the force required to start the sofa moving by the normal force, yielding μs = 102 N / 1050 N.

Explanation:

The coefficient of static friction μs is the ratio of the force of static friction Fs to the normal force N. It can be calculated using the equation μs = Fs / N, where Fs is the force required to start moving the object and N is the weight of the object acting perpendicular to the surface. Here, the normal force is equivalent to the weight of the sofa, which is the mass of the sofa multiplied by the acceleration due to gravity (g). With a mass of 105 kg and g approximated as -10 m/s2, the normal force is N = 105 kg × 10 m/s2 = 1050 N. The provided force to start the sofa moving is 102 N, so the coefficient of static friction is μs = 102 N / 1050 N.

Answer

given,

number of crest (N)= 5

time(t) = 50 s

distance between to successive crest = 32 m

a) Period

   [tex]T = \dfrac{t}{N}[/tex]

   [tex]T = \dfrac{50}{5}[/tex]

  [tex]T = 10\ s[/tex]

b) frequency

   [tex]f = \dfrac{1}{T}[/tex]

   [tex]f = \dfrac{1}{10}[/tex]

   [tex]f =0.1\ Hz[/tex]

c) wavelength

   distance between to consecutive crest is wavelength

    wavelength = 32 m

d) speed

         v = f λ

         v = 0.1 x 32

         v = 3.2 m/s

e) Amplitude

    We cannot determine amplitude because data is not given.

The period of the wave is 10.0 seconds, frequency is 0.1 Hz, wavelength is 32 meters, and speed is 3.2 m/s. The amplitude cannot be determined with the given data.

We can determine multiple properties of the wave based on the given information. Here are the steps and corresponding solutions:

Answer:

The velocity as a fraction of c is 0.986 c m/s

Solution:

As per the question:

Time measured by the astronaut, t = 15 yrs

Time measured in the frame of mission control, t' = 130 yrs

Now,

Using the formula of time dilation:

[tex]t' = \frac{t}{\sqrt{1 - \frac{v^{2}}{c^{2}}}}[/tex]

Substituting appropriate values in the above eqn:

[tex]130 = \frac{15}{\sqrt{1 - \frac{v^{2}}{c^{2}}}}[/tex]

[tex]\sqrt{1 - \frac{v^{2}}{c^{2}}}= \frac{15}{130}[/tex]

Squaring both the sides we get:

[tex]1 - \frac{v^{2}}{c^{2}}= (\frac{15}{130})^{2}[/tex]

[tex]\frac{v^{2}}{c^{2}} = 1 - (\frac{15}{130})^{2}[/tex]

v = 0.986 c m/s

The rocket must travel at about 99.45% of the speed of light for the astronauts aboard to age 15 years while those on Earth age 130 years, according to the theory of special relativity and the phenomenon called time dilation.

The question asks about the speed a rocket needs to travel as a fraction of the speed of light (c) for the astronaut aboard to age 15 years while those back on Earth age 130 years - an application of time dilation in special relativity. The solution to this is in the theory of relativity proposed by Albert Einstein, which states that time passes at different speeds for people depending on their relative motion.

The time dilation formula is given by Δt = γΔτ, where Δτ is the 'proper time' experienced by the moving astronaut, Δt is the time experienced by the stationary observers on Earth, and γ is the Lorentz factor, defined as γ = 1 / sqrt(1 - (v^2/c^2)).

Here, Δt is 130 years, Δτ is 15 years, and we are asked to solve for v/c. Plugging in the given values and solving for v/c, we find that v/c = sqrt(1 - (15/130)^2), approximately equals to 0.9945 or 99.45% of the speed of light. Therefore, the rocket must travel at about 99.45% of the speed of light for the astronaut to age 15 years while those on Earth age 130 years.

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Answer:

0.056 inches per minute

Explanation:

dh/dt = 8 inches per minute

dV/dt = 161 cubic inch per minute

h = 66 inches

V = 919 cubic inch

dr/dt = ? rate of change of radius

The volume of cylinder is given by

V = πr²h

where, r be the radius of cylinder

Differentiate both sides with respect to t

dV/dt = πr² x dh/dt + πh x 2r dr/dt .... (1)

When h = 66 inches, V = 919 cubic inches

So, 919 = 3.14 x r² x 66

r = 2.11 inch

Substitute the values in equation (1)

161 = 3.14 x 2.11 x 2.11 x 8 + 3.14 x 66 x 2 x 2.11 x dr/dt

dr/dt = 0.056 inches per minute

The rate of change of the radius of the cylinder, given the provided rates of change of volume and height and current volume and height, is approximately -0.123 inches/minute.

This problem is a classic example of related rates in calculus, specifically focusing on the cylinder. Given the volume of a cylinder is V = πr^2h, we know that the rate at which the volume is changing (dV/dt) is related to the rate at which the radius is changing (dr/dt) and the rate at which the height is changing (dh/dt). In this problem, we are given dV/dt (-161 cubic inches/minute) and dh/dt (-8 inches/minute). Using these given rates, the current volume and height, we can differentiate the volume formula with respect to time to find dr/dt.

Applying the chain rule, we get dV/dt = πr^2 dh/dt + 2πrh dr/dt. Substituting all given values and solving for dr/dt, we find that the rate of change of the radius when the height of the cylinder is 66 inches comes out to be approximately -0.123 inches/minute (rounded to three decimal places).

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Answer:

speed 2.997 10⁸, 2,254 10⁸, 1,999 10⁸ m / s

[tex]\lambda_{n}[/tex]  727.7, 547, 485 nm

Explanation:

The index of refraction is defined as the relationship between the speed of light in a vacuum and in a material medium

      n = c / v

Let's calculate the speed of light in the media

Air

The refractive index is very close to that of the vacuum n = 1,00029

In most experiments they are considered equal

     v = c/ n

     v = 2,998 10⁸ / 1,00029

     v = 2,997 10⁸ m / s

Water

n = 1.33

     v = 2.998 10⁸ / 1.33

     v = 2,254 10⁸ m / s

Glass

n = 1.50

     v = 2,998 10⁸ / 1,50

     v = 1,999 10⁸ m / s

Frequency and wavelength are related by the equation

      c = λ f

When a beam with a given frequency hits excites the electrons of the material and induces forced oscillations, which has the same frequency of the incident, so the frequency of the beam does not change when passing from one medium to the other.

As speed changes the only way that equality is maintained is that the wavelength changes

      [tex]\lambda_{n}[/tex] = λ₀ / n

Air

      [tex]\lambda_{n}[/tex] =727.7 nm

Water

       [tex]\lambda_{n}[/tex] = 727.7 / 1.33  

      [tex]\lambda_{n}[/tex] = 547.14 nm

Glass

     [tex]\lambda_{n}[/tex] = 727.7 / 1.50

    [tex]\lambda_{n}[/tex] = 485.13 nm

Answer:

[tex]\Delta V=0.0592\ L[/tex]

Explanation:

Given:

We have:

coefficient of volume expansion for Aluminium, [tex]\beta_a=75\times 10^{-6}\ ^{\circ}C^{-1}[/tex]

coefficient of volume expansion for steel, [tex]\beta_a=35\times 10^{-6}\ ^{\circ}C^{-1}[/tex]

Now, change in volume of the coolant after temperature rises:

[tex]\Delta V_c=V_c.\beta_c.\Delta T[/tex]

[tex]\Delta V_c=16\times 410\times 10^{-6}\times (105-95)[/tex]

[tex]\Delta V_c=0.0656\ L[/tex]

Now, volumetric expansion in Aluminium radiant:

[tex]\Delta V_a=V_a.\beta_a.\Delta T[/tex]

[tex]\Delta V_a=2\times 75\times 10^{-6}\times (105-95)[/tex]

[tex]\Delta V_a=0.0015\ L[/tex]

Now, volumetric expansion in steel radiant:

[tex]\Delta V_s=V_s.\beta_s.\Delta T[/tex]

[tex]\Delta V_s=14\times 35\times 10^{-6}\times (105-95)[/tex]

[tex]\Delta V_s=0.0049\ L[/tex]

∴Total extra accommodation volume created after the expansion:

[tex]V_X=\Delta V_s+\Delta V_a[/tex]

[tex]V_X=0.0049+0.0015[/tex]

[tex]V_X=0.0064\ L[/tex]

Hence, the volume that will overflow into the small reservoir will be the volume of coolant that will be extra after the expanded accommodation in the radiator.

[tex]\Delta V=\Delta V_c-\Delta V_X[/tex]

[tex]\Delta V=0.0656-0.0064[/tex]

[tex]\Delta V=0.0592\ L[/tex]

When the system is heated from 95 °C to 105 °C, approximately 0.066 liters of coolant would overflow to the reservoir, using the coefficient of volume expansion for the coolant.

To estimate how much coolant overflows due to thermal expansion when the system is heated from 95 °C to 105 °C, we use the coefficient of volume expansion for coolant (given as β = 410×10-6/°C). Calculate the change in volume (ΔV) with the formula:

ΔV = βVΔ0ΔT

where:

Plugging in the values, we get:

ΔV = (410×10-6/°C)(16 L)(10 °C)

ΔV = 0.066 L

Therefore, approximately 0.066 liters of coolant would overflow to the reservoir. Since metals like aluminum and steel also expand, this is an approximation as we are not factoring in the expansion of the radiator and engine housing.

Info:

weight: 96.1 kg

Length: 6 m

moved: 3.66 m

Answer:

m L = m d + M d

m L − m d = M d

m (L − x) = M x

M = m (L − x) / x

M = 96.1 kg (6 m − 3.66 m) / 3.66 m

M =  61.44098361 kg

The boats mass.

A 96.1 kg of man sits on a stem of a 6-meter longboat. The boat ouches the pier and but is not tied. The man notices a mistake and walks to the prow of the boat he moves a distance of 3.66 meters away from the pier. Thus assuming the given information the bot offers no resistance.

The mass of the boat will be equal to 61.4 kg.

Learn more about the man sits on the stern.

brainly.com/question/14519050.

Answer:

Part a)

[tex]KE = 101.4 J[/tex]

Part b)

[tex]N = 0.043 revolution[/tex]

Part c)

F = 2.7 N

Explanation:

Part a)

As we know that the rotational kinetic energy of the merry go round is given as

[tex]KE = \frac{1}{2}I\omega^2[/tex]

[tex]KE = \frac{1}{2}84.4(\omega^2)[/tex]

here we know that

[tex]\omega = 2\pi(\frac{14.8}{60})[/tex]

[tex]\omega = 1.55 rad/s[/tex]

Now we have

[tex]KE = \frac{1}{2}(84.4)(1.55^2)[/tex]

[tex]KE = 101.4 J[/tex]

Part b)

Now we know that work done due to torque = change in kinetic energy

[tex]W = KE_f - KE_i[/tex]

[tex]\tau (2N\pi) = 101.4 - 0[/tex]

[tex]375(2\pi N) = 101.4[/tex]

[tex]N = 0.043 revolution[/tex]

Part c)

In order to stop it in four revolutions we have

[tex]\tau(2\pi N) = \Delta KE[/tex]

[tex]FR(2\pi N) = 101.4[/tex]

[tex]F(1.5)(2\pi \times 4) = 101.4[/tex]

F = 2.7 N

The rotational kinetic energy is 100.64 J. The father needs to push approximately 0.0426 revolutions to start the merry-go-round. The required force to stop the merry-go-round after 4 revolutions is 2.68 N.

To answer this question, we first need to understand the concept of rotational kinetic energy, which is given by the equation K.E. = 0.5 * I * ω², where I is the moment of inertia and ω is the angular velocity. Next, we must familiarize ourselves with the concept of torque, which relates to the force applied to create rotational motion.

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