The angle below the horizontal the dart shot at 8 m/s horizontally and 9 m/s downward is 41.67°
In a right angled triangle,
tan θ = Opposite side / Adjacent side
Here the resultant velocity, horizontal and vertical components makes a right angled triangle.
Opposite side = Horizontal component = 8 m / s
Adjacent side = Vertical component = 9 m / s
tan θ = 8 / 9
tan θ = 0.89
θ = [tex]tan^{-1}[/tex] ( 0.89 )
θ = 41.67°
The formula used to solve the problem is a trigonometric ratio. Trigonometric ratios are applicable only on a right angled triangle. Some of the basic trigonometric ratios are:
sin θ = Opposite side / Hypotenusecos θ = Adjacent side / HypotenuseTherefore, the angle below the horizontal, the dart is traveling is 41.67°
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Two cars are moving along a stright line in the same direction with a velocity of 25 km/h and 30 km/h respectively. find the velocity of car a relative to car b
Answer:
Explanation:
V = Vb - Va = 30 - 25 = 5 km/h
A mass on the end of a spring undergoes simple harmonic motion. At the instant when the mass is at its equilibrium position, what is its instantaneous acceleration?.
A mass on the end of a spring undergoes simple harmonic motion. At the instant when the mass is at its equilibrium position, its instantaneous acceleration is zero
When the restoring force is proportionate to the displacement but acting in the opposite direction, an oscillating mass moves in a manner known as harmonic motion. The sine wave has a constant frequency and amplitude and can be used to describe harmonic motion because it is periodic. The motion of a weight on a spring is an illustration of this.
Simple Harmonic Motion, also known as SHM, is a motion in which the restoring force is inversely correlated with the body's deviation from its mean position. A particle moving in simple harmonic motion experiences acceleration given by the formula a(t) = − 2 x (t). The particle's angular velocity is given in this equation as.
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a conductor consists of an infinite number of adjacent wires, each infinitely long and carrying a current i (whose direction is out-ofthe-page), thus forming a conducting plane.
If there are n wires per unit length, magnitude of B measure at A or C is B = Ωo*n*I/2
A key concept in science is the concept of magnitude in physics. The general quantity or distance is referred to as magnitude. When it comes to the elements of movement, we can tie magnitude to an object's size and motion speed.
A particular object's magnitude is determined by its size or quantity. For instance, when it comes to speed, if a car is moving at a quicker rate than a nearby motorcycle, the magnitude of the automobile's speed is greater than the speed of the motorcycle. Although they contain directions as well as magnitude, vector quantities. Vector quantities include things like force, acceleration, speed, velocity, and many others. A vector's absolute value is referred to as its magnitude.
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describe how two objects can have the same speed but different velocities
Two objects can have the same speed but different velocities. The detailed description is given below.
We can take two escalators to explain the concept. The two escalators are moving up at a speed of 10 m/s. In this case, the two escalators have the same speed and they are moving in the same direction. So, they have the same velocity also.
Now one escalator is moving up at a speed of 10 m/s and the other escalator moving down at a speed of 10 m/s. In this case, both escalators move at 10 m/s, so their speed is the same. But they are not moving in the same direction. Hence their velocity is not the same. One has 10 m/s downwards and the other one has 10 m/s upwards velocity.
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Five ramps lead from the ground to the second floor of a workshop, as sketched below. All five ramps have the same height; ramps B, C, D and E have the same length; ramp A is longer than the other four. You need to push a heavy cart up to the second floor and you may choose any one of the five ramps. Assuming no frictional forces on the cart, which ramp would require you to do the least work?
1. Same work for ramps B, C, D or E; more work for ramp A.
2. Same work for the straight ramps A and B; less work for ramps C, D, and E.
3. Ramp D.
4. Ramp E.
5. Ramp B.
6. Ramp A.
7. Ramp C.
8. Same work for all five ramps.
9. Unable to determine without knowing the exact profiles of ramps C, D or E.
By assuming no frictional forces on the cart, Same work for all five ramps would require you to do the least work.
What exactly is a frictional force?The force produced by two surfaces coming into contact and sliding against one another is referred to as frictional force. The following variables impact the frictional force, Surface roughness and the amount of force pressing them together have the biggest an impact on these forces.
What is work-energy theory and how is it supported?According to the work energy theorem, the net change in a body's energy is equal to the work that is done on it. K.E. or P.E. Proof: Consider a mass'm' object travelling at a 'u' starting velocity. Allow a body to vary its velocity to v in response to a constant force, F.
Let h be the height of the ramps. Since there is no friction, we can use the
work-energy theorem.
Wtot = Wperson + Wgravity = ∆K
Hence for all the ramps,
Wperson = −Wgravity + ∆K = mgh + ∆K
In particular, if ∆K = 0 (the cart starts from rest and ends at rest),
Wperson = mgh, for all the ramps.
So, the Same work for all five ramps.
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The focal point is the point through which parallel incident rays reflecting off the surface of a concave mirror converge. Is this true or false?
When a beam of rays that are parallel to the principal axis is incident on a concave mirror converges at the focal point.
But, if any other set of parallel rays that are not parallel to the principal axis is incident on a concave mirror they will not converge at the focal point. They will converge at a distance of focal length, but not on the focal point.
Thus the given statement is not true.
two cars are diriving down the road. car a has a mass of 1,100 kg and is moving at 20 m/s. car b has a mass of 1000 kg and is moving at 30 m/s. which car has more kinetic energy and why
Answer:
Hope the pictures will help you
Light travels at a speed of about 3.0 108 m/s.(a) How many miles does a pulse of light travel in a time interval of 0.1 s, which is about the blink of an eye?Δx = mi(b) Compare this distance to the diameter of Earth. (Use 6.38 106 m for the radius of the Earth.)ΔxDE =
Given:
Speed of light = 3 x 10⁸ m/s
Let's solve for the following:
• (a). How many miles does a pulse of light travel in a time interval of 0.1 s, which is about the blink of an eye?
Apply the formula:
[tex]\Delta x=v*t[/tex]Where:
v is the speed of light
t is the time.
Thus, we have:
[tex]\begin{gathered} \Delta x=3.0\times10^8*0.1 \\ \\ \Delta x=3.0\operatorname{\times}10^7\text{ m} \end{gathered}[/tex]Now let's convert the answer from meters to miles.
Where:
1 mile = 1609.34 meters
[tex]\begin{gathered} 3.0\times10^7=\frac{3.0\times10^7}{1609.34} \\ \\ =18641.14\text{ mi} \end{gathered}[/tex]Δx = 18641.14 mi
• (b). Compare this distance to the diameter of Earth.
Apply the formula:
[tex]\frac{\Delta x}{D_E}=\frac{\Delta x}{2*r}[/tex]Where:
r = 6.38 x 10⁶ m.
Thus, we have:
[tex]\frac{\Delta x}{D_E}=\frac{3.0\times10^7}{2*6.38\times10^6}=2.35[/tex]ANSWER:
• (a). 18641.14 mi
,• (b). 2.35
A car travels south at 30 m/s for 5 minutes. How many seconds does it travel
for?
A. 350 s
B. 250 s
C. 200 s
D. 300 s
Answer:
The Answer is D. 300 s because in 5 minutes there are 300 seconds
two conductors made of the same material are connected across the same potential difference. conductor a has eight times the diameter and eight times the length of conductor b. what is the ratio of the power delivered to a to the power delivered to b?
The power given to A is 7 times more powerful than the power delivered to B. So, the ratio of the power delivered to a to the power delivered to b is 7:1.
A wire's cross sectional area is computed as follows:
A= πd²/4
A wire's resistance is calculated as;
R= pL/A
R= 4pL/πd²
opposition in wire A;
R= 4pALA/πd²A
opposition in wire B;
P = V²/R
wired power delivery;
P= V²A/RA
energy provided through cable A;
P= V²b/Rb
energy transferred through wire B;
Replace R's value in the power delivered through wire A;
PA= V²A/RA = V²Aπd²/4pALA
PA/PB = d²A/LA x LB/V²B/d²B
The diameter and length of wire A are both seven times greater than those of wire B;
PA : PB = 7 : 1
Consequently, the power given to A divided by the power transferred to B equals 7 : 1
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inner parts of the flattening cloud begin to fall freely inward, raining down on growing object at the center. gravitational potential energy of collapsing gas cloud is converted into heat and radiative energy.
These 2 statements are 2 steps of solar planet formation 1st statement is 3rd step 2nd statement is 4th step.
In the cosmos, there are a lot of planetary systems with solar planets around a host star, similar to our own. Because we refer to things that are connected to our star as "solar," our planetary system is sometimes known as "the solar system," after the Latin word for the Sun, "solis." The Sun, our star, and everything gravitationally connected to it, including the moons, planets, and dwarf planets like Pluto, Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, and Neptune, make up our solar system. Thousands of planetary systems orbiting other stars in the Milky Way have been found, in addition to our solar system. The Milky Way galaxy's outer spiral arm is where our solar system is situated. In our solar system, there is only the Sun.
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Since gravity is a conservative force, the work done against gravity can be replaced by gravitational potential energy. When an object is thrown vertically upward, its gravitational potential energy true or false?.
A ball's gravitational potential energy will rise as it is launched vertically upward.
An object's gravitational potential energy is the power it has as a result of being in a gravitational field. The gravitational potential energy is most frequently used for an object close to the Earth's surface, when the gravitational acceleration is believed to remain constant at around 9.8 m/s2. Since any point can be chosen as the gravitational potential energy zero (just like any coordinate system zero), the potential energy at a height h above that point is equal to the work that would be needed to lift the item to that height with no net change in kinetic energy. Its weight must be lifted with the same amount of force, so the gravitational potential energy must also be equal. The gravitational potential energy is most frequently used for an object close to the Earth's surface, when the gravitational acceleration is believed to remain constant at around 9.8 m/s2. Multiple factors affect the gravitational potential energy of an object: its mass, the gravitational acceleration it experiences from the earth, and its distance from the ground.
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A dart shot at a monkey is traveling 10 m/s horizontally, while simultaneously traveling 7 m/s downward. At what angle below the horizontal is the dart traveling? Answer in degrees
The angle below the horizontal the dart shot at 10 m/s horizontally and 7 m/s downward is 55°
In a right angled triangle,
tan θ = Opposite side / Adjacent side
Here the resultant velocity, horizontal and vertical components makes a right angled triangle.
Opposite side = Horizontal component = 10 m / s
Adjacent side = Vertical component = 7 m / s
tan θ = 10 / 7
tan θ = 1.43
θ = [tex]tan^{-1}[/tex] ( 1.43 )
θ = 55°
The formula used to solve the problem is a trigonometric ratio. Trigonometric ratios are applicable only on a right angled triangle. Some of the basic trigonometric ratios are:
sin θ = Opposite side / Hypotenusecos θ = Adjacent side / HypotenuseTherefore, the angle below the horizontal, the dart is traveling is 55°
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A horse pulls a cart with force F. As a result of this force the cart accelerates with constant acceleration. The
magnitude of the force that the cart exerts on the horse
A) is zero newtons. B) greater than the magnitude of F. C) equal to the magnitude of F. D).
less than the magnitude of F.
Answer:
c. equal equal to the magnitude of f
calculate the magnitude of the force, in newtons, exerted by a 0.115-mg chip of paint that strikes (and sticks to) a spacecraft window at a relative speed of 3.95 × 103 m/s, given the collision lasts 5.95 × 10– 8 s.
Paint chip impacting a spaceship window with a force of 6.67×103 N using a 0.100-mg mass.
Any action that seeks to preserve, modify, or deform a body's motion is considered to be a force in mechanics. Usually, Isaac Newton's three laws of motion from his Principia Mathematica are used to describe the concept of force (1687). A body at rest or moving uniformly in a straight path will stay in that state unless a force is applied to it, according to Newton's first law. According to the second law, any external force that interacts with a body causes it to accelerate (change its velocity) in the force's direction. A vector quantity, force is one that has both magnitude and direction. The rate at which an item changes its velocity is known as the vector quantity known as acceleration. When an object's velocity changes, it is said to be accelerating. On occasion, sports broadcasters will suggest that a person is accelerating if they are travelling quickly. Acceleration, however, has little to do with speed. Even though a person is travelling quickly, they may not be accelerating. A change in an object's speed is referred to as acceleration. An object is not accelerating if it is not changing its velocity.
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a ball is thrown in the air at 5m/s. If the ball was thrown at a 4 degrees angle. How long will it take to return to its original height?
Answer:
0.5seconds
Explanation:
where
initial velocity u=5m/s
gravity g=9.8m/s²
final velocity v=0m/s (since velocity at maximum height is 0)
time t=?
using
v=u-gt
0=5-9.8(t)
0=5-9.8t
9.8t=5
t=5/9.8
t=0.5102040816
t=0.5sec
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Jack and Jill carry a bag of bricks to the top of the hill to mend the well. If the bricks weigh 50 N and the hill is
30 m, how much work do they do between them?
Answer:
1500 J
Explanation:
Work = force * distance = 50 N * 30 M = 1500 J
.A drawing pin is pressed into the notice board. The pointed pin area is 0.25 mm² and the force exerted on the pin is 10 newtons. Compute the pressure.
The pressure exerted is 4 × 10⁷ N/m²
Pressure is the force carried out perpendicular to the surface of an item in step with the unit vicinity over which that force is sent. Gauge pressure is the pressure relative to the ambient strain. numerous units are used for the explicit strain.
Strain is a pressure carried out perpendicular to the surface of an item in keeping with unit location. Mathematically it is P = F/A, in which P is strain, F is force, and A is area. strain is a scalar amount, one that most effectively has value and no directional vector characteristics.
Calculation:-
Given,
area = 0.25 mm2
= 2.5 × 10⁻⁷ m²
Force = 10 N
Pressure = force/area
= 10 / 2.5 × 10⁻⁷
= 4 × 10⁷ N/m²
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An object moves 60.0 m on a bearing (angle from North) of 60.0°. If the object then moves 30.0 m North, how far is it from the start point? You may use a scale diagram or trigonometry to answer this question.
Answer: x(t2)−x(t1) over the time interval [t1,t2]
Explanation: hope this helps
A ship is at a location of 40° S 77° W. Which type of surface ocean current and tectonic plate boundary are located beneath this ship?
Cool ocean current and a convergent boundary
An ocean current is a continuous flow of water in an oceanic direction; this implies that the water is not the same water, but that it is exchanged within the current at a comparable rate and direction. Temperature and water salinity are only two examples of the elements that influence currents. A continuous, directed flow of ocean water is known as an ocean current, and it is caused by a variety of factors acting on the water, such as wind, the Coriolis effect, breaking waves, cabeling, and variations in temperature and salinity.
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according to a simplified model of a mammalian heart, at each pulse approximately 20 g of blood is accelerated from 0.25 m/s to 0.35 m/s during a period of 0.10 s. what is the magnitude of the force exerted by the heart muscle?
The magnitude of the force exerted by the heart muscle is 0.02N
since
F = m dv/dt
= 0.02(0.35-0.25)/0.10
F =0.02N.
A force is an influence in physics that can change the motion of an object. A force can cause a mass object to change its velocity, or accelerate. Intuitively, force can be described as a push or a pull. A force is a vector quantity because it has both magnitude and direction.
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Exercise write the peice wise
function {h(x) x
r(x) a<=x
K(x) x>=b} in terms
Of one function
A piecewise-defined function in mathematics is one that is composed of several smaller functions, each of which has a certain interval of the domain it applies to. Instead of being a property of the function itself, piecewise definition is a means to express the function.
In terms of r(x),
r(x) <= x when x >= b
A function that is defined by many sub-functions, each of which applies to a specific interval of the main function's domain, is referred to as a piecewise-defined function in mathematics (also known as a piecewise function or a hybrid function) (a sub-domain).
When an input value passes specific "boundaries," a rule or relationship changes. In these cases, we employ piecewise functions to explain the situation.
For instance, it happens frequently in business that the price per piece of a particular item gets decreased after the quantity bought exceeds a certain threshold.
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A trumpet plays middle C (262 Hz). How fast would it have to be moving to raise the pitch to C sharp (277 Hz)? Use 343 m/s as the speed of sound.
The trumpet would have to be moving at a speed of approximately 345.8 m/s to raise the pitch to C sharp.
What is speed?
In everyday language and kinematics, an object's speed (typically abbreviated as "v") is defined as the size of the change in position that occurs over time or the amount of change that occurs per period of time; it therefore a vector quantity. The instantaneous speed is the upper limit of the average speed as the time interval's duration gets closer to zero; it is calculated by dividing the distance travelled by the time interval's duration. Speed and velocity are distinct concepts.
Speed is measured as distance divided by time.
To raise the pitch of a note by one semitone, the speed of sound must be increased by approximately 6%. In this case, the trumpet would have to be moving at approximately 364 m/s to raise the pitch to C sharp.
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a change in state involves a change in the______of the particles
Answer: Energy
Explanation: Any change in the states of matter is the result of added or lost energy. For example, when Water is frozen, it loses all of its particle energy, which is why when it's ice, all the particles stick together, but if you boiled the water to make vapor, they fly around like crazy because they have a lot of energy.
Mr. Red Herring was found shot dead in his backyard. He was about a foot away from his back porch, lying next to his personal handgun. A bloody footprint was also found on the porch. Analysis of a bullet found nearby suggests that, based on the striation marks, the bullet that killed Herring came from a gun discarded in a nearby trash can. He apparently had a date that night with Mrs. Scarlet. Based on various evidence, the forensics team also created a digital rendering of the crime.
An example of demonstrative evidence is the digital rendering of the crime scene that shows where the gun was fired from. That is option B.
What is demonstrative evidence?A demonstrative evidence is the type of evidence that is being represented using visuals to help enhance the facts of a claim made against an opponent in the law court.
The components of demonstrative evidence include the following:
photos, x-rays, videotapes, movies, sound recordings, diagrams, forensic animation,maps and drawings.Based on the various evidence presented concerning the sudden death of Mr. Red Herring who was short dead in his backyard, the demonstrative evidence is when the forensics team also created a digital rendering of the crime showing where the gun was shot.
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Options of question:
In this story, which is an example of demonstrative evidence?
The fingerprint that showed that Mrs. Scarlet handled the gun
The digital rendering of the crime scene that shows where the gun was fired from
The report about bullet striations that prove the shot came from the discarded weapon
The DNA evidence gathered from the blood splatters
What is the distance from the moon to the sun?
Answer:
About 150 million kilometers
Explanation:
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A wire of a certain length (α = 0.0065 1/°C) has a resistance of 15 Ω at 20°C.
Calculate the temperature at which the resistance will be 22.8 Ω
The temperature at which the resistance will be 22.8 Ω is 100 °C
How to determine the temperatureThe following data were obtained from the question:
Coefficient of epansion (α) = 0.0065 °C¯¹ Original resistance (R₁) = 15 Ω Original temperature (T₁) = 20 °C New resistance (R₂) = 22.8 ΩNew temperature (T₂) =?The new temperature can be obtained as illustrated below:
α = R₂ – R₁ / R₁(T₂ – T₁)
0.0065 = 22.8 – 15 / 15(T₂ – 20)
0.0065 = 7.8 / 15(T₂ – 20)
Cross multiply
0.0065 × 15 (T₂ – 20) = 7.8
0.0975 (T₂ – 20) = 7.8
Divide both side by 0.0975
T₂ – 20 = 7.8 / 0.0975
T₂ – 20 = 80
Collect like terms
T₂ = 80 + 20
T₂ = 100 °C
Thus, the temperature is 100 °C
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the suspended 2.37 kg mass on the right is moving up, the 1.3 kg mass slides down the ramp, and the suspended 7.8 kg mass on the left is moving down. there is friction between the block and the ramp. the acceleration of gravity is 9.8 m/s 2 . the pulleys are massless and frictionless
In this, two frictionless, smooth inclined surfaces that have the same angle with the horizontal (57.7°) are connected to one another. Blocks are placed on the inclined surfaces.
The left one is white, whereas the right one is black. Then, a frictionless pulley is present here at the edge, and the two blocks are attached to one another using a light string weight made of the white blocks. Assume there are lots of M W. Its weight will therefore be M W G. The black block's weight. M. B. G. Component Here would be that.
This will also be 57.7 degrees if the angle is 57.7. Additionally, this component is M W G, costs 57.7 degrees, and runs horizontally. That is 57.7° M W G Sign. Next, the element perpendicular to this inclination surface for this black block. This part is B G Costs 57.7° and a component along the spring-bound incline of mbG sign 57.7° The blocks are shown to be travelling with an acceleration of A in the direction of the left.
Given to us are MB square markings traveling at 1.5 meters per second. The bulk of this white blog weighs 3.19 kilograms. It is absent. We need to locate it. First, as the white vlog is moving down, use the free body diagram of the white block. Therefore, M W G sign 57.7 degrees force will be more than that tension T for this white block. Thus, using Newton's second rule of motion, the net force will be equal to.
The block's mass times its acceleration equals the block's net force. Using a free body schematic of the ascending black bloc, continue. T will therefore be more for it. Therefore, this equals p – Mbg. indication of 57.7 degrees. Using Newton's second rule of motion, which is equal to M B A, once more This is equation #1, that was equation #1, this is equation #2, this is one, and this is equation #3. hence, adding 1 and 2. It is obvious that the tension will end and that G signed 57.7° will be seen as an exit signal.
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a parallel-plate capacitor is formed from two 4.0 cm x 4.0 cm electrodes spaced 2.0 mm apart. the electric field strength inside the capacitor is 1.0 x 106 n/c. what is the charge (in nc) on each electrode?
Equation Q/A = E Electric Field within a parallel plate capacitor
∴ Q = E*Aε
E = 10^6 N/C
A = 4*4 = 16cm^2 = 16 * 10^-4 m^2
ε = 8.852 * 10^-12 F/m
Q = +/- 10^6 * 16 * 10^-4 * 8.852 * 10^-12
= +/- 141.6 * 10^-10 C
= +/- 14.2 nC
You can think of an electric field as a physical field that surrounds all charged particles and pulls on them all.
Before the dielectric breaks down, a parallel plate capacitor can only hold a certain amount of energy. It can be stated as follows: The parallel plate capacitor is a device that uses two parallel plates connected across a battery to create an electric field between them.
A nonmetallic component of a circuit is made in touch with using an electrode, an electrical conductor. Depending on the type of battery, electrodes are a crucial component that can be made of a range of materials.
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1. on the planet arrakis a male ornithoid is flying toward his mate at 25.0 m/s while singing at a frequency of 1200 hz. if the stationary female hears a tone of 1240 hz, what is the speed of sound in the atmosphere of arrakis?
If the stationary female hears a tone of 1240 hertz, then the speed of the sound in the atmosphere of arrakis will be 775 meter per second.
The term "Ducler shift" refers to the apparent change in frequency caused by the source moving closer to the observer or by the relative motion between the source and the object. The formula: true frequency over 1 minus v s over v gives the observed frequency. Let's call this equation 1, shall we? The real frequency in our case is stated as 1200 hertz, but the perceived frequency is reported as 1240 hertz. It is stated that the source's velocity, vs, is 25.0 meters per second. Rearranging equation 1 yields the result that the real frequency over the absorbed is equal to 1 minus b s over v.
As a result, we can be represented as v s over 1 minus f, actual over f absorbed now 1 substituting the values we get 25.0 meter per and over 1 minus 1200 hertz over 1240 hertz. Frequency fur, the rearranging we get 1 minus f real over f absorbed, is equal to v s over v. The sound travels at a speed of 775 meters per second after further calculation.
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