Sure, here's an example implementation of the ewma function in Python:
import numpy as np
def ewma(data, alpha):
"""
Calculate the exponential weighted moving average of a given data array.
Args:
- data: a 1D numpy array containing the data points to be averaged.
- alpha: a float between 0 and 1 representing the degree of weighting decrease.
A higher value of alpha gives more weight to recent data points.
Returns:
- ewma: a 1D numpy array containing the exponentially weighted moving average of the input data.
"""
# Initialize variables
ewma = np.zeros_like(data)
ewma[0] = data[0]
for i in range(1, len(data)):
ewma[i] = alpha * data[i] + (1 - alpha) * ewma[i-1]
return ewma
To use this function, you can call it with your data array and the desired alpha value, like so:
data = np.array([1, 2, 3, 4, 5])
alpha = 0.5
result = ewma(data, alpha)
print(result)
This will output the exponential weighted moving average of the data array with the specified alpha value. You can change the value of alpha and the input data to generate different results.
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What is the current flowing through this circuit?
A) 1.3 A
B) 0.15 A
C) 15 A
D) 6.7 A
Answer:
6.7A
Explanation:
Firstly find out the net resistance,
in parallel combination of resistors,
R = R1 * R2 / R1 + R2
R = 6*2/6+2 Ω
R = 12/8Ω
R = 1.5 Ω
Now use Ohm's law,
v = iR
10 = i * 1.5
i = 10/1.5 A
i = 6.7 A
How much work is required to lift a 7.1-kg backpack 1.2 m to put it on?
Answer:
it requires approximately 83.5812 Joules of work to lift the 7.1-kg backpack 1.2 m.
Explanation:
The work done to lift the backpack can be calculated using the formula:
Work = Force x Distance x cos(theta)
where Force is the weight of the backpack, Distance is the height it is lifted, and theta is the angle between the direction of the force and the direction of the displacement.
The weight of the backpack can be calculated as:
Weight = mass x gravity
where mass is 7.1 kg and gravity is the acceleration due to gravity, which is approximately 9.81 m/s^2.
Weight = 7.1 kg x 9.81 m/s^2
Weight = 69.651 N
The distance the backpack is lifted is 1.2 m.
The angle between the direction of the force and the direction of the displacement is 0 degrees, since the force and displacement are in the same direction.
Therefore, the work done to lift the backpack is:
Work = 69.651 N x 1.2 m x cos(0°)
Work = 83.5812 Joules (J)
So, it requires approximately 83.5812 Joules of work to lift the 7.1-kg backpack 1.2 m.
The work required to lift a 7.1-kg backpack 1.2 meters is approximately 83.5 Joules. This is calculated using the physics equation for work, which is Work = Force x Distance, where Force is the weight of the object.
Explanation:In physics, the work done to lift an object is calculated by the equation Work = Force x Distance. The force required to lift an object is its weight, which is calculated by multiplying its mass by the gravitational acceleration (the approximate value is 9.8 m/s² on Earth).
So, to calculate the work done in lifting a 7.1-kg backpack 1.2 m, we would first calculate the force (or weight) required to lift the backpack: Force = Mass x Gravitational acceleration = 7.1 kg x 9.8 m/s² = 69.58 N.
Then we multiply this force by the distance the backpack is lifted: Work = Force x Distance = 69.58 N x 1.2 m = 83.5 Joules.
So the work required to lift the backpack is approximately 83.5 Joules.
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34) two points on a transverse wave that have the same magnitude of displacement from equilibrium are in phase if the points also have the
If two transverse wave points which have the identical magnitude of departure from equilibrium share the same orientation of departure and motion, the points are said to be in phase.
Describe the magnitude.In theoretical particle physics, magnitude is just "distance or quantity." It demonstrates the size, direction, and speed of an item in both relative and absolute terms. It's a term for describing the size or breadth of something.
Is magnitude a component of direction?Vectors contain quantities that include both both magnitude and direction. The terms force, momentum, displacement, and velocity are all examples of vector quantities. We refer to something like a vector's length as its absolute value. Only if the measured values of two vectors are equal can we draw the conclusion that they are similar.
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Two protons are moving directly toward one another. When they are very far apart, their initial speeds are 2.00x10^4 m/s. What is the distance of closest approach?
The distance of closest approach is 6.9 x 10⁻¹⁰ m.
What is the distance of closest approach?
The distance of closest approach between two protons can be determined using the law of conservation of energy.
Since the protons are moving directly toward one another, the total energy of the system is the sum of their kinetic energy and their potential energy.
rf = ( kq² ) / (1/2mv²)
where;
k is coulomb's constantq is the charge of the protonv is the speed of the protonrf = ( 9 x 10⁹ x (1.6 x 10⁻¹⁹)² ) / (0.5 x 1.67 x 10⁻²⁷ x ( 2 x 10⁴)²)
rf = 6.9 x 10⁻¹⁰ m
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A DC circuit with is driven by 12 volt supply and a DC load of 200 Ohms. Calculate I (Amps) and P (Watts). a. 720 A,60 W b. 2.4 mA,28.8 mW c. 60 mA,720 mW d. 12 A,200 W
A DC circuit with is driven by 12 volt supply and a DC load of 200 Ohms. 60 mA, 720 mW, so option (c) is correct.
What is circuit ?
A circuit is a closed circuit in which electrons can move. No electrons will move unless the circuit is complete, that is, it makes a complete circuit around the electrical source.
What is volt ?The volt is a unit of electrical potential, potential difference, and electromotive force in the metre-kilogram-second (SI) system. It is equal to the difference in potential between two conductor points carrying one ampere of current when there is a one-watt power loss between the points.
Voltage current x Resistance
V=IR
Putting the the given values in the above equations So,
12 = I x 200
Or
I = 12/200
I = 0.06A (here A stands for ampere which is unit of current) And we know that 1A = 10 mA (mA stands for milliampere} So
I = 0.06A = 0.06 x 10 mA = 60mA
I = 60mA [Answer]
Here we use the formula P = V x I, which is describe as follows. Power = Voltage x current
we put the values in the above equation
P = 12 x 60
P = 720mW [here mW is stands for milli watt which is unit of power} P=720mW [Answer]
Therefore, A DC circuit with is driven by 12 volt supply and a DC load of 200 Ohms. 60 mA, 720 mW, so option (c) is correct.
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two waves having the same amplitude and frequency are traveling in the same medium. maximum destructive interference will occur when the phase difference between the waves is
If two waves having the same amplitude and frequency are traveling in the same medium. maximum destructive interference will occur when the phase difference between the waves is 180⁰.
The resultant amplitude of two waves with the same amplitude and frequency that collide while traveling in the same direction depends on the phase difference.
While there is no phase difference between two nodes, there is a 180⁰ phase variation between two antinodes.
The formula for the resulting amplitude caused by the superposition of two waves with a phase difference is:
A² = A1² + A2² + 2A1A2 cos ϕ
ϕ = 2π/3
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The net force on a box is in the positive x direction. Which of the following statements best describes the motion of the box? Its velocity is parallel to the x axis Neither its velocity or its acceleration need be parallel to the x axis Both its velocity and its acceleration are parallel to the x axis Its acceleration parallel to the x axis
The statement "Both its velocity and its acceleration are parallel to the x axis" best describes the motion of the box when the net force on the box is in the positive x direction.
If a net force acts on an object in the positive x direction, the object experiences an acceleration in the positive x direction. According to Newton's second law of motion, the acceleration of an object is proportional to the net force acting on it and inversely proportional to its mass. As a result, the object will move in the positive x direction with a continually increasing velocity. Therefore, both the velocity and acceleration of the box are parallel to the x axis.
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The activation energy, Ea, for a particular reaction is 37.8 kJ/mol. If the rate constant at 280 K is 0.178 M/s, what is the value of the rate constant at 457 K? (R = 8.314 J/mol K)
The value of the rate constant at 457 K is 0.478 M/s.
The rate constant, k, at a given temperature can be related to the activation energy, Ea, and the gas constant, R, through the Arrhenius equation:
[tex]k = Ae^{(-Ea/RT)}[/tex]
where A is the pre-exponential factor and T is the temperature in Kelvin.
Given k1 = 0.178 M/s at T1 = 280 K, and Ea = 37.8 kJ/mol, we can calculate the rate constant, k2, at T2 = 457 K as:
k2 = A * [tex]e^{(-Ea/R * T2)}[/tex] = 0.178 * [tex]e^{(-37.8 kJ/mol / (8.314 J/mol K) * 457 K)}[/tex] = 0.478 M/s.
This means that the reaction will proceed faster at 457 K than it does at 280 K, due to the increase in temperature leading to an increase in the rate constant, k.
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1.If you looked back at Earth from the moon, what phase would Earth have when the moon was full? New? First quarter? Waxing crescent?
The phase that the Earth would have when the Moon was full if we looked from the moon would be new phase.
The Moon and Earth are both always partially lit by the Sun. However, from either world, you can see varied portions of that lighted half - or different phases of the Earth or moon - at any given time. The phases usually follow a pattern in which they are inverted relative or reversed to one another.
Any moon resident would see a narrow crescent Earth when the moon is nearly full. The moon, Earth, and sun form a line with Earth in the middle when we observe a full moon. The Earth would then be completely obscured by the sun's brightness, making it invisible to those on the moon. Therefore, the phase that the Earth would have looked from the Moon would be the new phase because the opposite of a full moon phase is a new moon.
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which of the following spectrums are used by wireless networks? [choose all that apply] 2.4 ghz 5 ghz 3.6 ghz 1.2 ghz
The 2.4 to 5 GHz band is used by a variety of wireless networks. Also, the speed that each sort of wireless network offers varies.
What is the spectrums are used by wireless networks?Seconds per meter Miles per hour, kilometres per hour, and meters per second (m/s) are the most popular speed measurement units (mph). An object's speed is the distance it travels in a predetermined length of time. The speed equation is defined as speed = distance x time.
If you know how far an object travels in a certain amount of time, you can calculate its speed. For instance, if a car travels 70 miles in an hour, it is going at a speed of 70 miles per hour.
Depending on where and how you use your Wi-Fi connection the most, you should choose between 2.4 GHz and 5 GHz.
Therefore, while a 5 GHz connection offers greater speeds at closer distances, a 2.4 GHz connection travels farther at slower speeds.
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What are the major energy transformations that occur between when energy starts from a primary energy source, becomes a piece of wood, which is then burned in a fire?
Sunlight to chemistry energy conversion, energy transfer as from sun to plants, kinetic energy is created by converting thermal energy. when wood is burned, mechanical energy is converted to thermal energy.
What are the primary six energy forms?Chemical, electrical, infrared, mechanical, thermal, et nuclear energy are the six main types of energy. Different research may focus on other forms, such as electric, acoustic, electromagnetic, and some others.
What is an indication of an energy revolution?Energy transition describes the change in the global energy industry away from fossil-based methods of hydropower, such as oil, natural gas, and coal, and toward rechargeable batteries with renewable sources of electricity like wind and solar.
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To construct an oxygen-hemoglobin dissociation curve in lab, you will use the spectrophotometer to measure the absorbance of hemoglobin samples at which of the following wavelengths?525nm550nm620nm660nm
The 660 nm wavelength light is absorbed more by the hemoglobin and can be measured using the spectrophotometer.
The strength with which oxygen binds to hemoglobin is affected by several factors and can be expressed as a left or right shift in the oxygen dissociation curve. Shifting the curve to the right indicates that hemoglobin has a reduced affinity for oxygen, so oxygen is actively pumped out. Oxygen-hemoglobin saturation/dissociation curves are affected by pH, temperature, and 2,3-bisphosphoglycerate (BPG). The oxygen dissociation curve is a graph with oxygen partial pressure on the horizontal axis and oxygen saturation on the vertical axis, showing an S-shaped relationship. Oxygen and carbon dioxide are carried in the blood as a result of changes in blood pressure
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In an experiment a negatively charged balloon (balloon X) is repelled by another charged balloon Y. However, an object Z is attracted to balloon Y. Which of the following can be the charge on Z? Select two answers. a. negative b. positive c. neutral d. cannot be determined
In this scenario, if balloon X is negatively charged and is repelled by balloon Y, then it is most likely that balloon Y is positively charged. If an object Z is attracted to balloon Y, then it is most likely that object Z is either negatively charged or neutral. Therefore, the charge on object Z could be either option a or c, which are negative or neutral respectively.
In the given scenario in this question, balloon X has a negative charge and is repelled by balloon Y. This suggests that balloon Y has a positive charge. The attraction of object Z to balloon Y indicates that it is either negatively charged or neutral.
Therefore, the charge on object Z is either negative or neutral, but not positive or indeterminate. This is due to the fundamental principle of electrical charges, where opposite charges attract each other and similar charges repel each other.
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a scooter starts from rest and move's with a constant acceleration of 1 .2 metres squared determine the velocity, after it has traveled for 60 meters
It is possible to write - v = u + at, v = 0 +1.2 x 60, v = 72 m/s by using the first motion equation.
How do velocity and speed differ?Velocity is the pace and direction of such an item's movement, whereas pace is the time rate which an entity is travelling along a route.
A first equation of movement is given by Ms. Reitman's scooter velocity,
which accelerates at a rate of 1.2 m/s2 from rest.
The formula is: [a] = 2 m/s2 [t] = 60 s.
Thus, It is possible to write - v = u + at, v = 0 +1.2 x 60, v = 72 m/s by using the first motion equation.
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In compressing the spring in a toy dart gun, 4 J of work is done. When the gun is fired, the spring gives its potential energy to a dart with a mass of 0.02 kg. a. What is the dart's kinetic energy as it leaves the gun?
b. What is the dart's speed?
c. The ceiling of an arena is 19.8 m above the floor. What is the minimum speed that a thrown ball would have to have to reach the ceiling?
The kinetic energy of the dart as it leaves the gun is 4 Joules, the dart speed is 10 m/s, and the minimum speed that a thrown ball would have to reach the ceiling is 19.8 m/s.
The kinetic energy of the dart can be calculated using the formula:
KE = PE
where PE is the potential energy stored in the spring, and KE is the kinetic energy of the dart.
Since 4 J of work was done in compressing the spring, the potential energy stored in the spring is 4 J. The kinetic energy of the dart can then be calculated as:
KE = PE = 4 J.
Therefore the kinetic energy of the dart as it leaves the gun is 4 Joules.
The speed of the dart can be calculated using the equation of kinetic energy:
KE = 0.5 × m × v²
where m is the mass of the dart and v is its speed. Substituting the values, we get:
4 J = 0.5 × 0.02 kg × v²
v² = (4 J) / (0.5 × 0.02 kg)
v = √((4 J) / (0.5 × 0.02 kg))
v = √400
v = 20 m/s.
Therefore, the speed of the dart is 20 m/s.
The minimum speed that a ball would have to have to reach the ceiling can be calculated using the equation of vertical motion:
v² = v_0² + 2 × a × h
where v is the final speed, v_0 is the initial speed (assumed to be 0), a is the acceleration due to gravity (9.8 m/s²), and h is the height of the ceiling (19.8 m).
v = √(2 × 9.8 × 19.8)
v = √(394.4)
v = 19.8 m/s.
So, the minimum speed that a ball would have to have to reach the ceiling is 19.8 m/s.
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What is the net force (in N) of a 3.00 N force and an 8.00 N force acting on an object for each of the following conditions?
b) The forces act in the same direction.
manually calculating the heat input or arc energy supplied to produce a weld is a method that can be used for which of the following? A.All of these
B. CC/CV
C. Pulse
D. AC (Alternating current)
Manually calculating the heat input or arc energy supplied to produce a weld is a method that can be used for CC/CV.
How do heat input and weld speed relate to one another?
As voltage, current, wire feed rate, or a combination of these, or all three, increase, more heat is applied to the weld metal. With an increase in welding speed, the heat input drops. As the heat input increases, the rate of cooling of the weldment reduces.
Before the process efficiency is taken into account, arc energy is the energy that the welding arc supplies to the workpiece. The following equation can be used to compute it: where: The voltage, expressed in volts, is V. I represents the used current in amperes.
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A ball is dropped from the top of a 93-m-high building. What speed does the ball have in falling 3.3 s?
Answer:
32.34 m/s
Explanation:
refer to the attachment
hope this helps
In an experiment in space, one proton is held fixed
and another proton is released from rest a distance
of 2.00 mm away.
What is the initial acceleration of the proton after it is released?
The proton's initial acceleration after being emitted is discovered to be 3.449 x 104 m/s².
When does a proton leave the body?because there is no magnetic force acting on a charged particle while it is at rest. The proton won't move or experience electric force unless it is forced out of its resting place. The direction of application of the electric force will match that of the acceleration.
One coulomb weighs how much?In coulombs, the SI's measuring unit for electric charge, it is determined how much charge is transported by a flow of one amp for one second. The ability of a chemical to cause electrical and magnetic effects could potentially be one of its properties.
According to the given information:F = Kq1 q2 / r²
Charge of a proton = 1.6022 x 10⁻¹⁹ c
Mass of a proton = 1.6726 x 10⁻²⁷ kg
r= 2mm => 2 x 10⁻³m
k= 8.99 × 10⁹ N ⋅ m² /C².
F= 8.99 × 10⁹ x (1.6022 x 10⁻¹⁹)² / (2 x 10⁻³)²
=> 5.769 x 10⁻²³N
F = M x a
5.769 x 10⁻²³ = 1.6726 x 10⁻²⁷ x a
=> Acceleration = 3.449 x 10⁴m/s²
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What is the peak wavelength of light coming from a star with a temperature of 5300 K?
(Submit your answer in nanometers. Remember 1nm = 10-9 m)
The peak wavelength of light coming from a star with a temperature of 5300 K is 2.0 x 10⁻⁷ m.
What is wavelength?Wavelength is a measure of the distance between two consecutive wave crests or troughs and is usually defined as the length of one full cycle of a wave. Wavelengths are typically measured in meters, centimeters, or nanometers (10-9 meters). Wavelength is inversely related to frequency, meaning that higher frequency waves have shorter wavelengths.
The wavelength of each energy level can be calculated using the equation λ = hc/E, where h is Planck's constant, c is the speed of light, and E is the energy level in electron volts. Using this equation, the four wavelengths of the emission spectrum are calculated as follows:
0.0 eV = 0.0 m, 1.5 eV
= 8.0 x 10⁻⁷ m, 3.0 eV
= 4.0 x 10⁻⁷ m
and 6.0 eV =
2.0 x 10⁻⁷ m.
Thus, the peak wavelength of light coming from a star with a temperature of 5300 K is 2.0 x 10⁻⁷ m.
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If the acceleration of an object is always directed perpendicular to its velocity, which of the following is true _____.a. this situation would not be physically possibleb. the object is slowing downc. the object is speeding upd. the object is turning
If the acceleration of an object is always directed perpendicular to its velocity, then the statement (the object is turning) is true due to the fact that the velocity vector of the object is always heading in a different direction.
The moving object is being accelerated in the direction of the center of rotation due to a centripetal force acting in that direction.
According to Newton's laws of motion, the path that the object would take if it did not experience this acceleration is a straight line.
An object's acceleration can be defined as the rate at which its velocity changes in relation to the passage of time. Accelerations are vector quantities. The orientation of the net force that is acting on an item is what determines the orientation of the acceleration the object is experiencing.
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The oxygen molecule (O2) may be regarded as two masses connected by a spring. In vibrational motion, each oxygen atom alternately approaches, then moves away from the center of mass of the system. If each oxygen atom of mass m = 2.67 ´ 10-26 kg has a vibrational energy of 1.6 ´ 10-21 J and the effective spring constant is 50 N/m, then what is the amplitude of oscillation of each oxygen atom?
Answer:
2.5 × 10^-11 m
Explanation:
The amplitude of oscillation for a simple harmonic oscillator is given by the equation:
A = √(2E / k), where E is the vibrational energy of each oxygen atom and k is the effective spring constant.
Substituting the given values:
A = √(2 * 1.6 × 10^-21 J / 50 N/m)
A = √(3.2 × 10^-21 J / 50 N/m)
A = √(6.4 × 10^-23 m^2 kg / s^2)
A = 2.5 × 10^-11 m
To find the 65th percentile, first find the location in the ordered data this value will occur. Recalling that n = 8, find 165: sp p (n + 1) 100 L65 (8 + 1) 100
The 65th percentile can be found by using the formula: p(n + 1) = 65/100 * (8 + 1) = 65/100 * 9 = 5.85
So, the location of the 65th percentile in the ordered data set is approximately 5.85. This means that approximately 5 of the 8 values are below the 65th percentile, and the other 3 values are above it. To get an exact value, you would need to interpolate between the 5th and 6th values in the ordered data set.
Interpolation is a method of estimating values between two known values. To interpolate the value of the 65th percentile, you can use the following formula: value = (5.85 - 5) / (6 - 5) * (value at position 6 - value at position 5) + value at position 5
In this formula, "value at position 5" refers to the 5th value in the ordered data set, and "value at position 6" refers to the 6th value in the ordered data set. By substituting these values into the formula, you can find an estimate for the value of the 65th percentile.
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The acceleration due to gravity at a given location is affected in what way as that locations distance from the planets center is doubled
The relation between, the acceleration due to gravity at a given location and when that locations distance from the planets center is doubled, in that case acceleration due to gravity will be 4 times less than at given location.
What is acceleration ?Acceleration is a vector quantity that describes the rate at which an object changes its velocity. It is the rate at which the velocity of an object changes in magnitude or direction, or both. In other words, it tells us how quickly an object is speeding up or slowing down. Acceleration has units of meter per second squared (m/s²) and its direction is the same as the direction of the change in velocity.
The acceleration due to gravity decreases as the distance from the center of the planet is doubled.
The formula for gravitational acceleration is given by:
g = G x M / r^2,
where G is the gravitational constant, M is the mass of the planet, and r is the distance from the center of the planet.
As r doubles, the value of g decreases by a factor of 4.
Hence, the acceleration due to gravity will 4 times less.
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much of tibet lies at altitudes over 18,000 feet where the pressure is about 500 mb. at such altitudes, the tibetans are above roughly
A. 10% of the air molecules in the atmosphere
B. 25% of the air molecules in the atmosphere
C. 50% of the air molecules in the atmosphere
D. 75% of the air molecules in the atmosphere
The air molecules are at least 75% of the air molecules at sea level.
What is air molecules?Air molecules are microscopic particles of matter that make up the atmosphere. They are composed of two atoms of oxygen and two atoms of nitrogen, which are held together by covalent bonds.
The atmospheric pressure at sea level is about 1,000 mb, which is equivalent to the weight of the air column over a given area. Since the atmospheric pressure in Tibet is 500 mb, this means that the air molecules at this altitude make up about half of the air molecules at sea level. This means that at 18,000 feet, the air molecules are at least 75% of the air molecules at sea level.
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bernouli’s equation is only for fluids that have :
A- low viscosity, incompressible with turbulent flow
B- high viscosity, compressible and streamline flow
C- low viscosity, compressible and turbulent flow
D- low viscosity, incompressible and streamline flow
E- none of the above
Answer:Bernoulli developed his principle from observations on liquids, and Bernoulli's equation is valid for ideal fluids: those that are incompressible, irrotational, inviscid, and subjected to conservative forces.
Explanation:
A car traveling at 20 m/s reaches 60 m/s in 4 seconds traveling in a straight line. The car has an average acceleration of _______ m/s2.
The car has an average acceleration of 10 m/s²
The rate at which the velocity changes over time is referred to as the average acceleration. To determine the average acceleration, we take the change in velocity and divide it by the amount of time that has passed. Average acceleration is calculated by the following formula:
Δv ÷ Δt
where:
Δv = the change in velocity
= 60 m/s - 20 m/s
= 40 m/s
Δt = the total time over the velocity is changing
= 4 seconds
Thus, the average acceleration of the car would be:
Average acceleration = 40 m/s ÷ 4 s
= 10 m/s²
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An automobile tire has a volume of 0.0185 m 3 3 . At a temperature of 294 K the pressure in the tire is 212 kPa. How many moles of air must be pumped into the tire to increase its pressure to 252 kPa, given that the temperature and volume of the tire remain constant?
The number of moles of the air will be 1.6.
What is an ideal gas equation?The equation of state for a fictitious ideal gas is known as the ideal gas law, also known as the general gas equation. Although it has some restrictions, it is a good approximation of the behaviour of many gases under various circumstances.
Given that an automobile tire has a volume of 0.0185 m ³. At a temperature of 294 K, the pressure in the tire is 212 kPa.
Calculate the volume at pressure P₂,
P₁V₁ = P₂V₂
V₂ = ( P₁V₁ ) / P₂
V₂ = ( 212 x 0.0185 ) / 252
V₂ = 0.0155 m³
The number of the moles will be calculated as:-
PV = nRT
n = ( P₂V₂ / RT)
n = ( 252 x 0.0155 x 1000 ) / ( 8.3145 x 294 )
n = 1.6 moles
Therefore, there will be 1.6 moles in the air.
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is the vertical component of velocity ever zero? if so, where?
a. yes, it is zero at points a and e. b. yes, it is zero at all points.
c. yes, it is zero at point c. d. no, it is never zer
c. Yes, it is zero at point c. The vertical velocity component can become zero when the projectile reaches its maximum altitude.
At the highest point of the projectile, its vertical component is instantaneous before it changes direction and the object begins to fall under the influence of gravity.
What Is that projectile motionProjectile motion is motion with a curved path in the form of a parabola curve. Due to this curved trajectory, the projectile's motion is included in two-dimensional motion. The meaning of two-dimensional motion is that the motion of objects can be projected in horizontal and vertical directions.
In physics, in the horizontal direction, there is no force affecting it so that the object moves at a constant speed. Conversely, in the vertical direction, the gravitational force pulls the object down so that the object moves at a constant speed.
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Prove that if P and Q are two longest paths in a connected graph then P and Q have at least one vertex in common. (b) Prove or disprove: Let G be connected graph of diameter k If P and Q are two geodesics of length k in vertex in G, then P and Q have at least one common.
If P and Q are two longest paths in a connected graph then P and Q must have at least one vertex in common.
Let P and Q be two longest paths in a connected graph G. Assume for contradiction that P and Q have no vertices in common. Without loss of generality, let P start from vertex u and end at vertex v, and let Q start from vertex w and end at vertex x.
Since G is connected, there exists a path between u and w and a path between v and x. Let's consider the path between u and w first. By definition, both P and the path between u and w have u as a common vertex. If the path between u and w is longer than P, then it contradicts that P is the longest path. Hence, the path between u and w is shorter than P.
Similarly, the path between v and x must also be shorter than Q.
So, we have two paths of length less than the length of P and Q connecting vertices that are not on P or Q, which means that the concatenation of these two paths along with P and Q form a cycle. The length of this cycle must be longer than P and Q, which again contradicts the assumption that P and Q are the longest paths in G.
(b) Disprove: The statement is false. Consider a cycle of length k in the graph G. The two diametrically opposite vertices are two geodesics of length k, but they do not have any common vertices. This shows that the statement "If P and Q are two geodesics of length k in vertex in G, then P and Q have at least one common" is not always true.
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