Where is the near point of an eye for which a contact lens with a power of +2.55 diopters is prescribed?Where is the far point of an eye for which a contact lens with a power of __.

Answer: London dispersion forces (i.e LDF), also known loosely Van dear Waals forces.

Explanation: The London dispersion forces is named after the German - American physicist called Fritz London.

The London dispersion forces describes the interaction between two atoms A and B after London discovered the "quantum mechanical theory".

London dispersion theory is similar to the quantum mechanical theory of "light dispersion", that is why it is called "dispersion effect". In Physics,dispersion can be explained as the variation of a quantity with frequency, which is the fluctuation of the electrons in the case of the London dispersion.

The intermolecular force found in all molecules and atoms is the London dispersion force, which occurs due to temporary fluctuations in electron distribution resulting in temporary dipoles and weak attractive forces.

The intermolecular force that can be found in all molecules and atoms is the London dispersion force. This force occurs due to temporary fluctuations in electron distribution, which can create temporary dipoles. These temporary dipoles can induce neighboring molecules or atoms to have temporary dipoles as well, leading to a weak attractive force.

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Answer:

18.6 m/s

Explanation:

[tex]h[/tex] = Initial height of the balloon = 11 m

[tex]v_{o}[/tex] = initial speed of the ball

[tex]v_{oy}[/tex] = initial vertical speed of the ball = 7 m/s

[tex]v_{ox}[/tex] = initial horizontal speed of the ball = 9 m/s

initial speed of the ball is given as

[tex]v_{o} = \sqrt{v_{ox}^{2} + v_{oy}^{2}} = \sqrt{9^{2} + 7^{2}} = 11.4 m/s[/tex]

[tex]v_{f}[/tex] = final speed of the ball as it strikes the ground

[tex]m[/tex] = mass of the ball

Using conservation of energy

Final kinetic energy before striking the ground = Initial potential energy + Initial kinetic energy

[tex](0.5) m v_{f}^{2} = (0.5) m v_{o}^{2} + mgh \\(0.5) v_{f}^{2} = (0.5) v_{o}^{2} + gh\\(0.5) v_{f}^{2} = (0.5) (11.4)^{2} + (9.8)(11)\\(0.5) v_{f}^{2} = 172.78\\v_{f} = 18.6 m/s[/tex]

Answer:

0.95 second

Explanation:

height, h = 11 m

ux = 9 m/s

uy = 7 m/s

Let it takes time t to strike the ground.

Use second equation of motion

[tex]h = u_{y}t + 0.5 gt^{2}[/tex]

- 11 = 7 t - 0.5 x 9.8 t²

-11 = 7t - 4.9t²

4.9t² - 7t - 11 = 0

[tex]t=\frac{-7\pm \sqrt{49+4\times4.9\times11}}{9.8}[/tex]

[tex]t=\frac{-7\pm 16.27}{9.8}[/tex]

take positive sign

t = 0.95 second

Thus, the time taken to reach the ground is 0.95 second.

Answer:

White Balance.

Explanation:

White balance is a configuration in our cameras to regulate how different types of light can be used to capture colors. When we take into account the "color temperature" of the light in our scene then we actually setting our white balance correctly.

Hence the correct answer to the question is white Balance.

Answer:

220 m/s²

Explanation:

given,

initial speed of car= 22 m/s

final speed of car= 0 m/s

time taken by car to stop= 0.1 s

acceleration of car is equal to change in velocity per unit time

  [tex]a = \dfrac{\Delta v}{t}[/tex]

  [tex]a = \dfrac{v_f-v_i}{t}[/tex]

  [tex]a = \dfrac{0-22}{0.1}[/tex]

         a = -220 m/s²

negative sign represent deceleration of the body

hence, deceleration of car is equal to a = 220 m/s²

Explanation:

We have equation of motion v = u + at

     Initial velocity, u = 7.3 m/s

     Final velocity, v = ?

     Time, t = 7.4 s

     Acceleration,a = 0.82 m/s²

     Substituting

                      v = u + at  

                      v = 7.3 + 0.82 x 7.4

                      v = 13.368 m/s

Final velocity is 13.37 m/s

Answer:

661748 J

Explanation:

kinetic energy =(1/2) (mass ) (SPEED)^2

                        = (0.5) ( 1125.00)( 34.2929)^2

                        = 661748 J UP TO 6 SIGNIFICANT FIGURES

Answer:

d) Black smokers

Explanation:

Hydrothermal vents form at locations where seawater meets magma.

A venting black smoker emits jets of particle-laden fluids. The particles are predominantly very fine-grained sulfide minerals formed when the hot hydrothermal fluids mix with near-freezing seawater. These minerals solidify as they cool, forming chimney-like structures. “Black smokers” are chimneys formed from deposits of iron sulfide, which is black. “White smokers” are chimneys formed from deposits of barium, calcium, and silicon, which are white.

Because deposits from hydrothermal vent fluid can contain iron, manganese, copper, zinc, and other minerals, vents have relevance to certain types of ore deposits.

The correct answer is (d)  black smokers

Torque can cause the angular momentum vector to rotate in UCM. This motion is called _Conservation of Angular momentum__________.

Answer:

Conservation of Angular momentum

Explanation:

The motion of an object in a circular path at constant speed is known as uniform circular motion (UCM). An object in UCM is constantly changing direction, and since velocity is a vector and has direction, you could say that an object undergoing UCM has a constantly changing velocity, even if its speed remains constant.

The law of conservation of angular momentum states that when no external torque acts on an object, no change of angular momentum will occur.

Key Points

When an object is spinning in a closed system and no external torques are applied to it, it will have no change in angular momentum.

The conservation of angular momentum explains the angular acceleration of an ice skater as she brings her arms and legs close to the vertical axis of rotation.

If the net torque is zero, then angular momentum is constant or conserved.

Angular Momentum

The conserved quantity we are investigating is called angular momentum. The symbol for angular momentum is the letter L. Just as linear momentum is conserved when there is no net external forces, angular momentum is constant or conserved when the net torque is zero. We can see this by considering Newton’s 2nd law for rotational motion:

τ→=dL→dt, where  

τ is the torque. For the situation in which the net torque is zero,  

dL→dt=0.

If the change in angular momentum ΔL is zero, then the angular momentum is constant; therefore,

⇒

L  =constant

L=constant (when net τ=0).

This is an expression for the law of conservation of angular momentum.

Example and Implications

An example of conservation of angular momentum is seen in an ice skater executing a spin,  The net torque on her is very close to zero,

because (1) there is relatively little friction between her skates and the ice, and (2) the friction is exerted very close to the pivot point.

Conservation of angular momentum is one of the key conservation laws in physics, along with the conservation laws for energy and (linear) momentum. These laws are applicable even in microscopic domains where quantum mechanics governs; they exist due to inherent symmetries present in nature.

Precession is the rotation of the angular momentum vector in uniform circular motion (UCM) caused by torque. Torque's direction aligns with the direction of the angular momentum it produces. Any alteration in angular momentum is influenced by the average torque and the time period of its exertion, adhering to the conservation laws of angular momentum.

The motion caused by torque making the angular momentum vector to rotate in UCM is called precession. In other words, precession is the circular motion of the pole of the axis of a spinning object around another axis due to torque. This is similar to how a spinning top wobbles as it continues to spin.

For example, if we consider a merry-go-round, torque is perpendicular to the plane formed by radius and force. This direction aligns with the direction your right thumb would point to if you curled your fingers in the direction of the force. This shows that the direction of the torque is the same as that of the angular momentum it produces.

It's important to note that angular momentum, like energy and linear momentum, is conserved when the net external torque is zero. This is a universally applicable law underlying unity in physical laws. The change in angular momentum is given by the product of average torque and the time interval during which the torque is exerted, embodying the conservation laws of angular momentum.

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Answer:

When the termination is a terminal block, care must be taken to ensure a good electrical connection without damaging the conductor. Terminals should not be used for more than one

Explanation:

The Terminal block being a modular block, having insulated frame, which can secure more than two wires in it. It has a conducting strip in it. These terminal clocks helps in making the connection safer as well as organised. These terminal blocks are used for power distribution in safer way. Its potential is it can distribute power from single to multiple output. The conductor is used for making it proper contact.

Answer:

the principle of original horizontality and the principle of superposition

Explanation:

The principle of horizontality states that layers of sediment are originally deposited horizontally under the influence of gravity.

The principle of superposition states that the oldest layer layer is at the bottom and each layer above it is younger, with the youngest being at the top.

Unconformities help us find the age of different layers. An unconformity is a surface in which no new solid matter is deposited after a long geologic interval. Angular unconformity is a type of unconformity which different kinds of stratum were tilted or folded before deposition of younger layers of solid matter above the unconformity. Once the layers were folded and tilted, the older layers of the solid matter eroded, then the younger layers were deposited on the older layers. There angular unconformity is the contact between young and old layers of solid matter.

Therefore, these two principles therefore describe how the tilted layers are older than horizontal layers.

Answer:

C) True   carrying large loads on the outside of the vehicle

Explanation:

The aerodynamic property of an object depends on its outer shape. In general, objects should be thin in the front and not completely flat in the back, to avoid the eddies that create a great Arrate, losing all the aerodynamics of the system.

With this we can review the final statements

A) False The air conditioner is used with the glasses raised, so the exterior shape of the car does not change and its aerodynamics remains unchanged.

B) Phallus. This does not change the outer shape, I get a small inclination,

C) True. External loads dramatically change the external shape of the vehicle significantly reducing its aerodynamic characteristics.

To avoid compromising your car's aerodynamic properties, avoid carrying large loads on the outside of the vehicle and taking turns at high speeds.

To avoid compromising your car's aerodynamic properties, you should avoid carrying large loads on the outside of the vehicle. Large loads increase drag and disrupt the flow of air around the car, negatively affecting its aerodynamics. It is also advisable to avoid taking turns at high speeds as it can create instability and affect the car's balance. Running the air conditioning system does not directly impact the aerodynamic properties of the car, so it is not necessary to avoid running your air conditioning system.

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Answer:

Explanation:

For first overtone

Standing waves will be formed lengthwise and breadth-wise in the enclosures  having dimension of .75m  x 1.5 m

A ) For the formation of lowest two frequencies formed by standing waves along the breadth  , fundamental note and first overtone may be considered.  

For fundamental note ,  

the condition is  

wave length λ = 2L = 2 x 0.75 m  

λ = 1.5 m  

frequency n = v / λ

= 343 / 1.5  

= 229  Hz approx

For first overtone

λ = L = 0.75m

frequency n = v / λ

n = 343 / 0.75  

= 457 Hz approx

B)

For the formation of lowest two frequencies formed by standing waves along the length , fundamental note and first overtone may be considered.  

For fundamental note ,  

the condition is  

wave length λ = 2L = 2 x 1.5 m  

λ = 3 m  

frequency n = v / λ

= 343 / 3  

= 114 Hz approx

frequency n = v / λ

n = 343 / 1.5  

= 229 Hz approx

A) The lowest two frequencies that correspond to resonances on the short axis for first overtone.

B) Standing waves will be formed lengthwise and breadth-wise in the enclosures  having dimension of .75m  x 1.5 m

Part A )

For fundamental note ,  

wave length λ = 2L = 2 x 0.75 m  

λ = 1.5 m  

frequency n = v / λ

frequency n = 343 / 1.5  

frequency n = 229  Hz approx

For first overtone

λ = L = 0.75m

frequency n = v / λ

n = 343 / 0.75  

frequency n= 457 Hz approx

Part B)

For fundamental note ,  

wave length λ = 2L = 2 x 1.5 m  

λ = 3 m  

frequency n = v / λ

frequency n= 343 / 3  

frequency n= 114 Hz approx

For first overtone

frequency n = v / λ

frequency n = 343 / 1.5  

frequency n= 229 Hz approx

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Answer:

a)   T = 2.997 s

b)   K = 14.3 J

c)   φ = 0.444 rad

Explanation:

a) Determine its period

  The pendulum simple’s period is:

  T = 2π[tex]\sqrt{\frac{l}{g} }[/tex]

        Where l: Pendulum’s length

                    g = 9.8 m/s2

  T = 2π[tex]\sqrt{\frac{2.23}{9.8} }[/tex]

  T = 2.997 s

b) Total energy

  Initially his total energy is kinetic

  K = [tex]\frac{mv^{2} }{2}[/tex]

  K = [tex]\frac{(6.74)(2.06)^{2} }{2}[/tex]

  K = 14.3 J

c) Maximum angular displacement

  φ = [tex]cos^{-1}(1-\frac{E}{mgl} )[/tex]

  φ = [tex]cos^{-1}(1-\frac{14.3}{(6.74)(9.8)(2.23)} )[/tex]

  φ = 0.444 rad

Final answer:

The period of the pendulum is 4.46 seconds. The total energy of the pendulum is 14.58 Joules. The maximum angular displacement of the pendulum is 26.86 degrees.

Explanation:

To determine the period of the pendulum, we can use the formula:

T = 2π√(L/g)

where T is the period, L is the length of the pendulum, and g is the acceleration due to gravity. Plugging in the values given, we get:

T = 2π√(2.23/9.8) = 4.46 seconds

The total energy of the pendulum is given by the formula:

E = mgh + (1/2)mv²

where E is the total energy, m is the mass, g is the acceleration due to gravity, h is the height, and v is the velocity. Since the pendulum is at its equilibrium position, the height is zero, so we only need to calculate the kinetic energy:

E = (1/2)mv² = (1/2)(6.74)(2.06)² = 14.58 Joules

The maximum angular displacement of the pendulum can be found using the formula:

θ = sin⁻¹(A/L)

where θ is the angular displacement, A is the amplitude, and L is the length of the pendulum. Plugging in the values given, we get:

θ = sin⁻¹(1/2.23) = 26.86 degrees

Answer:

4.5*10^12

Explanation:

5.5=2/3log(E/10^4.4)

8.25=log(E10^4.4)

10^8.25=E/10^4.4

E=10^4.4*10^8.25

E=10^12*4.5

Magnitude is an earthquake's greatest commonly used measure of size. It is a measure of the size of the source for just an earthquake. so, it is identical regardless of how or where you perceive it, and the further calculation can be defined as follows:

Given formula:

[tex]\to\bold{ magnitude\ M = \frac{2}{3} \log \frac{E}{E_0}}[/tex]

The minimum measure released by such an earthquake shall be allocated to where E is the amount of power released in Joules and [tex]\bold{ E_0=10^{4.4}}[/tex].

As 5.5, then put in the above equation this same magnitude is given:

[tex]\to\bold{ magnitude\ M = \frac{2}{3} \log \frac{E}{E_0}}[/tex]

                       [tex]\bold{5.5= \frac{2}{3} \log(\frac{E}{10^{4.4}})}\\\\ \bold{8.25=\log( \frac{E}{10^{4.4}})} \\\\ \bold{10^{8.25}=\frac{E}{10^{4.4}}}\\\\ \bold{E=10^{4.4}\times 10^{8.25}}\\\\ \bold{E= 4.5 \times 10^{12} }[/tex]

Therefore the final answer is "[tex]\bold{ 4.5 \times 10^{12} }[/tex]".

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Answer:

Explanation:

Diesel engines burn as much as 30% less fuel than gasoline engines of comparable size, as well as emitting far less carbon dioxide gas and far fewer of the other gasses that have been implicated in global warming.

(A) of comparable size, as well as emitting far less carbon dioxide gas and far fewer of the other gasses that have

(B) of comparable size, as well as emit far less carbon dioxide gas and far fewer of the other gasses having

(C) of comparable size, and also they emit far fewer carbon dioxide and other gasses that have

(D) that have a comparable size, and also they emit far fewer of the other gasses having

(E) that have a comparable size, as well as emitting far fewer of the other gasses having

A is the most appropriate statement above. Diesel engine consume less energy and release fewer gases than the gasoline engines .

Both engine(Diesel and gasoline) converts chemical energy to electrical energy.

Answer:

d. 1000 N.

Explanation:

For the seesaw to be in equilibrium the moment on left of the fulcrum and the moment to the right of the fulcrum must be equal.

Let L be the distance on either side of fulcrum at which the boulder is kept

F be the minimum force used to pushdown the left end

According to principle

L×1000= L×F

F= 1000 N

Hence option D is correct

Answer:

$9.702  per hour

Explanation:

The apprentice earns 55% of what the journeyman earns on a hourly scale.

Amount the apprentice makes per hour = 55% of $17.64

                                                             = (55/100) *17.64

                                                           = 0.55 *17.64

                                                          = $9.702

The apprentice would make $9.70 per hour if the Journeyman scale is $17.64, as 55% of $17.64 is $9.70.

Given:
Journeyman scale = $17.64/hour
Apprentice wages = 55% of Journeyman wages

Calculation:
Apprentice wages = 0.55 * $17.64
Apprentice wages = $9.702

Therefore, an apprentice would make $9.70 per hour.

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Answer:

Slip Rings

Explanation:

The wound rotor motor has a three-phase winding with each one connected to seperate slip rings. These slip rings contain brushes which form a secondary circuit where resistance can be inserted and this will allow for the rotor current to run more in phase with the stator current which will result in increased torque that is created

Answer:

6.1 m/s

Explanation:

Gradpoint

Answer:

[tex]\frac{dD}{dt} = -4 miles/hour[/tex]

negative sign indicates that the distance is decreasing with time

Explanation:

Let at any time t after noon that is 12 p.m.  

distance traveled by car A = 40t

distance traveled by car B = 90-60t

then distance between the two cars at time t

[tex]D^2= (40t)^2+(90-60t)^2[/tex]............1

also, at time 1 p.m.

distance [tex]D^2= (40\times1)^2+(90-60\times1)^2[/tex]

D=50 Km

differentiating equation 1 w.r.t. t we get

[tex]2D\frac{dD}{dt}= 2\times40t\times40+2(90-60t)(-60)[/tex]

put t= 1 and D= 50 we get

[tex]2\times50\frac{dD}{dt}= 3200\times1-3600\times1[/tex]

[tex]\frac{dD}{dt} = -4 miles/hour[/tex]

Answer:

option (b)

Explanation:

An object is said to be in stable equilibrium if its potential energy is minimum and the force acting on the object is zero.

When the base of an object is too broad so that the vertical line passing through its centre of gravity line passes though this base, it is said to be in stable equilibrium. \

Thus, option (b) is correct.

Final answer:

An object will be stable when its center of gravity lies over c. its base of support.

Explanation:

An object will be stable if its center of gravity lies over its base of support, which corresponds to option (b). Considering a person standing with feet narrowly-separated, they would be in a stable equilibrium to sideway displacements, as their center of gravity is above the base of support. However, even small displacements can make them unstable if it takes their center of gravity outside the base.

Therefore, enhanced stability can be achieved by lowering the center of gravity or expanding the base by spreading the feet farther apart. Furthermore, using a support device such as a cane increases stability by broadening the base of support. These principles are crucial in understanding why, for instance, children learning to walk experience more instability due to their higher center of gravity positioned between their shoulders.

Answer:

Physical

Explanation:

The study of the transmission of light and sound in the oceans is an example of Physical oceanography.

Physical oceanography is the analysis of physical conditions and mechanisms in the ocean, particularly ocean waters ' movements and physical characteristics. One of many sub-domains in which oceanography is divided is physical oceanography.

Final answer:

The study of light and sound in oceans relates to physical oceanography, which incorporates wave optics to explain phenomena like diffraction and apply principles to technologies like fiber optics.

Explanation:

The study of the transmission of light and sound in the oceans is an example of physical oceanography. This branch of oceanography explores the wave optics of light as it behaves in different media, specifically how light and sound waves propagate through water. One of the interesting phenomena is the diffraction of waves, which occurs when a wave encounters an obstacle or passes through an aperture and displays bending and spreading. This is not fully explained by geometric optics; instead, it illustrates the intricate nature of wave interactions that can be characterized by wave optics or physical optics. Understanding how light behaves when it exhibits wave characteristics can also lead to practical applications such as fiber optics, which involves the transmission of light down fibers of plastic or glass by employing the principle of total internal reflection.

Answer:

The elevator is accelerating downwards.

Explanation:

When an elevator accelerating downward it moves together with the person inside and the weight of the person does not change, but if the person is standing on a scale the contact force between the person and the scale is reduced.  The scale therefore has to push upward with less force on the person to support the person's weight. Therefore the Normal Force is smaller, so the reading on the scale becomes less than the true weight.

When you feel your weight decrease in an elevator, it means that the elevator is accelerating downwards. This is due to the equivalence principle in physics, where the downward acceleration counteracts some of gravity's pull making you feel lighter.

If you are standing on a scale in an elevator and suddenly notice your weight decreases, you can conclude that the elevator is accelerating downwards. The weight we feel is a combination of our actual weight and the effect of the elevator's motion. The apparent reduction in weight is because the downwards acceleration of the elevator is counteracting some of the pull of gravity, causing you to feel lighter.

This is a principle of physics known as the equivalence principle, which is a key part of Einstein's theory of general relativity. When the elevator accelerates downwards, we experience a sensation of decreased weight, as the floor of the elevator 'falls' away from us at an accelerated rate.

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Answer:

(b) The average speeds are the same, but the average velocities are different.

Explanation:

The average speed is a scalar quantity which is calculated on the total distance travelled. Distance is the length of path traced and the speed is calculated as distance per unit time.

Mathematically:

[tex]v=\frac{d}{t}[/tex]

[tex]v=\frac{(1500+1500)}{2\times 60}\ m.s^{-1}[/tex]

While the velocity is a vector quantity calculated on the displacement and is defined as the rate of displacement.

Mathematically:

[tex]\vec v=\frac{\vec s}{t}[/tex]

[tex]\vec v=\frac{\sqrt{1500^2+1500^2} }{2\times 60}\ m.s^{-1}[/tex]

Final answer:

The typical speed limit in a residential area is 25 miles per hour, which corresponds with option B) 25 mph. Always check local signs as limits can vary. Over this limit, like driving 31 mph in a 30 mph zone, may be tolerated but it's best to strictly follow posted speeds to ensure safety and avoid penalties.

Explanation:

The speed limit for cars in a residential area, unless otherwise posted, is generally 25 miles per hour (mph). This means that option B) 25 mph is typically the correct choice for such a setting. However, it's important to always observe local traffic signs as speed limits can vary depending on specific city, county, or state regulations.

For instance, the information given states that 50 kilometers per hour is approximately 31 miles per hour, suggesting that some residential areas might have a speed limit close to this value. However, in the context of the United States, 25 mph is a common residential speed limit, which is enforced to ensure the safety of the neighborhood, including pedestrians, cyclists, and playing children.

It's also important to note that speedometers and radar measurements can vary in accuracy. Therefore, while you may not get in trouble for driving slightly over the speed limit, such as 31 mph in a 30 mph zone, it's safest to adhere strictly to posted limits to avoid traffic violations and fines.

Answer:

The height at which the ladder safely reach on the garage is 12 meters.

Explanation:

It is given that,

Height of the ladder, H = 13 foot

Bottom of the ladder, B = 5 feet

To find,

How high can the ladder safely reach on the garage?

Solution,

The ladder and the wall follows the Pythagoras theorem. 13 foot is the height of the ladder. Distance between wall and the ladder is 5 feet. Let L is the height at which the ladder safely reach on the garage. On using Pythagoras theorem we get :

[tex]H^2=B^2+L^2[/tex]

[tex]L^2=H^2-B^2[/tex]

[tex]L^2=13^2-5^2[/tex]

L = 12 m

So, the height at which the ladder safely reach on the garage is 12 meters. Hence, this is the required solution.

Answer:

They can expect the size of the rocks to get smaller as the time passes.

Explanation:

They can expect the size of the rocks to get smaller as the time passes.

Answer:

The maximum height that the fish can jump is 2.19 m.

Explanation:

Hi there!

Please, see the attached figure for a better understanding of the problem.

The motion of the salmon is a parabolic one because when it jumps, it already has a horizontal velocity (see figure).

The position and velocity vectors of the salmon at a time t, can be calculated as follows:

r = (x0 + v0x · t, y0 + v0y · t + 1/2 · g · t²)

v = (v0x, v0y + g · t)

Where:

r = position of the salmon at time t.

x0 = initial horizotal position.

v0x = initial horizontal velocity.

t = time.

y0 = initial vertical position.

v0y = initial vertical velocity.

g = acceleration of gravity.

Looking at the figure, notice that at the maximum height, the vertical velocity is zero (because the velocity vector is horizontal). Using the equation of the vertical component of the velocity, we can obtain the time at which the salmon is at its maximum height:

vy = v0y + g · t

To find the initial vertical velocity, v0y, let´s look at the figure. Notice that the initial velocity is the hypotenuse of the triangle formed with the horizontal velocity and the vertical velocity. Then:

v0² = v0x² + v0y²

Solving for v0y:

v0y = √(v0² - v0x²)

v0y = √((6.75 m/s)² - (1.65 m/s)²)

v0y = 6.55 m/s

Now, using the equation of the vertical component of the velocity at the maximum height (vy = 0):

vy = v0y + g · t

0 = 6.55 m/s + (-9.8 m/s²) · t

-6.55 m/s / -9.8 m/s² = t

t = 0.67 s

Now, using the equation of the vertical position at t = 0.67 s, we can find the maximum height:

y = y0 + v0y · t + 1/2 · g · t²

y = 0 m + 6.55 m/s · 0.67 s + 1/2 · (-9.8 m/s²) · (0.67 s)²

y = 2.19 m

The maximum height that the fish can jump is 2.19 m.

Answer:

The angular speed wf of the neutron star is calculated to be [tex]5.19*10^{3} [/tex] rad/s

Explanation:

The reason for such a rapid spin-rate is due to the principle of angular momentum. The angular momentum of a system can be given as:

Angular Momentum (L) = Mass * Radius^2 * Angular Velocity (w)

Applying this principle to our context, we would say that the angular momentum of the star before and after collapsing is constant. In order to not break this principle, we know that the mass of the star did not change but the radius shrank by a significant amount after collapsing, and so in order to keep the angular momentum (L) constant after collapse, the star had to increase it's angular velocity, which is evident in our answer.

The calculations of the answer are as follows:

Star's Initial Radius Ri = [tex]8.0 * 10^{5}[/tex] km ( [tex]8.0 * 10^{8}[/tex] m)

Star's Initial Angular Velocity wi = [tex]\frac{2\pi} {35 days * 24 hrs * 3600 sec}[/tex] = [tex]2.077 * 10^{-6}[/tex] rad/sec

Star's final radius Rf = [tex]16 * 10^{3}[/tex] m

Now, we can equate the initial and final states of the star i.e. the angular momentum of star before and after the collapse as following:

Li = Lf (where i and f denote initial and final state)

Solving of Final Angular Velocity we have:

wf = wi * (Ri / Rf) ^ 2

Plugging in our known values:

wf = [tex]2.077 * 10^{-6}[/tex] x [tex](\frac{8 * 10^{8}}{16 * 10^{3}} )^{2}[/tex] = 5.19 * 10^3 rad/s

Final answer:

The neutron star's angular speed is found by using the conservation of angular momentum. With the star's initial rotation period of 35 days, the initial angular speed is calculated and then adjusted for the changes in the radius of the star upon collapse. The resulting angular speed of the neutron star is approximately 6.57 x 10³ radians/second.

Explanation:

When a star collapses into a neutron star, its angular momentum is conserved. To calculate the neutron star's angular velocity, we use conservation of angular momentum. The original star rotated once every 35 days, and we can convert this period into angular speed, \, using the formula \ = [tex](2\pi)[/tex] / T, where T is the period of rotation in seconds.

Firstly, convert the days into seconds: 35 days × 24 hours/day × 3600 seconds/hour = 3,024,000 seconds. Now, calculate the initial angular speed: \initial = [tex](2\pi)[/tex] / 3,024,000 = 2.08 x 10⁻⁶ radians/second.

Since angular momentum L = I\ must be conserved (where I is the moment of inertia and \ is the angular velocity), and I = (2/5)mR² for a sphere, where m is mass and R is the radius, the relation can be expressed as I-initial\initial = I-final\final. Mass m cancels out and assuming the radius R changes from 8.0 x 10⁵ km to 16 km, we can solve for \final.

The final angular velocity \final = (Rinitial2 / Rfinal2) \initial = ((8.0 x 10⁵ km)² / (16 km)²) (2.08 x 10⁻⁶ radians/second) = (6.4 x 10¹¹ / 256) (2.08 x 10⁻⁶ radians/second) = 6.57 x 10³ radians/second.

Therefore, the angular speed of the neutron star is approximately 6.57 x 10³ radians/second, significantly faster than its predecessor due to the drastic reduction in radius.