shot from a cannon in 1998, david "cannonball" smith set the distance record for being shot from a cannon (56.64 m). during a launch in the cannon’s barrel, his speed increased from zero to 80 km/h in 0.40 s. while he was being stopped by the catching net, his speed decreased from 80 km/h to zero with an average acceleration of 180 m/s2m/s2. what can you determine about smith’s flight using this information?

At a distance of 1.7 cm, the horn will begin to cause pain.

The source is an isotropic point source.

Let the distance at which the horn is barely audible be

[tex]r _2.[/tex]

[tex]r _2= 17 km[/tex]

Let the distance at which the horn will cause pain to be

[tex]r _2.[/tex]

[tex]A _{phere} = 4\pi \times r ^{2} [/tex]

The intensity ratio between barely audible and painful threshold is,

[tex]I = \frac{P }{A}[/tex]

[tex] \frac{I _2}{I _1 } = \frac{\frac{P}{4\pi \times r ^{2} _2 } }{ \frac{ P}{4\pi \times r ^{2} _1 }} [/tex]

[tex] = ( \frac{r _1 }{r _2 } ) ^{2} [/tex]

[tex]10 ^{ - 12} \: is \: ratio \: of \: the \: intensity [/tex]

between barely audible and painful threshold.

So,

[tex] \frac{I_2 }{I _1 } =( \frac{r _1 }{r _2 } ) ^{2} [/tex]

[tex] \frac{I_2 }{I _1 } = 10 ^{ - 12} [/tex]

[tex]r _2 = 17000 \: m[/tex]

The distance at which the horn will begin to cause pain is,

[tex]r _1 = r _2 \sqrt{10 ^{ - 12} } [/tex]

[tex]r _1 = 17000 \sqrt{10 ^{ - 12} } [/tex]

[tex]r _1 = 0.017 \: m[/tex]

[tex]r _1 = 1.7 \: cm[/tex]

Therefore, at a distance of 1.7 cm horn will begin to cause pain.

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Explanation:

12:30pm -> 04:00pm = 3hrs 30mins

3hr 30mins= 3.5hrs

average speed=total distance/total time

=213÷3.5

=60.8571428571

round to 2 decimal places

=60.86 mph

If a pendulum clock is running fast, the length of the pendulum should be increased to correct the problem.

The time period of a simple pendulum clock is:

 T= 2π√(l/g)

Where,

l is the length of the simple pendulum and g is the gravity.

From the formula, we can see that the time period is directly proportional to the square root of the length. Decreasing the length will decrease the time period and the clock will move faster.

In order to slow the clock, increase the length of the pendulum to increase the time period.

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There are C different ways to choose two different automobiles (12, 2).

In mathematics, a choice is made from a set of various components where the order of the choices is unimportant (unlike permutations).

For instance, there are three conceivable combinations of two given fruits, such as an apple, an orange, and a pear: an apple and a pear; an orange and an apple; or an orange and a pear. Formally speaking, a set S's k unique components make up a subset known as a k-combination. In other words, two combinations are same only if all of their members are the same.

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The Volume of Copper Cube with mass 153.6 g and density 8.96 g/cm³ is 17.14 cm³ and its Edge is 2.58 cm long.

We have a Copper Cube of mass 153.6 g and density 8.96 g/cm³.

We have to calculate the volume and length of the cube in cm³ and cm respectively.

The density and mass of body are related as follows -

M = ρV

Where -

M - mass of body

ρ - density of body

According to the question, we have →

Mass of copper cube = 153.6 g

Density of copper cube = 8.96 g/cm³

Using the formula discussed above -

M = ρV

V = M/ρ = 153.6/8.96 = 17.14 cm³

We know that the volume of cube is -

V = a x a x a

a³ = 17.14 cm³

a = 2.58 cm

Hence, the Volume of Cube is 17.14 cm³ and its Edge is 2.58 cm long.

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With the use of formula, the maximum height reached by the ball in term of h is 4h

A projectile is any object thrown into the space or atmosphere which take a trajectory path.

If you toss a ball straight up, and it reaches a maximum height h above the launch position, Then the maximum height reach will be

v² = u² - 2gh

But at maximum height, v = 0

u² = 2gh

h = u² / 2g ...... (1)

Also, the time taken will be;

v = u - gt

since v = 0,

u = gt

Substitute u into equation 1

h = (gt)² / 2g

If you want to double the length of the time interval during which the ball stays in the air above the launch position, then,

u = g2t and the maximum height will be

H = (g2t)² / 2g

H = 4g²t² / 2g

H = 4(gt)² / 2g

but h = (gt)² / 2g

H = 4h

Therefore, the maximum height you have to throw it in terms of h will be 4h.

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There are distinct emission lines indicating discrete energy levels.

When a component transmits energy in the form of radiation, a spectrum of colors is produced on a photographic plate. This spectrum can be both continuous and discrete. The spectrum persists without distinction between two regions in a continuous spectrum. This represents the uninterrupted radiation emission and thus the uninterrupted emission of energy.

The line spectrum, on the other hand, is made up of discrete and sharp lines that show the emission of radiation in a specific amount over a specific time period, with a break between emission. As a result, the line spectra supports energy quantization.

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Answer:the magnitude of the hikers resultant displacement

Explanation:

We have the given equation as [tex]\frac{7x}{(x+6)(3x+2)}[/tex] that we have to convert through partial fraction decomposition.

The partial fraction decomposition or partial fraction expansion of a rational fraction in algebra is the process of expressing the fraction as the product of a polynomial (possibly zero) and one or more fractions with a simpler denominator.

A rational fraction is defined as one that has a polynomial as both the numerator and the denominator.

We have to find the form of the partial fraction decomposition of the function.

The given rational function has two factors in multiplication form in the denominator.

Also, the degree of the numerator is less than the denominator. Hence, the form of partial fraction decomposition of the function is:

[tex]\frac{7x}{(x+6)(3x+2)}[/tex] = [tex]\frac{A}{x+6} + \frac{B}{3x+2}[/tex]

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Answer:

false

Explanation:

The average speed for the whole trip will be 40 miles per hour.

The average speed is the ratio of the total distance over the total time taken. Then the average speed is given as,

Average speed = (Total distance) / (Total time)

You drive for 30 minutes at 30 miles per hour. Then the distance covered will be

D₁ = 30 x 30 / 60

D₁ = 15 miles

And then for another 30 minutes at 50 miles per hour. Then the distance covered will be given as,

D₂ = 50 x 30 / 60

D₂ = 25 miles

Then the average speed for the whole trip will be

Average speed = (15 + 25) / (0.5 + 0.5)

Average speed = 40 / 1

Average speed = 40 miles per hour

Thus, 40 miles per hour will be the average speed for the whole trip.

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A 0.900 kg block that is attached to a spring with spring constant 13.0 n/m when hit with the hammer has the amplitude of oscillation as 11.637 x 10^-3 cm.

When an object’s motion repeats in a predetermined cycle, it is said to be in periodic motion. The motion described here is an oscillation.

Spring and pendulum motion are two straightforward instances of oscillations, but there are numerous additional instances as well.

The fact that the item is in a stable equilibrium position is a key characteristic of periodic motion. A restorative force that is pointed in that direction as well. The application of force occurs in spring.

If x is the compression of the spring after it is hit,

1/2 k x² = 1/2 m v²

13 x² = .90 x (41 x 10⁻²)² 1681

x² = 116.37 x 10⁻⁴

x = 11.637 x 10^-5m

11.637 x 10^-3 cm

Amplitude of oscillation = 11.637 x 10^-3 cm

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Minimum volume must the slab have so that a 45 kg boy can sit on the slab without it sinking is 0.465 m³.

What is buoyant force?

The buoyant force is the upward force exerted on an item that is fully or partially submerged in a fluid. This upward thrust is also known as an upthrust. Because of the buoyant force, a body submerged partially or entirely in a fluid appears to  be lighter or to lose weight.

Given:

Density of the styrofoam, ρ' = 32 kg/m³

Now, let the volume of the slab = V

the submerged volume be = V ;

now, the volume of water displaced will be V  

thus,

the buoyant force acting will be = ρVg

{where,

ρ is the density of water

g is the acceleration due to gravity}

now,

total downward force acting = weight of the boy + weight of the slab

total downward force acting =45 × g + ρ' × V × g

For the no sinking condition, buoyant force should be equal to the total downward force.

thus,

ρ × V × g = 45 × g + ρ' × V × g

or

ρ × V = 45 + ρ' × V

on substituting the values

V ( 1000 - 32 ) = 45 ;

or

V = 0.465 m³

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The correct answer is 47 units.

Arrows typically serve as a vector's geometric representation. The magnitude of the vector is determined by its length and the direction in which the arrow is pointing. When two vectors have the same magnitude and direction, they are said to be equal. Additionally, the magnitude and direction of vectors are unaffected by the vector's position.

A quantity with both magnitude and direction is referred to as a vector quantity. One example of a vector quantity is velocity. A two-dimensional vector can be expressed as,

A=A_Xi+A_Yj

Vector A=31 j

A+B=-16 j

Thus vector B is

B=(A+B)-A

B=(-16j)-31j

B=(-47)j

As a result, vector B has a magnitude of 47 units and is oriented in a negative Y direction.

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a) As carbon dioxide is formed the shorter candle's flame goes off first, followed by the taller candle. This shows, that in absence of air, the flame goes off. Hence, the air is necessary for combustion.

b) Although both reactants are common home chemicals and foods, care should be taken to avoid splashing in the eyes, and protective clothing should be used. The reaction's byproducts can be disposed of by thoroughly filling the sink with water and washing down the sink with no chemicals touched.

Baking soda and vinegar react with one another to create carbon dioxide gas. The carbon dioxide gas sinks to the bottom of the bowl because it is heavier than the air around it. More and more carbon dioxide gas is produced as the reaction progresses, progressively filling the bowl as it does so. The flame will go out owing to a shortage of oxygen once the level of carbon dioxide reaches that of the flame.

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Answer:

sp3 d 2

Explanation:

The g - string will stretch by 0.0016 mm.

We have a g - string of a guitar with given specifications.

We have to determine how many mm does a 75-cm-long g - string stretch when it’s first tuned.

According to the question -

The force of tension in the string -

[tex]$v = \sqrt{\frac{T}{\mu} }[/tex]

T = [tex]$v^{2} \mu[/tex] = 250 x 250 x 0.0011 = 68.75 N

The Yung modulus of steel = 2 x [tex]10^{11}[/tex] N/[tex]m^{2}[/tex]

the amount by which the g - string will be stretched is given by -

[tex]$\delta L = \frac{LT}{Y(\pi r^{2})}[/tex]

Substituting the values -

[tex]$\delta L = \frac{0.75\times 68.75 }{(2\times 10^{11} )\times (\pi (2.2 \times 10^{-4}\times 2.2\times 10^{-4}) )}[/tex]

[tex]\delta L=[/tex] 0.0016mm

Hence, the g - string will stretch by 0.0016 mm.

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[ The given question is incomplete. The complete question is

" The G string on a guitar is a 0.46-mm-diameter steel string

with a linear density of 1.1 g/m. When the string is properly

tuned to 196 Hz, the wave speed on the string is 250 m/s. Tuning

is done by turning the tuning screw, which slowly tightens—and

stretches—the string. By how many mm does a 75-cm-long G

string stretch when it’s first tuned? "]

1905, Albert Einstein. The theory of special relativity explains how speed affects space, time, and mass. Small amounts of mass (m) can be interchangeable with large amounts of energy (E), as defined by the classic equation E = mc2, according to the theory, which offers a means for the speed of light to define the link between energy and matter.

When talking about extremely high energy, incredibly fast speeds, and astronomical distances without the difficulties of gravity, special relativity is typically employed. With the publication of his general relativity article in 1915, Einstein formally incorporated gravity into his ideas.

The mass of an object and the energy needed to move it both grow unlimited as it gets for any matter to go faster than light travels. This cosmic speed limit inspires new realms of physics and science fiction, as people consider travel across vast distance closer to the speed of light. Therefore, it is not possible.

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The correct answer is 0.024cm.

The density of a substance determines how heavy it will be in a given volume. It is technically the mass of that material per unit volume. It is implied by this that a specific material weighs a specific quantity relative to its volume.

A substance's density determined how heavy it would be at a particular size. It is an inherent quality that is not affected by geography, such as a shift in the globe.

density of copper =  8.93 g/cm3

mass = 3.1118 g

Density= mass/volume

8.93= 3.1118 /volume

volume=3.1118/8.93

=0.348 cm^3

Volume = l×b×t

T= volume/ l×b

=0.348 cm^3/12.10×11.67

=0.348 /141.2

=0.0024×10mm

=0.024cm

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The correct answer is 1.07m.

The area surrounding an electric charge where its impact may be felt is known as the electric field. When another charge enters the field, the presence of an electric field may be felt. The electric field will either attract or repel the charge depending on its makeup. Any electric charge has a property known as the electric field. The charge and electrical force working in the field determine the strength or intensity of the electric field.

Here, is the charge per unit length, r is the distance from the wire, and

is the free space permittivity  ε_0. Electric field due to the long straight wire is,

E= λ/2πε_0r

Rearrange the equation for r.

r=λ/2πε_0E

Substitute 2.41 N/C for E,

E=1.44×10^-10C/m

λ=8.85×10^-12C^2/Nm^2

r=(1.44×10^-10C/m)/(2(3.14)(8.85×10^-12C^2/Nm^2)(2.41N/C))

r=1.07m

At a distance of 1.07 m the magnitude of electric field is 2.41 N/C.

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The part of river's current moves at a 1.486 m/s speed.

the distance between two points, objects, lines, etc. Remoteness is the quality of being physically separated from another thing or person. a line drawn in the universe. To walk seven miles in one hour would be too time-consuming.

The difference between the change in distance and the change in time is used to compute the rate of change.

Rate: times the distance Time

The distance is 16.5 miles, and the time is 5.5 hours.

If we enter this into the formula above, it yields:

16.5 - 5.5 / 10.9 - 3.5 = 11/7.4 = 1.486 m/s is the rate of change.

Calculations show that the constant rate of change is 1.486 m/s.

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The value of matrix p will be[tex]\left[\begin{array}{ccc}9&1\\14&4\end{array}\right][/tex].

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Ecosystem A has more diversity, because it has greater species evenness than Ecosystem B.

All the organisms and the physical setting they interact with make up an ecosystem. The nutrient cycles and energy flows connect these biotic and abiotic elements. Photosynthesis is how energy reaches the system and is absorbed by plant tissue.

Forest Ecosystem.

Grassland Ecosystem.

Tundra Ecosystem.

Desert Ecosystem.

Fundamentally, the way an ecosystem works is through the transfer of nutrients and energy up the food chain. The planet's plant and animal life, as well as the breakdown of organic matter and the creation of biomass, are all supported by these exchanges.

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The linear speed of the helicopter blade is 33.51 m.

The tangential speed of the helicopter blade is calculated as follows;

v = ωr

where;

ω  = 80 rev/min

ω = 80 x 2π rad/rev x 1 min/60s

ω = 8.378 rad/s

v =  8.378 rad/s x 4 m

v = 33.51 m

Thus, the linear speed of the helicopter blade is 33.51 m.

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The complete question is below:

Find the tangential speed of the helicopter's blade.

The lowest 19.152 [tex]\frac{w}{m^{2} }[/tex] frequency that will produce the maximum intensity (Imax) at the observer, assuming the observer will still hear an intensity of 6 w/m2 when [tex]S_{1}[/tex] or [tex]S_{2}[/tex] is heard alone.

We have [tex]I_{1} =I_{2}[/tex]

[tex]= 6 w/m^{2}[/tex]

Path difference

δ = 5.6568 - 4

δ = 1.6568 m

v = 335 m/s

Intensity I = [tex]4I_{1} cos^{2}[/tex](πδ/λ)

[tex]= 4I_{1} cos^{2}[/tex](πδf/v)

[tex]= 4 * 6 cos^{2}(\frac{\pi *1.6568*30}{335} )[/tex]

I = 19.152 [tex]\frac{w}{m^{2} }[/tex]

the lowest frequency is selected to cowl the N-point signal at its coarsest scale with the aid of the default wavelet's two-time popular deviations. the very best frequency wavelet bandpass filter out loses half of of its height importance at the Nyquist frequency because of the most frequency.

guy's voice has the lowest frequency in comparison to other sounds seeing that frequency and pitch cross hand in hand. Pitch denotes the voice's shrillness. the man's voice is the selection with the least strident tone. It, therefore, has the bottom pitch of all and for this reason the bottom frequency.

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The average time between two drops falling t = 2/5 sec.

To calculate average time use formula,

t + t / product

So,

given,

time = 20 s

drops = 50

average time = ?

From this,

measured time for 50 drops = 20sec

Time required for 1 drop = 20/ 50

Average time between two drops = (2/5 + 2/5) / 2

Hence,

The average time between two drops t = 2 / 5

Average Time on Page is a web analytics metric that gauges how long, on average, all website visitors stay on a single page. Only the average amount of time that users spend on non-exit pages is measured by this metric, which ignores exit pages and bounces.

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Mass of disc m =16.84 kg

Moment of inertia of disc about axis perpendicular to the plane of disc and passing through its centre = MR²/2

12 =  MR²/2 × 5.7

12 =  M(0.5)²/2 × 5.7

Mass = 12 × 2 /5.7 × 0.5² = 16.84 Kg

The atomic mass of an detail is described because the weighted common mass of that detail’s is False

Atomic mass (Also referred to as Atomic Weight, even though this denomination is incorrect, for the reason that mass is belongings of the frame and the burden relies upon at the gravity) Mass of an atom similar to a positive chemical detail).  mean "unit of atomic mass". This unit is likewise typically referred to as Dalton (Da) in honor of the English chemist John Dalton.

It is equal to 1 12th of the mass of the nucleus of the maximum ample isotope of carbon, carbon-12. It corresponds more or less to the mass of a proton (or a hydrogen atom). It is abbreviated as "uma", even though it could additionally be located with the aid of using its English acronym "amu" (Atomic Mass Unit). However, the advocated image is simply "u".

The atomic masses of chemical factors are typically calculated using the weighted average of the masses of the exceptional isotopes of each detail while taking into account the relative abundance of each one. This is the cause of the discrepancy between an element's atomic mass in umas and the range of nucleons that contains the nucleus of its maximum uncommon place isotope.

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mU1 + mU2 = mV1 + mV2

(5 × 6) + (3 × 4) = 5V + 3V

30 + 12 = 8V

42 = 8V

V = 5.25m/s

The velocity of the ball after the collision is 5.25m/s.

While velocity refers to the speed and direction of an object's motion, speed is the rate at which an object moves along a path over time.

The rate at which something moves in a certain direction is referred to as its velocity. as quickly as a car traveling north on a highway or a rocket taking flight. The magnitude of the velocity vector's absolute value will always be equal to the motion's speed because it is a scalar.

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The calculated value is 2.5×10⁷ m.

Velocity is a term that describes the speed and direction of a point's motion. For example, a circular path's direction is always perpendicular to a line from the point to the circle's center. A point always moves in a direction that is tangent to its path (a radius). A vector measurement of the rate and direction of motion is what is meant by the term "velocity." Simply said, velocity is the rate of movement in a single direction.

From energy conservation, since the velocity will be 0 at highest point,

1/2 m (10000) ²− GMm/R

=− GMm/d

=10⁸/2 −(9.8) (6400000)

=−(9.8) *(6400000) ²/d

d≈2.5×107 m

Answer is 2.5×10⁷ m.

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