a stone is dropped into a lake, creating a circular ripple that travels outward at a speed of 40 cm/s. find the rate (in cm2/s) at which the area within the circle is increasing after each of the following.

The resultant forces in each case is;

a) 22.3 Km

b) 158 Km

c) 15.7 Km

Let us note that the resultant force is the force that would have the same effect in magnitude and direction as the the two force that are acting together.

In this case we have been asked to find the resultant of the forces and we would use the triangle method.

a) R = √(10)^2 + (20)^2

R = 22.3 Km

b) R = √(150^2) + (50)^2

R = 158 Km

c) R = √(7)^2 + (14)^2

= 15.7 Km

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Kinetic energy is a type of energy that is present in a particle or object in motion. When work, which entails the transfer of energy, is done on an object by applying a net force, that object acquires kinetic energy.

The energy of motion is known as kinetic energy, and it can be observed in the motion of a particle, an object, or a collection of particles. A person walking, a baseball being thrown, a piece of food falling from a table, or a charged particle in an electric field are all examples of moving objects that consume kinetic energy.

There are five different types of kinetic energy:  radiant, thermal, acoustic, electrical, and mechanical.

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According to the given statement:

a)It take time to reach the ground is 3.69 s.

b)The helicopter when the package lands far above the ground is 144.18 m.

Constant speed refers to a speed that remains constant throughout the duration of the motion. Constant speed is demonstrated in our example of using cruise control while driving a car.

Using this formula:

t= √(h/g)  

h= 125m

g= 9.2 m/s

t = √(125/9.2)

t = √13.59

t= 3.69 s

The package must touch the ground in 3.69 seconds.

From equation of motion  s = u t + 1/2 a t².

Here a= 0, then s= ut

s= 5.2x 3.69 = 19.18 m.

Total height = 19.18 + 125 = 144.18 m.

Helicopter is 144.18m far above from the ground when the package lands.

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The total distance travelled by the glider before it leaves the ground is 867 meters.

Velocity is the change in displacement divided by time taken. Here the displacement is unknown. The glider reaches its launch speed of 51.0 m/s after accelerating for 17.0 s. The velocity of the glider is 51.0 m/s and time taken is 17.0 s. The equation to calculate the total distance travelled by the glider before it leaves the ground is given below.

velocity = displacement/time

displacement = velocity*time

displacement = 17.0*51.0 = 867 meters

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The acceleration the block if the incline is frictionless is 3.28m/s² and the acceleration of the block if the coefficient of kinetic friction between the block and incline is 0.11 is 2.26 m/s².

what is newtons law of motion?

Newton's laws of motion are three basic laws of classical mechanics that describe the relationship between the motion of an object and the forces acting on it. These laws can be paraphrased as follows: A body remains at rest, or in motion at a constant speed in a straight line, unless acted upon by a force.

given:

mass of the block (m) = 5.3kg

angle of incline (x)= 21°

force exerted on the block up the incline (F) = 36 newtons

coefficient of kinetic friction = 0.11 u

a)

the sine component of the weight will act as the resistive force and will act against the 36 newtons force that is acting parallel to the incline.

i.e.

net force = 36 - (m × g × sin 21°)

m × net acceleration = 36 - 18.6

net acceleration = 17.4/5.3

net acceleration = 3.28 m/s²

b)

now in this case similarly the friction will also act against the intention of motion, such that:

net force = 36 - (m × g × sin 21°) - coefficient of kinetic friction ×m × g × cos 21°

net force = 36 - 18.6 - 5.33

net force = 12

net acceleration = 12/5.3

net acceleration = 2.26 m/s²

therefore, the acceleration the block if the incline is frictionless is 3.28m/s² and the acceleration of the block if the coefficient of kinetic friction between the block and incline is 0.11 is 2.26 m/s².

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Answer:

Explanation:

Answer : D that’s the answer

After 11 seconds the tangential acceleration becomes equal to the centripetal acceleration.

What is tangential acceleration?

Similar to linear acceleration, tangential acceleration is directed only in that direction. This has to do with rotational motion. As a result, tangential acceleration is the rate at which a particle's tangential velocity changes in a circular orbit. It always points in the direction of the body's tangent.

ac, also known as centripetal acceleration.

at is acceleration along a tangent.

The frictional force between the car wheel and the road surface supplies the necessary centripetal force when the vehicle moves in a circular motion over a curved path.

at=1.2m/sec2

The centripetal acceleration equation is given by,

ac=V2r

V2r=at

V2=at×r

V=√at×r  ... (1)

Think of the equation for motion.

V=u+at×t

V=0+at×t

V=at×t

t=Vat

t=√at×ra2t

t=√rat

t=√1451.2

t=11seconds

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The relationship between Linear Expansivity and Cubic Expansivity is as follows: Cubic / Volume expansivity = 3 Linear expansivity

Now, consider a sheet of metal of Length (l), Breadth (b), and Height (h). Let the initial Length be (l₁), the initial Breadth be (b₁) and the initial Height be (h₁). Let the final Length be (l₂), the final Breadth be (b₂) and the final Height be (h₂) after the metal is heated through a temperature change of θ.

Considering,

the initial volume of the metal be V₁ = l₁*b₁*h₁

and, the final volume of the metal be V₂ = l₂*b₂*h₂

Then,

Using the formula of linear expansivity,

l₂ = l₁ (∝∆θ + 1 )

b₂ = b₁ (∝∆θ + 1 )

h₂ = h₁ (∝∆θ + 1 )

Remember that Volume = l * b*h

Therefore,

V₁ = l₁*b₁*h₁

V₂ = l₂*b₂ *h₂

V₂ =l₁ (∝∆θ + 1 ) * b₁ (∝∆θ + 1 ) * h₁ (∝∆θ + 1 )

V₂ = l₁* b₁*h₁ (∝∆θ + 1 ) * (∝∆θ + 1 ) * (∝∆θ + 1 )

V₂ = l₁* b₁*h₁ ((∝∆θ * (∝∆θ + 1 ) + 1 * (∝∆θ + 1 ) ) * (∝∆θ + 1 )

Let's open the brackets, now we get,

V₂ = l₁* b₁*h₁(∝²(∆θ)² + ∝∆θ + ∝∆θ + 1 ) * (∝∆θ + 1 )

V₂ = l₁* b₁*h₁(∝²(∆θ)² + 2∝∆θ +1 ) * (∝∆θ + 1 )

V₂ = l₁* b₁*h₁(∝²(∆θ)² * (∝∆θ + 1 ) + 2∝∆θ * (∝∆θ + 1 ) +1* (∝∆θ + 1 ) )

V₂ = l₁* b₁*h₁(∝³(∆θ)³ +∝²(∆θ)² + 2∝²(∆θ)² + 2∝∆θ +∝∆θ + 1 )

V₂ = l₁* b₁*h₁(∝³(∆θ)³ +∝²(∆θ)² + 2∝²(∆θ)² + 3∝∆θ + 1 )

V₂ = V₁(∝³(∆θ)³ + 2∝²(∆θ)² + 3∝∆θ+1 )

Remember that ,

V₂ = V₁ ( ϒ * ∆θ + 1 )

Let us substitute for V₂ in the above formula. Then we will get,

V₁ ( ϒ * ∆θ + 1 ) = V₁(∝³(∆θ)³ + 2∝²(∆θ)² + 3∝∆θ+1 )

ϒ * ∆θ + 1 = ∝³(∆θ)³ + 2∝²(∆θ)² + 3∝∆θ+1 (V₁ canceled V₁ and the brackets are removed)

ϒ * ∆θ = ∝³(∆θ)³ + 2∝²(∆θ)² + 3∝∆θ ( 1 cancelled 1 )

At this point,∝ tends to be zero because its value starts from 0.0000... Upward. Therefore,∝² and ∝³ are approximately zero. i.e. ∝² and ∝³ are = 0.

Therefore, we put zero in place of ∝² and ∝³. Now we get,

ϒ * ∆θ = 0*(∆θ)³ + 2*0*(∆θ)² + 3∝∆θ

ϒ * ∆θ = 0 + 0 + 3∝∆θ

ϒ * ∆θ = 3∝∆θ

ϒ = 3∝ ( ∆θ cancelled. ∆θ )

Therefore,

Cubic / Volume expansivity = 3 Linear expansivity

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Answer: 1280 J

Explanation: Work is calculated by multiplying the displacement (8m) by the force (160 N) which will give you 1280 J (joule)

A charge of 4.8 x 10 5 C is present on each capacitor plate.

B. The capacitor has a 4.5 x 10 6 J energy capacity.

Describe the capacitor.

A capacitor is a device used to store electrical power and charge. It is composed of at least two separated electrical conductors. Although usually referred to as "electrodes," these electrical conductors are actually "capacitor plates." A capacitor is referred to as a "vacuum capacitor" if the space between capacitors is nothing more than a vacuum. However, the space is often filled with a dielectric, an insulating material. How much storage space a capacitor has is determined by its capacitance attribute.

A. Establishing the charge

Capacitor (C) = 4 F = 4 10 6

Voltage = 12 volts.

Charge (Q)  = ?

Q = CV

Q = 4×10¯⁶ × 12

Q = 4.8×10¯⁵ C

B. Measuring the amount of energy the capacitor has stored.

Voltage (V) equals 1.5 V.

Energy (E) =? E = 12CV Capacitor (C) = 4 F = 410 6

²\sE = ½ × 4×10¯⁶ × 1.5²

E = 2×10¯⁶ × 2.25\sE = 4.5×10¯⁶ J

A. There is 4.8 x 10 5 C B of charge on each capacitor plate. The capacitor has 4.5 x 10 6 J of stored energy.

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The initial velocity of the car, given that it takes 6.0 seconds to slow down to a stop is 30 m/s

The initial velocity of the car can be obtained by doing the following:

First, we list out the given parameters from the question. This is given below:

Finally, we shall determine the initial velocity of the car as illustrated below:

s = (v + u)t / 2

90 = [(0 + u) × 6] / 2

90 = [u × 6] / 2

90 = 6u / 2

Cross multiply

6u = 90 × 2

6u = 180

Divide both sides by 6

u = 180 / 6

u = 30 m/s

From the calculations made above, we can conclude that the initial velocity of the car is 30 m/s

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The average velocity is 2 meters/second. Option B.

Explanation:

This average velocity can be found using the following formula:

v = x / DT

where:

x = displacement = 18 [meters]

dt = time interval = 9 [seconds ]

v = 18 / 9

v = 2 [m/s]

The average velocity of a particle moving from one point to another over a time interval is equal to the ratio of the displacement between the two points to the time it takes the particle to move that displacement. To find the average speed take the total distance traveled divided by the time interval. To find the average velocity. Since the displacement is always less than or equal to the distance traveled, the magnitude of the average velocity is always less than or equal to the average velocity.

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The change in the speed of the automobile occurred at points A to B.

The change in the speed of an object is the rate at which the distance traveled by the object changes with time.

The change in speed of the object from point O to A is calculated as follows;

ΔV = Δx/Δt

where;

ΔV = (5 - 0) / (15 - 0)

ΔV = 0.333 km/min

The change in speed of the object from point A to B is calculated as follows;

ΔV = (15 - 5) / (30 - 15)

ΔV = 0.67 km/min

From this we can conclude that speed of the automobile changed at points O to A, A to B and B to P.

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The brain, not the eye, is what actually sees. Information is sent from the eye to the brain, but certain aspects of the signal are lost or changed in the process.

The human eye can perceive between 30 and 60 frames per second, according to some scientists. Some claim that the human eye cannot actually comprehend more than 60 frames per second.

Higher rates are seen as motion by the human visual system, which can process 10 to 12 pictures per second and perceive each one separately. The majority of participants in studies see modulated light (such a computer display) as steady when the rate is more than 50 Hz.

The screen will look smoother to the human eye the higher the number. This implies that a 120Hz display, which updates itself 120 times per second, would seem noticeably smoother and more natural than your typical 60Hz screen, which refreshes itself just 60 times each second.

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1)

Answer:

d. 12.25J

------------------------

2)

According to the conservation of energy:

Answer:

b. 12.25

-------------------------------

3)

Answer:

d. 0 kg∙m/s

-----------------------------------------

4)

Using conservation of momentum:

Answer:

b. 0 kg•m/s

Given data:

* The angle of the inclined plane is,

* The speed of the duck along the inclined plane is v = 5 m/s.

Solution:

The diagrammatic representation of the given case is,

From the triangle ABO,

Substituting the known values,

Thus, the inclined plane makes an angle of 55 degrees with the negative of the y-axis.

Similarly, the angle of the velocity of the duck along the inclined plane with the negative y-axis is 55 degrees.

Thus, the vertical component of the velocity is,

The horizontal component of the velocity is,

Thus, the horizontal component of velocity is 4.096 meters per second, and the vertical component of velocity is -2.88 meters per second.

Answer:

59, 720 Joules

Explanation:

[tex]q = mc(t2 - t1) + m(lf) + mc(t2 - t1)[/tex]

first term=ice to 0 degrees

second term=water to ice

third term-water to 30 degrees

[tex]q = 0.12 \times 2100 \times 20 + 0.12 \times 3.36 \times {10}^{5} + 0.12 \times 4200 \times 30[/tex]

[tex]q = 59720 \: joules[/tex]

Change in momentum =  -1.9 kg m/s

Momentum is the vector quantity because it has both magnitude and direction.

Momentum is given as the product of mass and velocity. It is represented as P = mv. Here, P is the momentum, m is the mass and v is the velocity.

Given,

Momentum = MV

The difference between the initial and final momentum will be the change of magnitude of the momentum.

To find the change in momentum,

Taking M as common

= M (V - U)

= 0.10 (-12 - 7)

= 0.10(-19)

= -1.9 kg m/s

Hence, the change in magnitude of momentum is -1.9 kg m/s.

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Sound waves have entered Natalie’s ear and traveled through to her auditory nerve. The process of perception took place in which she identifies what the sound is.

Perception is the ability to see, hear and become aware of something through the senses.

Sound waves from the environment enter the outer ear and are directed to the ear drum

The eardrum vibrates when sound waves are received, and the vibrations are sent to the oval window through the ossicles of the ear, .

From the oval window, these vibrations are transmitted to the fluid of the cochlea, where waves are generated in the lymph.

These waves generate vibrations in the basilar membrane that bends the hair cells and push them against the tectorial membrane, and hence are sent to the brain which gives signal to the organ to react.

Hence perception is used by Natalie to react.

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A.) Runway has to be 181.5 long.

B.) Plane takes 11 second for the plane to take off.

Change in velocity (Δv) divided by the change in time (Δt), is called acceleration that can be represented by the equation

a = Δv/Δt.

This lets you measure how fast a  velocity changes in (m/s^2). Acceleration a vector quantity, that is it has both magnitude and direction

Meter per second squared is the SI unit of acceleration.

Given, a small plane must reach a speed of 33m/s for takeoff, starting from rest and constant acceleration is 3.0m/s^2

Let the  time be 't'

hence,

(33-0 )/t = 3

33 = 3t

t = 11 sec

Time taken by the plane to take off is 11sec.

Average velocity = (33 + 0)/t

= 16.5 m/sec

Distance = speed * time

= 16.5 * 11

= 181.5 m

Runway has to be at least 181.15 meters long.

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This study reveals that only if the flow conditions in the holding tube are provided for comparison with commercial HTST systems can continuous laboratory and pilot-scale pasteurizers be utilized to evaluate the inactivation of microorganisms.

In order to make sure that laboratory or pilot-scale HTST apparatus meets the Pasteurized Milk Ordinance standards for pasteurizing milk and can be used for obtaining thermal inactivation data, we present a method in this study for calculating the fastest moving particle (FMP) and residence time distribution (RTD) in a pilot-scale high temperature, short time (HTST) pasteurizer.

The plate used in the pasteurizer had overall measurements of 75 x 115 mm, a thickness of 0.5 mm, and an effective diameter of 3.0 mm. The pasteurizer had standard hold tubes measuring 21.5 and 52.2 seconds, and its variable flow capacity ranged from 0 to 20 L/h.

FMP durations were established using tracer investigations, and flow parameters were established using RTD data. In comparison to the nominal timings of 21.5 and 52.2 s, respectively, the FMP times for the short and long holding sections using brine milk as the tracer were 18.6 and 36 s, respectively, at 72 degrees C.

According to the RTD investigation, the short hold section for whole milk at 72 degrees C had 45% back mixed and 55% plug flow.

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The low-density, cold disks seen around some stars are distinct from the dense, hot disks found around some other stars because of their varied densities, temperatures, and positions.

- About circumstellar disc :

- A circumstellar disc (or circumstellar disk) is an accretion disk of matter in orbit around a star that has the shapes of a torus, pancake, or ring. It is made up of gas, dust, planetesimals, asteroids, or impact fragments. They are the sources of material where planets may form around the young stars.

- Gaseous clouds gradually collapse under the pull of gravity to become stars. As they fall toward the protostar, the atoms and molecules in the gas impart a slight rotation. The protoplanetary disk, a rotating plate of gas and dust, is produced by this rotation, which also gives the star its spin.

- A rotating circumstellar disk of dense gas and dust known as a protoplanetary disk surrounds a young, newly formed star, a T Tauri star, or a Herbig Ae/Be star.

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Security mirrors are placed above the ceiling of establishments to deter stealing. A spherical mirror has a 25 cm focal length. R = 50 cm is the radius of curvature.

It has been found that the radius of curvature for spherical mirrors with small apertures is equivalent to double the focal length. R therefore equals 2f. It is evident that the main focus of a spherical mirror is located in the middle, halfway between the curvature's centre and the pole. A curve's radius of curvature at any given location is, roughly speaking, the radius of the circle that fits the curve there the best. One divided by the radius of curvature is the curvature, indicated by the symbol. You must locate the circle that fits that point the best in order to calculate the curvature there. The osculating circle is what's known as this. The reciprocal of the curve's curvature at that point is known as the osculating circle radius.

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A 14.0-kg bucket is vertically dropped by a rope with 163 n of tension at any given time. The acceleration of the bucket is upward-directed and has a value of 2.06 ms^-2.

Let's imagine that two bodies are attached by a rope, causing the system to move with an acceleration an in opposition to the force of gravity acting on one of the bodies. By dividing a body's mass (m) by the net force (F n e t) exerted on it, one can calculate the acceleration (a) of the body.

Please direct the bucket's acceleration in an upward direction.

The tension T supplied to the bucket is resisted by the weight mg acting downward, which causes the bucket to rise with an acceleration.

Applying the force balance we have as a result,

ma = T-mg

14a = 163-14 x 9.8

   a = 1.84 m/s²

We can see that the acceleration is 1.84 m/s² times larger than the speed and since a has a positive sign, we can infer that the direction is upward.

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The average angular acceleration of a Blu-ray disc is 0.089 rad/s².

Angular acceleration refers to the time price of exchange of angular speed. As there are types of angular velocity, namely spin angular velocity and orbital angular velocity, Angular speed is the rate of change of angular displacement and angular acceleration is the rate of trade of angular pace.

Angular Acceleration is described as the time rate of change of angular velocity. it is usually expressed in radians in keeping with second in line with second. as a result, α = d ω d t. Angular acceleration is also known as rotational acceleration.

t = time duration = 6 h = 6 x 3600 sec

α = angular acceleration = (Wmax - Wmin )/t = (315 - 121)/(6 x 3600 ) = 0.089 rad/s²

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The net charge on the sphere is 3.7×10⁻⁵C and the total electric flux leaving the surface of the sphere is 4.1×10⁶ N.m²/C.

The distribution of the electric field or the velocity at which the electric field moves through a specific area can both be measured as electric flux. The Greek letter is used to represent electrical flux. Voltmeters (Vm), often known as Nm 2 C – 1, is the SI unit for electric flux.

Procedure:

(a) The charge on the surface of the sphere is the product of the surface charge density σ and the surface area of the sphere which is 4πr².

Thus, q=4πr²σ

= 4π(1.2m/2)²(8.1×10⁻⁶)

=3.7×10⁻⁵C

(b) We select a spherical-shaped Gaussian surface with a slightly greater radius that is concentric with the conducting sphere.

∅=q/∈°

= 4.1×10⁶ N.m²/C

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As a result, neither the astronauts nor the others sharing the space station can feel the force that supports them from the structure's solid surface.

Space stations are constantly in a free-fall situation, which means their acceleration is the same as the local gravitational acceleration. As a result, neither the astronauts nor the other space station residents can feel the support force generated by the station's solid surface.

Thus, by rotating the space station around its center, we produce center-directed forces from the space station's wall in the absence of gravity.

Gravitational acceleration is equal to centripetal acceleration.

A = g

r2 = g r 2 = /g r 2 = 9.81 m s 2/ 55 m 2 = 0.178 r a d 2 s/ 2 = 0.422 r a d / s

Therefore, the angular speed of the space station is 0.422 rad/s.

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Determine the energy of an ultraviolet photon with a wavelength of 250 nm using E = hc/(wavelength) . After that, deduct the Cs work function energy, e* (work function in volts)

The entire mass of a nucleus is described in Section 44.1's discussion of 12C is smaller than the total of each nucleon's separate masses. The confined system's (the nucleus') energy is lower than the sum of the rest energies of the nucleon separation. The binding energy of this difference in energy the nucleus and can be understood as the additional energy required for a nucleus.

To separate it into its constituent parts. Consequently, to divide a nucleus into protons and neutrons, the system needs to be supplied with energy. Energy conservation and the mass-energy equivalence principle of Einstein demonstrate that any nucleus's binding energy, measured in MeV, is where mn is the mass of the neutral hydrogen atom and M(H) is its atomic mass.

nuclear, M(AZX) is a representation of the isotope A's atomic mass.

and the ZX Atomic mass units are used for all masses. The weight of the Z electrons in M (H) within a narrow range, cancels the mass of the Z electrons in the phrase M(AZX).

Discrepancy related to the electrons' atomic binding energy. Because

nuclear binding energies and atomic binding energies are both generally several electron volts.

With energies in the millions of electrons volts range, this difference is small.

Using the formula E = hc/(wavelength), calculate the energy of a UV photon having a wavelength of 250 nm (wavelength). Subsequently, subtract the Cs work function energy, e* (work function in volts)

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A spring with  a damping constant 5 (kg/s) can be held stretched 1 meters beyond its natural length by a force of 2 newtons. The mass m = 3.12 kg that would produce critical damping

From hooke's law, force required to stretch the spring is

                            k (1) = 2

          Spring Constant, k = 2

For critical damping, c²-4mk =0

                              m = c² / 4 k

                c= damping constant (from question)

                m = Mass to produce critical damping

There fore, m = (5²/4*2) =   3.12  kg  

According to Hooke's law, the restoring force is equal to -kx, where k is a positive number known as the spring constant. Since c is a positive constant that is also known as the damping constant, we assume that the damping force is -c(dx/dt). Robert Hooke, an English scientist, developed the law of elasticity in 1660. According to Hooke's law, for relatively minor deformations of an item, the displacement or amount of the deformation is directly proportional to the deforming force or load.

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Alice and bill throw the ball with same speed [tex]V_{A}[/tex]=[tex]V_{B}[/tex].

The speed at which an object's location changes in any direction. The distance traveled in relation to the time it took to travel that distance is how speed is defined. Given that it just has a direction and no magnitude, speed is a scalar number.

Okay, so let's imagine that there are two persons, Bob and Alice, standing on the edge of a cliff. We want to know how the speeds compare when the balls strike the ground so that as throws her ball downward at a speed of v and bill throws his ball upward at a speed of v from the same height.

Bill's will therefore rise to this height, strike 0 at that point, and then descend again. When it reaches this height, it will really be moving at the same speed as when it left Bill's hand, just in the opposite direction.

As a result, it will appear as though you tossed it straight down at the same speed, which implies When they both strike the ground, Alice's and Bill's balls will do so at the same pace.

The trajectory of Bill's ball will be symmetrical about this point in terms of the velocity or have the same speed going up as it did coming down or coming down as it did up, if you look at it because there is essentially no air resistance or anything.

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#SPJ4

The complete question is:

"Alice and Bill are at the top of a cliff of height H. Both throw a ball with initial speed v0, Alice straight down and Bill straight up. The speeds of the balls when they hit the ground are [tex]V_{A}[/tex] and [tex]V_{B}[/tex]. If there is no air resistance, which is true? A)[tex]V_{A}[/tex] <[tex]V_{B}[/tex] B) [tex]V_{A}[/tex]=[tex]V_{B}[/tex] C) [tex]V_{A}[/tex]>[tex]V_{B}[/tex] D) impossible to tell"