(ii) The net displacement at a point on the string where the pulses cross is 0.2 m.
The term "displacement" refers to a shift in an object's position. It has a magnitude and a direction, making it a vector quantity. An arrow pointing from the starting point to the finishing point serves as its symbol.
A string that is connected to a post at one end is used to transmit a sequence of pulses, each measuring 0.1 meters in amplitude.
At the post, the pulses are reflected and return along the string without losing any of their amplitude.
Now, let's say the ends are free.
There is no inversion on reflection if the end is free. The amplitude at their intersection is 2A.
Now, since A = 0.1 m
Then, 2A = 2(0.1) = 0.2 m
As a result, the net displacement at the string's intersection of two pulses is 0.2 m.
The correct option is (c).
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WHAT IS NUCLEAR FISSION
PLEASE ANSWER QUICK
PLEASE HELP HURRY a penny dropped out a window reaches a speed of 35 m/s. how far did it fall? initial velocity is 0 m/s and gravity is 9.8 m/s
Answer:
use v²=u²+2as
v=35
u=0
a=9.8
35²=0²+2*9.8s
1225/2=9.8s
s = 62.5m
answer=62.5m
Answer:
The height from which the coin fell:
H = 63 m
Explanation:
Given:
V₀ = 0 m/s
V = 35 m/s
g = 9.8 m/c²
___________
H - ?
The height from which the coin fell is calculated by the formula:
H = (V² - V₀²) / (2·g)
H = (35² - 0²) / (2·9.8) ≈ 63 m
A car slows down from +32 m/s to +8 m/s in 4s. Calculate the acceleration
If a car slows down from +32 meters / seconds to +8 meters / seconds in 4 seconds, then the acceleration of the car would be -6 meters / second².
What is acceleration?The rate of change of the velocity with respect to time is known as the acceleration of the object.
We can calculate the acceleration of the car by using the first equation of motion,
v = u +at
8= 32 + a×4
a =8-32 / 4
a = -6 meters / second²
Thus, the acceleration of the car would be -6 meters / second².
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when charge 2 is 3.0 m away from charge 1, the strength of the electric force on charge 2 by charge 1 is 0.80 n. if instead, charge 2 were 6.0 m away from charge 1, what would be the strength of the electric force on charge 2 by charge 1 in that case?
The strength of the electrostatic force is inversely proportional to the square of the distance
between the charges. If the distance is doubled, the force is 1/4.
The new force is 0.80/4 = 0.20 N.
What is electrostatic force?Electrostatic force is the attractive or repulsive force that exists between two charged particles. Also known as Coulomb interaction or Coulomb force. For example, the electrostatic forces between the protons and electrons of an atom are responsible for the stability of the atom.
The force acting along a line joining two point charges is directly proportional to the product of the two charges and inversely proportional to the square of the distance between them.
[tex]F=K |\frac{q_{1} q_{2}}{r^{2} } |[/tex]
In the above formula, k is arbitrary and can be chosen to be any positive value. Since k is a constant, I chose to give the value of k as follows:
Therefore, with q₁ and q₂ values of 1 and r = 1 (two charges with 1 Coulomb charge each at a distance of 1 m), we get F = [tex]9 \times 10^9[/tex] N. In the above equation, ε₀ is given as the permittivity of free space and its value in SI units is [tex]8.854\times10^{-12} C^{2} N^{-1} m^{-2}[/tex].
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what does it mean by the term self demagnetization.
Answer:
Self demagnetization means when magnets' poles are free (suspended) for too long, their magnetic attraction becomes weaker and thus, self demagnetizes.
What function does large volumes of moving water have in generating electricity
Impoundment or dams are used to collect the water to enhance the amount of running water. Gravity is used to direct water down a pen stock pipe from a hole in the dam. The turbine is spun by the flowing water, and this rotation of the magnets inside the generator produces power.
What is Hydroelectric Energy?Hydroelectric energy, also known as hydroelectric power or hydroelectricity, is a type of energy that uses the force of moving water to produce electricity, such as water running down a waterfall. This force has been utilized by people for ages. Greeks have been grinding wheat into flour for over 2,000 years by using flowing water to turn their mill's wheel.
The majority of hydroelectric power plants feature a water reservoir, a gate or valve to regulate the amount of water that flows out of the reservoir, and an outlet or location where the water ends up after flowing downstream. Just before water rushes over the top of a dam or cascades down a hill, it gains potential energy. Water flowing downhill changes potential energy into kinetic energy. When a turbine's blades are turned by water, electricity is produced and sent to the power plant's users.
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Two boxes are at rest…
The pair of forces include;
Normal force of mass 1 on mass 2(F₁₂) and the reaction of mass 2 on mass 1 (F₂₁)
Normal force of mass 2 on the table A (F₂A) and the reaction of the table on the mass 2 (FA2).
What is normal force?
The normal force is an everyday force that is felt when a surface pushes against an object that is placed on that surface.
Normal force acts in opposite direction to the weight of the object.
Based on Newton's third law of motion, for every action, there is an equal and opposite reaction.
The downward force exerted on the table, is equal to the reaction of the table on the masses.
The pair of forces acting on the masses stacked together include the following;
Normal force of mass 1 on mass 2(F₁₂) and the reaction of mass 2 on mass 1 (F₂₁)Normal force of mass 2 on the table A (F₂A) and the reaction of the table on the mass 2 (FA2).Learn more about normal forces here: https://brainly.com/question/14486416
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A generator produces 24.0V when turning at 900 rev/min. What emf does it produce when turning at 500 rev/min?
The EMF that will be produced is 13.3 V
What does EMF mean ?EMF is an acronym for Electromotive Force which can be defined as the potential difference between the terminals of a cell when it is not delivering any current in an external circuit.
Given that a generator produces 24.0V when turning at 900 rev/min. What EMF does it produce when turning at 500 rev/min?
The EMF produced by a generator is proportional to the angular speed at which the generator turns. That is, E [tex]\alpha[/tex] w
E1 = 24 VE2 = ?W1 = 900 rev/minW2 = 500 rev/minE1/E2 = W1/W2
24/E2 = 900/500
Reciprocate both side.
E2/24 = 500/900
E2 = 0.5556 x 24
E2 = 13.33 V
Therefore, the EMF that will be produced is 13.3 V
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starting from rest, a boulder rolls down a hill with constant acceleration and travels 4.00 m during the first second.
Starting from rest, a boulder rolls down a hill with constant acceleration and travels 4.00 m during the first second, 8 m first it is moving.
What is acceleration?Speed increase is the name we provide for any cycle where the speed changes. Since speed is a speed and a heading, there are simply two different ways for you to speed up: change your speed or shift your course — or change both. In mechanics, speed increase is the pace of progress of the speed of an item as for time. Speed increases are vector amounts (in that they have size and heading). The direction of an article's speed increase is given by the direction of the net power following up on that item. The extent of an articles. An item's typical speed increase throughout some undefined time frame is its adjustment of speed, partitioned by the span of the period. Numerically, Momentary speed increase, in the meantime, is the constraint of the typical speed increase over a microscopic time period. In the terms of analytics, immediate speed increase is the subsidiary of the speed vector regarding time.
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2. A bookshelf is 200 cm and 40 N weight, with supports at its ends (X and Y).
a. A book weighing 12 N is placed in the middle of the shelf. What are the upward forces at X and Y?
b. The book is moved so that it is 40 cm from B. Use moments to calculate the forces at X and Y.
Answer:
force =m×a=40=200×a=a=200-40=160m/second sguaredExplanation:
always accerelation it measures in m/second sguared.
Two waves are traveling in the same direction along a stretched string. The waves are 90.0° out of phase. Each wave has an amplitude of 4.00cm . Find the amplitude of the resultant wave.
The resultant wave is calculated by adding the magnitude of both the waves traveling in same direction.The resulting wave is of the amplitude 5.66cm or 5.66 x 10⁻²m
Let us take A be the amplitude of both the waves that are travelling
We are given that waves are moving 90 degrees out of the phase
Let the equations of the waves be
y1= Asin(ωt-kx)
y2=Acos(ωt-kx)
Since the waves are ninety degrees travelling out of phase ,
The resultant wave is
y=y1+y2
= Asin(ωt-kx) +Acos(ωt-kx)
=√2 A sin(ωt-kx+π/4)
So, we can conclude resultant wave is √2A = √2 *4 =5.66cm
=5.66* 10 ⁻²m
Hence the resultant wave is 5.66cm
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You throw a dart horizontally towards the center of a dartboard. The dart reaches the board below the center with a velocity of 1.2 E 1 m/s at an angle of 355o.
a. Determine the distance below the center of the board where the dart hits.
The distance below the center of the board where the dart hits is 0.00056 m.
Distance below the center of the board reached by the dart
The distance below the center of the board reached by the dart is calculated as follows;
v² = u² + 2gh
where;
v is the final vertical velocity of the dartu is the initial vertical velocity of the darth is the distance below the center of the board reached by the dartThe initial vertical velocity of the dart = 0
v² = 0² + 2gh
v² = 2gh
h = v² /2g
h = (v sinθ)²/2g
where;
θ is the angle of projectionh = (1.2 x sin355)²/(2 x 9.8)
h = 0.00056 m
Thus, the distance below the center of the board where the dart hits is 0.00056 m.
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M A uniformly charged ring of radius 10.0cm has a total charge of 75.0μC . Find the electric field on the axis of the ring at from the center of the ring.(d) 100 cmat from the center of the ring
The electric field on the axis of the ring at the center of the ring at 100.00cm is 6.64×〖10〗^5N/C
Where a positive charge (q) is given, always note that the charges are pointing away from the electric field. The expression used to calculate the electric field away from the center of the ring is given by the equation below,
E=(K_e×b)/(r^3×Q)
Given that;
E = Electric field
Ke = electric field constant
a = radius of the charge q from the center of the circle
Q = electric charge = 75.0μC
The radius of the charge is a = 10cm= 0.1m
Distance from the electric field is 100cm = 1m
Ke is a constant given as 8.99×〖10〗^(9) Nm^2/c^2
E=(8.99×〖10〗^(9 ) Nm^2/c^2×1)/(〖0.1〗^3×75×〖10〗^(-6) )
E=6.64×〖10〗^5N/C
Therefore, the electric field away from the center of the ring is 6.64×〖10〗^5N/C away from the center of the ring.
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A toy snake was horizontally thrown from a height of 115 m. It lands 595 m away. What is the toy snake’s initial speed? (TWO decimal places!!)
Initial speed for the toys snake will be 122.88 m/s
Given,
Height from where it has been dropped, h = 115 m
Height where the toy lands, s = 595 m
As we know that [tex]t = \sqrt{\frac{2h}{g} }[/tex]
here 'g' is acceleration due tp gravity = 9.81 m/s²
therefore [tex]t = \sqrt{\frac{2 * 115}{9.81\\ }[/tex]
[tex]t = \sqrt{23.445}[/tex]
t = 4.842 s
Now, According to the Second Equation of the Motion which relates distance with the acceleration and time, we can say that
[tex]S = ut + \frac{1}{2}at^{2}[/tex]
The toy snake is thrown horizontally, therefore acceleration acting on the toy will be zero (0).
s = 595 m
t = 4.842 s
therefore [tex]u = \frac{s}{t}[/tex]
[tex]u = \frac{595}{4.842}[/tex]
u = 122.88 m/s
The initial speed of the toy snake will be 122.88 m/s.
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When the speaker is lowered into water, does the frequency of the sound increase, decrease, or remain the same?.
Answer: it remains the same
Explanation:
the frequency of a sound wave cannot change as it crosses the water-air boundary
in a parallel circuit with four 6-ohm resistors across a 24-volt battery, what is the total voltage across resistor-three (vr3) in the circuit?
The total voltage across resistor- three in the circuit is 24V
acc to ohm's law
the electrical current flowing through any circuit is directly proportional to the voltage applied across it.
i.e. V ∝ I
V= IR
I = current
v = voltage
R = resistance (proportionality constant)
R in parallel
(1/Rp = 1/R1 + 1/R2 + 1/R3 +1/R4)
on rearranging the above equation (V=IR)
I = V/R
I = 24/6 = 4A
I is the current in each resistor.
in the parallel circuit voltage across the component is same and total current is the sum of the current flowing through each component.
the total voltage across resistor-three (vr3) in the circuit is
V= IR₃ = 4×6= 24 volt
the total voltage across the resistor three (vr3) in the circuit is 24volt.
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Why increasing the resistance in a series circuit decreases the current in the circuit?
Answer:
Explanation:
In a series curcuit Current is divided across the resistors meaning the more you add resistors the more current is taken. The formula I= V/R also makes it easier to understand. The resistance is in the denominator. The more you increase it the more the current decreases.
Keep in mind Adding more resistors in a series curcuit reduc current.
Match The Following:
1.Aristotle a. They believed the Earth to be flat
2.Kepler b. Thought that the Earth did not move
3.Egyptians c. How the planets move around the Sun
4.Ellipse d. Suggested the modern model of the Solar System
Answer:
1. A
2. D
3. B
4. C
Explanation:
1. A- Aristotle thought that the Earth was flat and that anyone who sailed off the edge of the ocean would fall of Earth, this theory of course later got disproved by Kepler and other scientists
2. D- Kepler suggested the modern model of the Solar System because after months and months of looking out the telescope and making models of the Solar System, Kepler finally made the conclusion of the official Solar System.
3. B- Egyptians thought did not move and all the planets, including the sun revolved around it. Later, Kepler disproved this theory with the modern Solar System.
4. C- This is the path that planets follow to revolve around the Sun. People first thought that planets moved in a circular motion but actually they moved in a ellipse because the Sun's gravity pulled planets closer at some parts more than others.
the more matter an object has, the more ________ it has
Answer:
Mass
No matter where an object is in the universe, the more matter an object has, the more mass it will have as well.
In the electron-transport chain, as electrons move along a series of carriers, they release energy that is used to do what?.
In the electron-transport chain, as electrons move along a series of carriers, they release energy that is used to pump protons across a membrane.
In plants and animals, the electron transport chain refers to the consistent streaming of electrons between cells where electron donors donate electrons and electron acceptors accept electrons through a redox reaction.
An electrochemical gradient is created as a result of the redox reaction and ATPs are produced.
In this chain, there are 4 major protein complexes that are transferred across the plasma membrane.
This cellular process occurs in mitochondria and is responsible for photosynthesis and cellular respiration. Its primary steps are Krebs' cycle, glycolysis, oxidative phosphorylation, and pyruvate oxidation.
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The speed of light in water is 230Mm/s. Suppose an electron is moving through water at 250 Mm/s . Does that violate the principle of relativity? Explain.
It does not violate the principle of relativity because the speed of the electron in water can explained as its relative speed with water.
What is principle of relativity?
The principle of relativity states that there is no physical way to differentiate between a body moving at a constant speed and an immobile body.
If the speed of light in water is 230Mm/s and an electron is moving through water at 250 Mm/s, it does not violate the principle of relativity because the speed of the electron in water can explained as its relative speed with water.
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suppose a radio signal travels from earth and through space at a speed of 3.0 × 108 m/s. how far into space did the signal travel during the first 20.3 minutes?
The signal will travel into the space as far as 3.654 x 10^11 meters.
What is Speed ?Speed is the distance travel by a body per time taken. Speed is a scalar quantity.
Suppose a radio signal travels from earth and through space at a speed of 3.0 × 108 m/s. how far into space did the signal travel during the first 20.3 minutes?
Speed V = 3.0 x 10^8 m/sTime t = 20.3 min x 60 = 1218 sDistance s = ?Speed V = distance / time
3 x 10^8 = s / 1218
s = 3 x 10^8 x 1218
s = 3.654 x 10^11 m
Therefore, the signal will travel into the space as far as 3.654 x 10^11 meters.
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An airplane mechanic notices that the sound from a twin-engine aircraft rapidly varies in loudness when both engines are running. What could be causing this variation from loud to soft?
Hence , the rise and fall of the amplitude of the sound causes the variation from loud to soft .
Principle of Superposition - The resultant displacement of 2 or additional waves traveling at the same time in an exceedingly medium while not moving the motion of 1 another is capable the resultant of the displacement created by the 2 or additional waves singly.The variation from loud to soft sound created by a twin-engine craft may be explained by the idea of formation of beats.
When 2 sound waves of nearly equal frequencies square measure created at the same time, then the intensity of the resultant sound created by their superposition will increase and reduces as an alternative with time. This increase and reduce within the intensity of sound square measure referred to as the development of beats.
Let us suppose that at a specific time the 2 waves of slightly totally different frequencies square measure in section, i.e. the crest of the primary wave falls on the crest of the second wave, thus at this point the resultant amplitude is most, therefore we tend to hear a louder sound. however since there's a small variation in frequencies there comes a time once the 2 waves square measure out of section, I.e. the crest of 1 wave falls on the trough of the opposite, here the resultant amplitude becomes zero and that we hear no sound. This rise and fall of amplitude continue and what we tend to hear could be a beat. Similar is that the case in an exceedingly twin-engine craft which ends within the variation of loud and soft sound.
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Read the following scenario about Greg's adventure to the symphony. Greg hasn't learned any concert etiquette.
What are the SIX mistakes that Greg makes according to Concert Etiquette 101?
What is the ONE thing that Greg does correctly (even though by accident) according to Concert Etiquette 101?
A man wearing a ball cap, who has a cold, attends a concert (let's call him Greg). After the concert begins, Greg walks through the door and takes a seat in the middle of the second row without saying a word. He frantically opens his program to find out what he has missed so far. Due to his cold, he also opens a cough drop for his cough. After the first piece (that he has heard since he arrived to the concert), he begins to clap and whistle - only to find out that nobody else is clapping with him. At the intermission, he finds a vending machine and buys a candy bar for the second half of the concert. After the concert, Greg remembers that he dropped the candy bar wrapper between the seats, and lifts his seat up to get the wrapper (at least he can put it in a trash can when he finds one - his mom always told him not to litter!).
Answer:Never stand or move around while music is being performed.
Explanation:
What happens to the period when we change the​ amplitude​ (drop point) of the pendulum? question 2 options: the period does not change when we change the amplitude of the pendulum the period increases when we change the amplitude of the pendulum the period decreases when we change the amplitude of the pendulum
When we change the amplitude of the pendulum, the period does not change when we change the amplitude of the pendulum.
What is a pendulum?A pendulum is device that could be used to show oscillatory motion. The motion of the pendulum is that of an object that is tossed from one side to another. Typically, the simple pendulum is used in most school labs to show a motion that is regular and repeating.
Now we know that the amplitude refers to the point of highest displacement of the pendulum. The point of the highest displacement would depend on the angle at which the pendulum was displaced. The period has to do with the time that it takes for a particular pendulum to complete a full cycle.
We know that the period of the pendulum does not have an effect on the amplitude of the pendulum. It then follows that; When we change the amplitude of the pendulum, the period does not change when we change the amplitude of the pendulum.
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A cubical surface surrounds a point charge q. Describe what happens to the total flux through the surface if (b) the volume of the cube is doubled
The net electric flux is not dependent on the volume of the cube and hence no change to the electric flux.
According to Gauss law, which states that the electric flux is defined as the electric field multiplied by the area of the surface in a plane perpendicular to the field.
Φ=Q ϵo
Where;
Q is enclosed charge
ϵo is the permittivity of the free space
According to the above gaussian relation, If the volume of the cube is doubled, then flux will neither be doubled or changed. It remains the same. This is because there is no direct relationship between the total flux and volume of the cube in the electric field. This means that there is no change to the electric flux.
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When a wave encounters an obstacle or a slit that is comparable in size to its wavelength, it bends around it. This characteristic is called ________.
When a wave encounters an obstacle or a slit that is comparable in size to its wavelength, it bends around it. This characteristic is called diffraction.
The term 'diffraction' was coined by an Italian scientist named Francesco Grimaldi Maria in 1660 when she first recorded accurate observations of this phenomenon. Diffraction is a wave phenomenon that describes the bending of waves when it encounters an obstacle or a slit. It is more pronounced when the obstacle or slit the wave encounters is in comparable size to its wavelength.
Diffraction occurs in all waves, including light, water waves, sound waves, electromagnetic waves like X-rays and even gravitational waves. In recent years, it has been observed that matter also demonstrates this wave-like property, but only at the atomic and subatomic level.
Diffraction can be observed in everyday life. The rainbow pattern seen on CDs and DVDs is as a result of diffraction of light. It can also be observed in ocean waves as they diffract around rocks, jetties and other obstacles.
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1) In a standard lab, students drop blocks on moving carts. A cart with a mass of 3.4 kg is moving with a velocity of 23.9 m/s. A block with a mass of 2 kg is dropped onto the moving cart. What is the velocity of the cart after the block is dropped?
A. 3.4 m/s
B. 5.4 m/s
C.15.1 m/s
D. 23.9 m/s
2) Suppose that the vertical forces on a box are balanced, but the horizontal forces are not. There is a force due west of 50 N, and a force due east of 75 N. The weight of the box is 196 N. What is the net force and the acceleration?
A. The net force is 125 N and the acceleration is 1.25 m/s/s due east.
B. The net force is 25 N and the acceleration is 500 m/sec/sec due east.
C. The net force is 25 N and the acceleration is 1.25 m/s/s due east.
D.
The net force is 3750 N and the acceleration is 500 m/sec/sec due east.
3)
A car traveling with an initial speed of 25 m/s decelerates at −5 m/s2 to a complete stop. What best approximates the distance the car travels during its deceleration?
A. 25 m
B. 63 m
C. 125 m
D. 113 m
4) A 2000-kilogram car at rest at point A accelerates at a constant rate from point A to point B in 5.0 seconds, attaining a maximum speed of 30 meters per second at point B. What is the kinetic energy of the car at point B?
A. 60000 J
B. 590000 J
C. 900000 J
D. 1800000 J
5) Which of the following situations has the greatest momentum?
A. a car that accelerates from rest to 3.0 m/s
B. a rocket that crashes back to Earth with a force of 50.0 N for 0.3 m/s
C. a boxer that hits a punching bag with a net force of 30.0 N for 0.5 s
D. a baseball hit with a net force of 10.0 N for 3.0 s
6) Two objects are moved apart so that they are separated by three times their original distance of separation. Compared to the magnitude of the original gravitational force between them, the magnitude of the new gravitational force is which of the following?
A. one-ninth the amount
B. one-third the amount
C. three times the amount
D. nine times the amount
7) Carter and Sam want to find out about the motion of cars traveling on a stretch of highway. They measure out a segment on the highway and measure the time it takes for a car to pass along that segment. Using this data, which of the following pieces of data are they collecting?
A. Average acceleration
B. Instantaneous speed
C. Average speed
D. Instantaneous acceleration
8) Tommy wants to explore how the rate of change in the speed of a marble rolling down changes at different angles. Which of the following formulas should Tommy use to compare each trial in the experiment?
A. Distance traveled/time
B. Change in velocity/change in time
C. Distance traveled in a direction/time
D. Change in displacement/time
Please Explain
The correct responses are;
1) The velocity is 15.0 m/s
2) The net force is 25 N and the acceleration is 1.25 m/s/s due east.
3) The distance covered is 63 m
4) The kinetic energy is 900000 J.
5) The greatest momentum is displayed by a baseball hit with a net force of 10.0 N for 3.0 s
6) The force is now is one-ninth of the original amount.
7) The data that Carter and Sam want to find out is the Instantaneous speed
8) The appropriate formula is change in velocity/change in time
What is the momentum?The term momentum has to do with the product of the mass and the velocity of a body.
1) We know from the principle of the conservation of momentum that the momentum before collision is the equal to the magnitude of the momentum after Collison in a closed system thus;
3.4 * 23.9 m/s = (3.4 + 2) v
v = 3.4 * 23.9 m/s / (3.4 + 2)
v = 15.0 m/s
2) Mass of the box = 196/9.8 = 20 Kg
The net force that acts on the box = 75 N - 50 N = 25 N
Acceleration = 25 N/ 20 Kg
= 1.25 m/s/s due east.
Thus, the net force is 25 N and the acceleration is 1.25 m/s/s due east.
3) v^2 = u^2 - 2as
v = 0 m/s
u^2 = 2as
s = u^2/2a
s = (25 m/s )^2/ 2 * 5 m/s2
s = 63 m
The distance covered is 63 m
4) Kinetic energy = 1/2 mv^2 = 0.5 * 2000 * (30)^2
= 900000 J
The kinetic energy is 900000 J.
5) The greatest momentum is displayed by a baseball hit with a net force of 10.0 N for 3.0 s
6) The new magnitude of the force between them is one-ninth of the original amount.
7) The data that Carter and Sam want to find out is the Instantaneous speed
8) The formula that should be used is change in velocity/change in time.
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Doug, who runs track for his high school, was challenged to a race by his younger brother, matt. Matt started running first, and doug didn’t start running until matt had finished a quarter-mile lap on the school track. Doug passed matt as they both finished their sixth lap. If both boys ran at a constant speed, with doug running 2 miles an hour faster than matt, what was matt’s speed?.
The speed at which Matt ran is 10 miles per hour. Therefore, option (B) is the correct answer.
Matt runs at a speed of x miles per hour, whereas Doug does it at a speed of 2 miles per hour faster. Doug's speed will thereafter be equal to x + 2 miles per hour. Since there are four quarter-mile laps, Doug completes 1.5 miles in the time it requires Matt to complete 1.25 miles.
Matt:
Speed = x
Distance = 1.25
Time = [tex]\frac{1.25}{x}[/tex]
Doug:
Speed = x+2
Distance = 1.5
Time = [tex]\frac{1.5}{x+2}[/tex]
Making an equation by putting the two timings on the chart equal to one another and then solving for x will reveal that the two boys took the same amount of time from the moment Doug started.
[tex]\frac{1.5}{x+2}[/tex] = [tex]\frac{1.25}{x}[/tex]
1.5x = 1.25 (x+2)
0.25x = 2.5
x = 10
Therefore, Matt’s speed is 10 miles per hour.
The complete question is:
Doug, who runs track for his high school, was challenged to a race by his younger brother, Matt. Matt started running first, and Doug didn’t start running until Matt had finished a quarter-mile lap on the school track. Doug passed matt as they both finished their sixth lap. If both boys ran at a constant speed, with Doug running 2 miles an hour faster than Matt, what was Matt’s speed?
A. 10.5 miles per hour
B. 10 miles per hour
C. 9 miles per hour
D. 8 miles per hour
E. 7.5 miles per hour
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Answer:
The primary mirror in a telescope is curved so that it changes the path of the light hitting its surface.
Explanation:
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Answer:
the primary mirror in a telescope is curved because it changes the path of the light hitting its surface.