The cnoidal wave theory gives more accurate results for waves with higher amplitudes, while the small-amplitude theory is more accurate for waves with lower amplitudes.
According to the cnoidal wave theory, the wave celerity and wavelength can be calculated using the formulas below, for a wave having a period of T and a height of H in water having a depth of d:
\($$c = \sqrt {\frac {gd} {2} \left( {1 + \frac {2H} {d}} \right)} $$\)
and\($$L = \frac {T} {2\pi } \sqrt {\frac {gd} {2} \left( {1 + \frac {2H} {d}} \right)} $$\)
where g is the acceleration due to gravity.
Using the given values, we have:
Period T = 12 s
Height H = 3 m
Depth d = 3.5 m
Acceleration due to gravity g = 9.81 m/s²
The wave celerity c is given by:
\($$c = \sqrt {\frac {gd} {2} \left( {1 + \frac {2H} {d}} \right)} $$\)
Substituting the given values, we have:c = sqrt ((9.81 x 3.5) / 2 (1 + (2 x 3) / 3.5)) = 6.76 m/s
The wavelength L is given by:
\($$L = \frac {T} {2\pi } \sqrt {\frac {gd} {2} \left( {1 + \frac {2H} {d}} \right)} $$\)
Substituting the given values, we have:
L = (12 / 2π) sqrt ((9.81 x 3.5) / 2 (1 + (2 x 3) / 3.5)) = 42.04 m
We can also calculate the wave celerity and wavelength using the small-amplitude theory, which is given by the formulas below:
\($$c = \sqrt {\frac {gd} {2}} $$\)
and
\($$L = \frac {gT^2} {2\pi } $$\)
Using the given values, we have:
Period T = 12 sDepth d = 3.5 m
Acceleration due to gravity g = 9.81 m/s²
The wave celerity c is given by:
\($$c = \sqrt {\frac {gd} {2}} $$\)
Substituting the given values, we have:
c = sqrt ((9.81 x 3.5) / 2) = 5.31 m/s
The wavelength L is given by:
\($$L = \frac {gT^2} {2\pi } $$\)
Substituting the given values, we have:
L = (9.81 x 12²) / (2π x 2) = 147.87 m
Comparing the results obtained from the two theories, we see that the cnoidal wave theory gives a wave celerity of 6.76 m/s and a wavelength of 42.04 m, while the small-amplitude theory gives a wave celerity of 5.31 m/s and a wavelength of 147.87 m. Therefore, we can conclude that the cnoidal wave theory gives more accurate results for waves with higher amplitudes, while the small-amplitude theory is more accurate for waves with lower amplitudes.
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a 0.639 h inductor is connected in series with a fluorescent lamp to limit the current drawn by the lamp. if the combination is connected to a 59.9 hz, 169 v line, and if the voltage across the lamp is to be 24.7 v, what is the current in the circuit? (the lamp is a pure resistive load.)
The current in the circuit is 0.698 A.
We can start by finding the reactance of the inductor using the formula:
XL = 2πfL
where XL is the inductive reactance, f is the frequency, and L is the inductance.
XL = 2π(59.9 Hz)(0.639 H) = 240.3 Ω
Since the lamp is a pure resistive load, its resistance is equal to the voltage across it divided by the current flowing through it:
R = V/I
where R is the resistance, V is the voltage, and I is the current.
R = 24.7 V / I
The total impedance of the circuit is given by:
Z = √(\(R^2\)+ X\(L^2)\)
Since the inductor and lamp are connected in series, the current flowing through both is the same, and we can use Ohm's Law to find the current:
I = V/Z
Substituting in the values we have:
Z = √(R^2 + X\(L^2\)) = √[(24.7 Ω/I\()^2\) + (240.3 Ω\()^2\)] = 242.2 Ω
I = V/Z = (169 V)/(242.2 Ω) = 0.698 A
Therefore, the current in the circuit is 0.698 A.
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Help plz will give brainliest
Answer:
The forces acting on the root beer is the ice cream. This means that the 'air' in the ice cream keeps it at the top of the root beer enabling it to float right at the top.
An earthquake occurs 7,250 km from a seismograph. The P.waves arrive 11.8 minutes later. How fast is the P-wave traveling (in km/s)? If the tag time between P - and 5 -waves is 10.8 minutes, how fast are the S-waves traveling (in km/s)? Using the shadow of S-waves you determine that the radius of the core is 55 N, of the Earth's 6,378−km radius. How many kilometers from the surface is this (in km)?
The speed of the P-wave is approximately 614.41 km/s. The speed of the S-wave is approximately 564.81 km/s. The distance from the surface to the radius of the Earth's core is approximately 6,323 km.
To calculate the speed of the P-wave, we use the formula: Speed = Distance / Time. Given that the earthquake is 7,250 km from the seismograph and the P-waves arrive 11.8 minutes later, we can convert the time to seconds and calculate the speed of the P-wave.
For the S-wave, we use the same formula: Speed = Distance / Time. Given that the time between the P- and S-waves is 10.8 minutes, we convert the time to seconds and calculate the speed of the S-wave.
Next, using the concept of seismic wave shadow zones, we can determine the distance from the surface to the radius of the Earth's core. The radius of the Earth is given as 6,378 km, and the radius of the Earth's core is 55 N (which corresponds to the inner core radius of 1,220 km). By subtracting the radius of the Earth's core from the Earth's radius, we can find the distance from the surface to the core.
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Help!!
Remember W = mg, 1 kg = 2.2 lbs. S
1) If you have a 12 lbs. bag of potatoes what is its mass? What is its weight?
Answer:
5.5 KG is the mass
53.9 is the Weight
A bidy moves south at 20m/s and changes direction by moving north at 30m/s. calculate
a) the change in speed
b) the change in velocity
Explanation:
the speed=30-20=10m/s
velocity=30-(-20)=50m/s
Please show workings
Find question attached
The charge on the oil drop is 4.93 x 10⁻¹⁵ coulombs.
The charge on the oil drop can be found using the formula:
q = mg(d + b)/V(E + mg/k)
where q is the charge on the oil drop, m is its mass, d is the distance between the plates, b is the radius of the oil drop, V is its volume, E is the electric field strength, g is the acceleration due to gravity, and k is the viscosity of air.
First, we can calculate the mass and volume of the oil drop:
m = (4/3)πr³ρ = (4/3)π(1.000 x 10⁻³ m)³(860 kg/m³) = 3.02 x 10⁻¹⁰ kg
V = (4/3)πr³ = (4/3)π(1.000 x 10⁻³ m)³ = 4.19 x 10⁻¹⁰ m³
Next, we can calculate the force acting on the oil drop due to gravity:
Fg = mg = (3.02 x 10⁻¹⁰ kg)(9.81 m/s²) = 2.96 x 10⁻⁹ N
We can also calculate the viscosity of air:
k = 1.816 x 10⁻⁵ kg/m/s
The electric field strength can be found using the formula,
E = V/d
where V is the potential difference and d is the distance between the plates,
E = (3000 V)/(0.5000 x 10⁻² m) = 6.000 x 10⁵ V/m
The upward force due to the electric field is given by:
Fe = qE
where q is the charge on the oil drop. At terminal velocity, the upward electric force is equal and opposite to the downward force due to gravity, so:
Fe = Fg
qE = mg
Substituting the values we have calculated, we get:
q = (mg)/(E)
q = (2.96 x 10⁻⁹ N)/(6.000 x 10⁵ V/m)
q = 4.93 x 10⁻¹⁵ C
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Which of the following claims best describes what happens to the intensity of light when it is incident on a clear glass window? A The intensity of the reflected light must be equal to the intensity of the incident light. B The intensity of the transmitted light must be equal to the intensity of the incident light. C The intensity of the reflected light must be equal to the intensity of the transmitted light. D The sum of the intensities of the reflected and transmitted light must be less than the intensity of the incident light.
The correct answer to the question is B: "The intensity of the transmitted light must be equal to the intensity of the incident light."
When light is incident on a clear glass window, a portion of the light is reflected and a portion is transmitted through the glass. The intensity of the reflected light depends on the refractive indices of the glass and the surrounding medium. However, the intensity of the transmitted light is directly proportional to the intensity of the incident light. This means that if the incident light has an intensity of 100 units, then the transmitted light will also have an intensity of 100 units, assuming there is no absorption or scattering by the glass. Option B
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most comets are discovered when their coma develops, giving them a fuzzy appearance instead of stellar such as asteroids. group of answer choices T/F
True. Most comets are discovered when their coma develops, giving them a fuzzy appearance instead of a stellar one like asteroids. Comets are celestial objects composed of ice, dust, and rock. When they approach the Sun, the heat causes the ice to sublimate, releasing gas and dust particles.
This process forms the coma, which is a temporary atmosphere surrounding the comet's nucleus. The solar radiation and solar wind cause the dust and gas in the coma to form a glowing tail, which can extend millions of kilometers into space. This distinct, fuzzy appearance is what distinguishes comets from other celestial objects such as asteroids, which are primarily composed of rock and metal and do not have a coma.
Asteroids are often found in the asteroid belt between Mars and Jupiter, while comets usually originate from the outer regions of our solar system, such as the Kuiper Belt and the Oort Cloud. The appearance of a comet's coma and tail make it easier for astronomers to discover and differentiate them from asteroids and other celestial bodies.
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Assuming that the Earth is a sphere of radius 6378 km, calculate the magnitude of the centrifugal force and force of gravity acting on a 400.0 kg mass located at a place of latitude 40°. The gravitational constant is 6.6742 × 10⁻¹¹ m³ kg⁻¹s⁻² and the Earth's mass is about 5.9722 x 10²⁴ kg. Round-off final values to 2 decimal places.
By assuming that Earth is sphere and it have radius of 6378 km, then its magnitude of the centrifugal force is 293.14 N and Magnitude of the force of gravity is 1.94 x 10⁴ N.
To calculate the magnitude of the centrifugal force and force of gravity,
Centrifugal force:
F_centrifugal = m * ω² * r
Force of gravity:
F_gravity = G * (m * M) / r²
It is given that, Mass of the object (m) = 400.0 kg, Radius of the Earth (r) = 6378 km = 6,378,000 m, Gravitational constant (G) = 6.6742 × 10⁻¹¹ m³ kg⁻¹ s⁻², Mass of the Earth (M) = 5.9722 x 10²⁴ kg, Latitude (θ) = 40°.
First, we need to calculate the angular velocity (ω) using the latitude:
ω = 2π * (1 day) / (1 sidereal day)
1 day = 24 hours = 24 * 60 * 60 seconds
1 sidereal day = 23 hours 56 minutes 4.1 seconds = 23 * 60 * 60 + 56 * 60 + 4.1 seconds
ω = 2π * (24 * 60 * 60) / (23 * 60 * 60 + 56 * 60 + 4.1)
ω = 7.2921 × 10⁻⁵ rad/s
(a) Centrifugal Force:
To calculate the centrifugal force, we need to convert the latitude to radians:
θ (in radians) = θ (in degrees) * π / 180
θ (in radians) = 40 * π / 180
Now we can calculate the centrifugal force:
F_centrifugal = m * ω² * r * sin(θ)
F_centrifugal = (400.0 kg) * (7.2921 × 10⁻⁵ rad/s)² * (6,378,000 m) * sin(40°)
F_centrifugal = 293.14 N
(b) Force of Gravity:
To calculate the force of gravity, we use the formula:
F_gravity = G * (m * M) / r²
F_gravity = (6.6742 × 10⁻¹¹ m³ kg⁻¹ s⁻²) * (400.0 kg) * (5.9722 x 10²⁴ kg) / (6,378,000 m)²
F_gravity ≈ 1.94 x 10⁴ N
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a. how long must a 0.60-mm-diameter aluminum wire be to have a 0.50 a current when connected to the terminals of a 1.5 v flashlight battery?
To learn the resistance, flashlight and terminal points.
What is flashlight?
A light bulb on a wire makes up a type of circuit that is a flashlight. Simply put, a light bulb converts the energy of moving (-) charges into light. The circuit is created by connecting the wire with the light bulb to the battery by depressing the flashlight's switch.
What is terminal?
A terminal is the place where a conductor from a part, device, or network ends. As the reusable interface to a conductor and a point where external circuits can be connected, an electrical connector at this endpoint is another type of terminal.
a)R = v/i = 1.5/0.5 = 3 ohm
R = rho*L/A
L = R*A/rho = 3*3.14*(0.0003)^2/2.8*10^-8 = 30.2 m
b)
R = 3/2 = 1.5 ohm
i = V/R = 1.5/1.5 = 1 A
so
resistance=1.5/0.54
=2.778 ohm.so,
2.778=(2.8*10^-8*l)/(0.25*3.142*(6*10^-4)^2)
=28.0558 m
b)resistance will become half=1.389 ohm
so current=1.5/1.389
=1.08 A
You need to get the resistance of the wire.
Then do V = I * R
In your book you should have a table that says how to calculate the resistance of a wire for that diameter, material, and length.
Then just plug in the values and solve for I.
1.5 = I * R
Therefore, the connecting terminals is 1.5v.
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18. A vertical spring has a length of 25cm when a 150g mass is hung from its end and its length is 30cm with 250g hanging from it. What is the spring constant? a) 19.6N/cm b) 19.6n/m c) 109.6N/m d) 19.6N/m e) 19.6N/km
The spring constant of the spring is 19.6 N/m.
The correct answer is option D.
What is the spring constant of the spring?
The spring constant of the spring is calculated by applying the following equation as shown below.
Mathematically, the formula of Hooke's law is given as;
F = kx
where;
F is the applied forcek is the spring constantx is the extension of the springk = F / x
the extension of the spring when the 250 g mass was hung on it is calculated as;
x = 30 cm - 25 cm
x = 5 cm = 0.05 m
The spring constant of the spring is calculated as;
k = ( mg ) / x
where;
m is the additional mass = 250 g - 150 g = 100 gk = ( 0.1 x 9.8 ) / ( 0.05 )
k = 19.6 N/m
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12 A car travels in a straight line at speed v along a horizontal road. The car moves
against a resistive force F given by the equation
F = 400+kv²
where F is in newtons, v in ms-1 and k is a constant.
At speed v = 15ms-1, the resistive force F is 1100 N.
a
Calculate, for this car:
i the power necessary to maintain the speed of 15ms-¹,
ii the total resistive force at a speed of 30 ms-¹,
iii the power required to maintain the speed of 30ms-¹.
Answer:
i) Power = Force * Velocity = 1100 * 15 = 16500 W = 16.5 kW(ii) Find the value of k first: F = 400 + k(15^2) k = 28/9 F = 400 +(28/9)(30^2) = 320
Explanation:
Wondering if you have enough rope to rappel to the ground, you drop a rock off the top, and hear the sound of it hitting the bottom 4.2 seconds later. Find the height of the cliff ignoring the time that the sound takes to travel back to you from the bottom.
Answer:
86.5 m
Explanation:
\(s = ut + \frac{1}{2} at {}^{2} \\ s = (0)(4.2) + \frac{1}{2} (9.81)(4.2) {}^{2} \\ s = 86.5m \)
Answer:
86.5 m
Explanation:
Bx = -1.33 m and By = 2.81 m
Find the magnitude of the
vector.
Answer:
Explanation:
The formula for the magnitude of a vector is
\(B_{mag}=\sqrt{(-1.33)^2+(2.81)^2}\) and then round to the hundredths place:
3.11 m. Since we are in Q2, we can also find the direction of this vector:
\(tan^{-1}(\frac{2.81}{-1.33})=-64.7\) but since we are in Q2, we add 180 degrees to the result, getting the angle to be 115.3
Answer:115.33
Explanation:
Where is the south pole of the bar magnet, based on the magnetic field lines
shown?
A. On the right end
B. On the bottom edge
C. On the left end
D. On the top edge
SUBMIT
it would be on the right end I believe. Forgive me if I am incorrect.
Why is rust formed on iron
the mass of the earth is 6 × 10²² kg and that of the moon is 7.4× 10²² Kg if the distance between the earth and moon is 3.84 × 10⁵ km . calculate the force of the earth exerted by it on the moon . Take G = 6.67×10¹¹ Nm² / kg²
Answer:
Force = 20.08 x 10⁴⁷ N
Explanation:
Given:
M1 = 6 × 10²⁴ kg (rectified)
M2 = 7.4× 10²² Kg
Radius r = 3.84 × 10⁵ km
G = 6.67×10¹¹ Nm² / kg²
Find:
Force
Computation:
F = GM1M2 / r²
Force = [(6 × 10²⁴)(7.4× 10²²)(6.67×10¹¹ )] / (3.84 × 10⁵)²
Force = [296.148 × 10⁵⁷] / [14.7456 × 10¹⁰]
Force = 20.08 x 10⁴⁷ N
can a person run at a speed of 20 meters per second
Answer:
No
Explanation:
The fastest recorded time for a person to run 100 metres is 9.58 seconds, which is the equivalent of 10.4 metres per second
Answer:
No
Explanation:
Humans can run as fast as 19.3m/s, using their full possible energy.
You are playing baseball and hit a single, running to first base. Your distance and displacement are
Answer choices:
A. Both 90 feet
B. Both 0 feet
C. Distance 90 feet Displacement 0 feet
D. Distance 0 feet Displacement 90 feet
Answer:
C. Distance 90 feet Displacement 0 feet
if you had something the size of a sugar cube that was made of white dwarf matter, it would weigh about as much as
If you had a sugar cube that was made of white dwarf matter, it would weigh about as much as an elephant.
White dwarfs are the smallest type of stars in the universe, and they have a density of around 100 million times greater than that of water. This means that if you took a sugar cube that was made entirely out of white dwarf matter and put it on your kitchen counter, it would weigh about as much as an elephant!
But don't worry—you're not going to find any white dwarfs at your local grocery store or restaurant. White dwarfs are formed when red giants collapse in on themselves after burning through their fuel. And if you did happen to find one, you'd need a really big countertop.
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If a chemical reaction has a AH value of -125 kJ, it would be considered what?
A. an exothermic reaction
B. a reaction that absorbs energy
C. an endothermic reaction
D. A reaction that probably gets cold
exothermic
Explanation:
negative means it's losing energy
__________ takes place when an object is given a charge by bringing it close to a charged object.
The answer is Induction. "Induction" takes place when an object is given a charge by bringing it close to a charged object.
Induction is that process in which an object acquiring a charge by coming into the contact with any of the charged object. During that induction, electric field of the charged object induces an electric field in the uncharged object.
This electric field creates an electric dipole moment in uncharged object, that causing its charges to move and redistribute themselves in such a way that object acquires the net charge. This process occurs without any of physical contact between two objects and is also used to charge the objects like capacitors.
Induction can also be used to create a current loop in any conductor, which can be used to measure or to detect the strength of the specific magnetic field.
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a local fm radio station broadcasts at a frequency of 99.7 mhz. calculate the energy of the frequency at which they are broadcasting.
660.62 × 10⁻²⁵ Joule energy of radio wave at which radio station is broadcast.
We use the relationship between the energy of photons and the plank constant. The constant shows how the energy and frequency of a photon are related. (E = hν)
E = Energy of photon, h = plank constant, ν = frequency of wave
now, ν = 99.7 mhz h = 6.62607015×10−34 joule-hz−1
Then, E = 99.7 × 10⁹ hz × 6.62607015 × 10⁻³⁴ joule-hz−1
= 660.62 × 10⁻²⁵ joule
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Explain your thinking. What definition, rule, or reasoning did you use to decide
whether something is a solid?
Answer:
Explanation:
A Solid is one of the three main states of matter. By definition a solid is something whose molecules are so densely packed together that it allows it to keep its shape. Therefore if the item has a definite shape that does not change on it's own it is a solid. As opposed to a liquid which will take and fill the shape of it's container.
A helicopter is hovering at an altitude of 1km when a panel from its underside breaks loose and plummets to the ground. The mass of the panel is 15kg and it its the ground with a speed of 45m/s. How much mechanical energy was dissipated by air resistance during the panel’s descent?
Answer:
The right answer is "131812.5".
Explanation:
The given values are:
Mass,
m = 15 kg
Velocity,
v = 45 m/s
As we know,
⇒ \(PE_1=mgh\)
On putting the values, we get
⇒ \(=15\times 9.8\times 1000\)
⇒ \(=147000 \ J\)
According to the question,
\(KE_1=0 \ J\)
\(PE_f=0 \ J\)
⇒ \(KE_f=\frac{1}{2}\times 15\times 45^2\)
⇒ \(=\frac{1}{2}\times 15\times 2025\)
⇒ \(=15187.5 \ J\)
hence,
⇒ \(PE_i=KE_f+W_{air}\)
or,
⇒ \(W_{air} = PE_i-KE_f\)
⇒ \(=147000-15137.5\)
⇒ \(=131812.5 \ J\)
The battery has a voltage of 12V. R1 = R2 = 100Ω.
I1 = A I2 = A IT =
Word Bank:
0.360.240.830.120.060.120.006
Answer:
FOR PARALLEL CONNECTIONI1 = 0.12AI2 = 0.12A IT =0.24AFOR SERIES CONNECTIONI1 = I2 = 0.06AIT =0.06AExplanation:
According to ohms law, V =ITRt
V is the supply voltage
IT is the total current flowing in the circuit
Rt is the total equivalent resistance
Given R1= R2= 100Ω
V= 12V
FOR PARALLEL CONNECTION;
To calculate the total current IT in the battery, we need to calculate the total equivalent resistance RT first. For a parallel connected circuit, the equivalent resistance in the circuit is the sum of the reciprocal of its individual resistances as shown;
\(\frac{1}{RT} = \frac{1}{100} + \frac{1}{100}\\\frac{1}{RT} = \frac{2}{100} \\\frac{RT}{1} = \frac{100}{2}\\\)
RT = 50Ω
from the equation above;
IT = V/RT
IT = 12/50
IT = 0.24A
Note that in a parallel connected circuit, different current flows through the resistances but the same voltage is across them.
IT = I1+I2
For current in resistance R1;
I1 = V/R1
I1 = 12/100
I1 = 0.12A
Since both resitance are the same, they will share the total current equally. Therefore I2 = 0.12A
FOR SERIES CONNECTION;
The total equivalent resistance in the circuit will be the sum of their individual resistances.
\(RT = R1+ R2\)
RT = 100Ω+100Ω
RT = 200Ω
IT = V/RT
IT = 12/200
IT = 0.06A
Since the resistances are connected in series, the same current will flow through them but different voltages. The total current flowing in the circuit will be the same current flowing through the resistors.
Therefore I1 = I2 = 0.06A
what does waining mean?
Answer:
(of the moon) have a progressively smaller part of its visible surface illuminated, so that it appears to decrease in size.
Explanation:
each drawing shows three points along the path of a projectile, one on its way up, one at the top, and one on its way down. the launch point is on the left in each drawing. which drawing correctly represents the acceleration a of the projectile at these three points?
The acceleration of the particle is constant \((a=9.8 m/sec^2)\), and it is vertically downward. Therefore, the correct option is diagram no 4.
In the case of a projectile launched into the air, the acceleration acts vertically and is influenced by gravity.
Let's analyze the three points along the path of the projectile:
1. On its way up: At this point, the projectile is moving upwards, and gravity is acting in the downward direction. Therefore, the acceleration of the projectile at this point is directed downward to oppose the upward motion and eventually bring the projectile to a stop.
2. At the top: The projectile reaches its maximum height and momentarily comes to a stop before starting to fall back down. At this point, the acceleration is solely due to gravity, and it acts vertically downward. The acceleration at the top of the projectile's path is directed downward.
3. On its way down: The projectile is now moving downward, and gravity continues to act in the downward direction. The acceleration at this point is again directed downward, assisting the downward motion of the projectile.
Considering these factors, the drawing that correctly represents the acceleration of the projectile at these three points should show the acceleration vector pointing vertically downward in all three positions.
This represents the consistent influence of gravity on the projectile throughout its motion.
Therefore, the correct option is diagram no 4. The acceleration of the particle is constant \((a=9.8 m/sec^2)\), and it is vertically downward.
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What’s I called when a HORIZONTAL VELOCITY DIVIDED BY VELOCITY.
I need help with the Reasoning to support my claim please.