The resultant wave at point (5, 2) is Ψ = 5.99 cos [ 7.15 - (20/s) t]
What are the plane waves:
A plane wave is a special case of wave or field: whose value, at any moment, is constant through any plane that is perpendicular to a fixed direction in space. plane waves are free-space modes.Here,
Two plane waves are given:
c (5, t) = 4 cos [(8π/3) - (20/s) t]
c (2, t) = 2 cos [(3π/2) - (20/s) t]
now, the waves as imaginary exponentials,
separating the spatial parts, and then adding them together
we get The resultant:
Ψ = [ 4 sin (8π/3) + 2 sin (3π/2) ]^2 + [ 4 cos(8/3 π) + 2 cos(3/2π) ]^2
Ψ = 5.99 tan(a) = 0.747/ 5.95
a = 7.15
Ψ = 5.99 cos [ 7.15 - (20/s) t]
hence,
The resultant wave is Ψ = 5.99 cos [ 7.15 - (20/s) t]
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Your question is incomplete, but most probably the full question was:
Two plane waves with the same frequency and with vibrations (measured by Psi) in the z-direction are given by c (x, t) = (4cm.) cos [pi/3cm. x - 20/s t + pi] c (y, t) = (2cm.) cos[pi/4cm. y - 20/s t + pi]
Express the waves as imaginary exponentials, separate the spatial parts, and add them together using a phasor diagram to find the resultant at the point x = 5cm. y = 2cm
A baseball outfielder throws a 0.150-kg baseball at a speed of 40.0 m/s and an initial angle of 30.08 to the horizontal. What is the kinetic energy of the baseball at the highest point of its trajectory
The kinetic energy of the ball at the highest point of its motion is equal to 90.2 Joules.
Given the following data:
Mass of baseball = 0.150 kg
Speed of baseball = 40.0 m/s
V = v Cos(θ)
V= v cos 30
V= 40 x 0.867
V=34.68 m/s
K.E =1/2 MV^2
K.E= 1/2 x 0.150 x 34.68^2
K.E= 90.2 Joules.
Kinetic energy is a type of energy that an object or particle has due to its motion. When work is done on an object by applying a net force that transfers energy, the object accelerates, thereby gaining kinetic energy.
Kinetic energy has three subcategories: vibration, rotation, and translation. Naturally, the oscillating kinetic energy is caused by a vibrating object. Rotational kinetic energy is generated by moving an object, and translational kinetic energy is caused by the collision of an object.
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What is a standard drink measurement
The standard drink measurement should contain 14 grams of pure alcohol in United States of America.
What is standard drink measurement?Standard drink measurement can be defined as the measurement of alcohol that is expected by an individual to consume daily without having a bad health effect.
In the United States of America, an amount of 14 grams of pure alcohol which can be found in 12 ounces of beer is regarded as normal.
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A track & field jumper goes into the long jump with a speed of 5.0 m/s at an angle of 20⁰ above the horizontal. what is the jumper's horizontal speed as they jump? what is their vertical speed?
Answer: Horizontal Speed = 4.6 m/s
Vertical Speed = 1.7 m/s
Explanation:
Jumper's velocity = 5 m/s
Angle = 20 degrees
the angle is theta, so theta = 20 degrees
Theta is the angle between the hypothenuse and the adjacent side.
The horizontal side will be the adjacent side, and the vertical side will be the opposite side.
The hypothenuse = 5 m/s
First, let's calculate the adjacent side (horizontal speed)
We have cosine of theta, which is equal to adjacent side / hypothenuse
So, [tex]cos(20) = adjacent/5[/tex]
Multiply 5 on both sides, to get the 5 on the right side canceled.
5cos(20) = adjacent side.
4.6 = adjacent side
Horizontal Speed = 4.6 m/s
Now, let's calculate the vertical speed.
To do that, we need to calculate the opposite side.
We can calculate the opposite side with the help of sin.
The sin of theta equals to opposite side / hypothenuse
[tex]sin(20)=opposite/5[/tex]
We do the same thing, multiply 5 on both sides.
5sin(20) = opposite
1.7 = opposite
Vertical Speed = 1.7 m/s
Hope I Helped!
Boxes A and B are being pulled to the right on a frictionless surface. Box A has a larger mass than B. How do the two tension forces compare
Answer:
Tension T1 is less than tension T2.
T1 < T2
Explanation:
According to given data,
mass of box A ( mA) is grater than mass of box B (mB)
we can write,
m(A) > m(B)
Newton's second law states that:
Tension of object is directly proportional to the mass of the system.
T ∝ m
here Boxes A and B are being pulled to the right on a frictionless surface,
so Tension T1 generates due to the mass of box A m(A)
and Tension T2 arises due to mass of the system m(A) + m(B)
Thus tension T1 will be less than tension T2
T1 < T2
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A person has a choice of either pushing or pulling a book of ice with a mass of 50kg at a constant velocity. Assuming a coefficient of friction on 0.2 and pushing or pulling at the angle depicted, calculate the applied force needed for situations (a) and (b).
The applied force needed for situation a and b are 211. 31 Newton and 453. 15 Newton respectively.
How to determine the applied forceWe have that the force for situation 'a' is on an angle of inclination of 25° with the book of ice.
Thus,
Applied force = mg × sine of angle of inclination
Where mass, m = 50kg
g = acceleration due to gravity = 10m/s^2
Applied force = 50 × 10 × sin 25
Applied force = 50 × 10 × 0. 4226
Applied force = 211. 31 Newton
For situation 'b', the mass of block is adjacent to the book of ice, thus
Applied force = mg × cos of angle of inclination
Applied force = 50 × 10 × cos 25
Applied force = 50 × 10 × 0. 9063
Applied force = 453. 15 Newton
Thus, the applied force needed for situation a and b are 211. 31 Newton and 453. 15 Newton respectively.
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A leaf fell from a tree branch. The path it followed is shown in the diagram below.
Which of these best describes why the leaf fell in a crooked path instead of straight down?
The leaf fell at the crooked path instead of straight down because air currents and gravity applied changing and unbalanced forces to the leaf.
What is an air current?An air current is defined as the changes in atmospheric pressure that causes the movement of air from one area to another.
When a leaf is detached naturally from the tree, it won't fall straight down to the floor but will fall a distance away from the tree due to the action of air current and some unbalanced forces.
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A car engine changes chemical energy into what types of energy? A. Mechanical and thermal B. Thermal and light C. Mechanical and nuclear D. Electromagnetic and mechanical A car engine changes chemical energy into what types of energy ? A. Mechanical and thermal B. Thermal and light C. Mechanical and nuclear D. Electromagnetic and mechanical
Howdy,
B. Thermal and light.
A converging lens of focal length 15cm is used to obtain a real image magnified 1½ times. calculate the distance of the image from the lens
a. 37.5cm
b. 22.5cm
c.15.0cm
d.7.5cm
e.3.3cm
Answer:
don't know the answers sorry
Why is a white car an example of a poor blackbody radiator?
A. It reflects most of the light that hits it.
B. It absorbs most frequencies of electromagnetic radiation.
C. It emits more light when it is heated up.
D. It gives off only one frequency of electromagnetic radiation.
A white automobile is a bad example of a blackbody radiator since it reflects the majority of the light that strikes it.
Why is a white car a bad example of a radiator in a black body?The same colour as an ideal absorber, an ideal radiator, sometimes known as a blackbody, absorbs all radiation that strikes it. White, on the other hand, is a poor radiator and absorber. Like a mirror, a white object reflects all radiation.
What does a subpar blackbody radiator look like?Certainly, a red laser pointer is a poor choice for a black body, for the following reasons: A heated object, like a chunk of red-hot metal from a furnace, produces a black body spectrum.
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Metal a has acofficient of linear expantion that is four times the cofficient of linear expantion of meta b. how does their cofficient of areal expantion of metalb, compare?
The coefficient of aerial expansion for metal b is one-fourth of the coefficient of aerial expansion for metal a.
Note: Most probably your question was to find the relation between the coefficient of aerial expansion for metal a and metal b.
Coefficient of linear expansion:
The ratio of the change in length of a solid to its original length when there is a unit change in temperature at constant pressure is called the coefficient of linear expansion. It is given by the formula,
α=ΔL/(Lo*ΔT)
where α is the coefficient of linear expansion, ΔL is the change in length Lo is the original length, and ΔT is the change in temperature.
Coefficient of aerial expansion:
The ratio of the change in surface area of a solid to its original surface area when there is a unit change in temperature at constant pressure is called the coefficient of aerial expansion. It is given by the formula,
β=ΔA/(Ao*ΔT)
where β is the coefficient of aerial expansion, ΔA is the change in surface area, Ao is the original surface area, and ΔT is the change in temperature.
Relation between α and β:
The relation between the coefficient of linear expansion and aerial expansion is given by the formula,
β=2α
Given that metal a has a coefficient of linear expansion four times that of metal b. It can be written.
α₁=4α₂
where α₁ is the coefficient of linear expansion for metal a and α₂ is the coefficient of linear expansion for metal b.
Then from the above relation, the ratio of the coefficient of aerial expansion β₁ and β₂ for metal a and metal b respectively is,
β₁/ β₂ = 2*(α₁)÷(2*(α₂))
β₁/ β₂= 2*(4α₂)÷(2*(α₂))
β₁/ β₂=4
β₂= β₁/4
Therefore, the coefficient of areal expansion of metal b is one-fourth of the coefficient of aerial expansion of metal a.
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A generator produces 30 pulsesin 5 second. its frequency is?
Answer:
6 pulse per second
Explanation:
if,
5 secs = 30 pulse
1 sec = 30/5
1 sec = 6
An object is launched upwards at an initial speed of 3 m/s. What is the maximum height reached by the object from where it was launched
Answer:
the maximum height reached by the object from where it was launched is 0.4591 m
Explanation:
initial speed of the object, u= 3 m/s
The velocity at the maximum height will always be 0.
Therefore, final velocity, v= 0 m/s
Using the Newton's equation of motion,
v^2 - u^2 = 2*g*h(max)
0 - u^2= 2*g*h(max)
h(max) = -u^2 /2* g
where g is the gravitational acceleration.
g= - 9.8 m/s^2
substituting the values in equation,
h(max)= - (3*3) / 2*(-9.8)
h(max) = 0.4591 m
the maximum height reached by the object from where it was launched is 0.4591 m
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PLEASE HELP! Place these bodies of our solar system in the proper order of formation.
(THIS NOT PHYSICS THIS IS ASTRONOMY)
- solar nebula
- inner planets
- outer planets
- the sun
- planetesimals
Answer:
1. Solar Nebula
2. The Sun
3. Planetesimals
4. Inner planets
5. Outer planets
Explanation:
A star is formed in a molecular cloud of gas and dust, mainly composed of hydrogen and helium. The Nebular Theory establishes, for the formation of the solar system, that the cloud starts to collapse under its own gravity when it receives a shock wave from a near event, for example, a supernova explosion. That results in the cloud breaking in small pieces, and those pieces constitute a possible future star.
Then it begins to accrete and rotate as a consequence of the angular momentum. In the center of that disk when it reaches the necessary temperature and pressure a protostar will born.
Around the star, in this case the Sun, fragments of dust combine until they get a meaningful size (planetesimals). According with chemical distribution on the disk of the future solar system, rocky and iron were closer to the Sun and gasses and ice were in the outer part of disk. That may explain why the inner planets are terrestrial and the outer planets are giant gasses.
. A pilot diverted a fighter jet 20.0 km [S 38.0° E] to avoid thunderstorm, and then flew 60.0 km [S 55.0° W] to get back on track. If the diversion lasted a total of 2.00 minutes, what was the average velocity of the jet during the diversion?
The average velocity of the jet during the diversion is 518.75 m/s.
Displacement of the pilot
The displacement of the pilot from the starting position is calculated as follows;
d² = 20² + 60² - 2(20)(60) x cos(θ)
where;
θ is the angle between 20 km and 60 km leg of triangle formed from the motion.θ = (90 - 38) + (90 - 55) = 87⁰
d² = 20² + 60² - 2(20)(60) x cos(87)
d² = 3874.39
d = 62.25 km
Average velocity of the pilotV = total displacement/total time
where;
time = 2mins = 0.033 hourV = (62.25 km)/(0.033 hr)
V = 1,867.5 km/hr = 518.75 m/s
Thus, the average velocity of the jet during the diversion is 518.75 m/s.
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Energy released by the sun results from the process where atomic nuclei
a) none of these
b) combine
c) both of these
d) break apart
Answer:
b) combine
Explanation:
The energy from the sun is due to Nuclear Fusion where lighter nuclei combine to form heavier and stable nuclei this releasing a lot of energy in this process.
Two vertical parallel straight wires carry currents upward and are separated by 8.2 cm. Wire 1 exerts a force on the other wire of 7.7 X 10-5 N/m and is carrying a current of 23.0 A. What is the current in the other wire
The current in the second wire is 1.37 A.
Current in the second wireThe current in the second wire is calculated from the magnetic force between the two wires.
F/L = (μI₁I₂)/(2πr)
where;
μ is permeability of free spaceI₂ is current in the second wireF/L is force per unit lengthr is the distance between the two wiresμI₁I₂ = (F/L 2πr)
I₂ = ((F/L 2πr) / (μI₁)
I₂ = (7.7 x ⁻⁵ x 2π x 0.082)/(4π x 10⁻⁷ x 23)
I₂ = 1.37 A
Thus, the current in the second wire is 1.37 A.
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What must the amplitude of a traveling wave of frequency 72.0 Hz be in order for the average power carried by the wave to be 0.363 W
The amplitude of the wave is determined from the tension in the wire, speed of the wave, frequency of the wave and average power of the wave.
Amplitude of the wave
The amplitude of the wave travelling at the given frequency and power is calculated as follows;
U = (¹/₂)(T/v²)(ω²)(A²)(v)
U = (¹/₂)(T/v)(ω²)(A²)
U = (¹/₂)(T/v)(2πf)²(A²)
where;
U is the average power of the waveT is the tension in the wireω angular frequency of the waveA is amplitude of the wavev is the speed of the wavef is frequency of the waveThus, the amplitude of the wave is determined from the tension in the wire, speed of the wave, frequency of the wave and average power of the wave.
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You have a spring-loaded air rifle. When it is loaded, the spring is compressed 0.3 m and has a spring constant of 150 N/m. In joules, how much elastic potential energy is stored in the spring
The potential energy of the spring is 6.75 J
The elastic potential energy stored in the spring is given by the equation:
[tex]E= \frac{1}{2} kx^2[/tex]
where;
k is the spring constant
x is the compression/stretching of the string
In this problem, we have the spring as follows:
k = 150 N/m is the spring constant
x = 0.3 m is the compression
Substituting in the equation, we get
[tex]E=\frac{1}{2} (150) (0.3)^2[/tex]
[tex]E=6.75J[/tex]
Therefore. the elastic potential energy stored in the spring is 6.75J .
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give the phases into which matter can be classified, and an example of each
Explanation:
there are 4 phases in which matter could be classified.
1. Solid: an example of this would be the metal copper.
2. Liquid: an example of this would be H2O or water.
3. Gas: an example of this would be oxygen gas or O2
4. Plasma: an example of this would be lightning.
hope this helps :)
A uniform mixture consist of 30cm3 of water and 40cm3of ethanol. if the densities of water and ethanol are 1g/cm3 and 0.85g/cm3 respectively. determine the densities of the mixture.
The total density of the mixture is 0.485 g/cm^3
What is density:
The density, of a substance is its mass per unit volume. Density is denoted with symbol ρThe formula of density:
ρ = m / vhere,
volume of water, v1 = 30 cm^3
volume of ethanol, v2 = 40 cm^3
density of water, ρ1 = 1 g/cm^3
density of ethanol, ρ2 = 0.85 g/cm^3
so, according to formula,
for water
ρ1 = m1 / v1
m1 = ρ1 * v1
m1 = (1) * (30)
m1 = 30 grams
for ethanol
ρ2 = m2 / v2
m2 = ρ2 * v2
m2 = (0.85) * (40c)
m2 = 34 grams
total mass, M= m1 + m2
M= 30 + 34
M= 64 grams
total volume, V= v1 + v2
V= 30 + 40
V= 70 g/cm^3
Density of the mixture:
ρ = M / V
ρ = 34 / 70
ρ = 0.485 g/cm^3
Hence The total density of the mixture is 0.485 g/cm^3
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Which equation describes the sum of the two vectors plotted below?
A. r=x+ý
B. r = x + 4y
C. r= 2x 1 3y
D. r 4X+ ý
The equation which describes the sum of the two vectors plotted is x + 4y; option A.
What is a vector?A vector is a quantity that has both magnitude and direction.
From the graph:
a = (-2,3)
b = (1,4)
Vector, OA = -2x + 3y
Vector, AB = 3x + y
Using the triangular law of the vector addition;
r = -2x + 3y + 3x + y
r = x + 4y
In conclusion, the triangular law of vector addition is useful in adding vectors.
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A small girl applies a horizontal force of 2 Newtons to a 10-Newton box which slides across the floor with a constant speed of 3 m/s. What is the frictional force, in Newtons, by the floor on the box
2N is the frictional force by the floor on the box.
According, Newton's 2nd law[tex]F=mA[/tex]
where,
F = Horizontal force
m = Mass
a = Acceleration
But, a = 0 as Constant speed = 0 acceleration.
v = constant
Hence, there should be no net force. The frictional force is opposing the girl's force and should be equal to one another.
Frictional force = 2N
Therefore, the horizontal force applied by a small girl on the box is equal to the frictional force by the floor on the box.
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As you stand near a railroad track, a train passes by at a speed of 34.7 m/s while sounding its horn at a frequency of 215 Hz. What frequency do you hear as the train approaches you
When the train is approaching then the frequency is 239.2 Hz.
What is the frequency?This is the total number of times a periodic event happens within a given period of time. Wavelengths are used to measure periodic phenomena, which are frequently waves like sound waves. The frequency is the total number of wavelengths throughout time.
given,
speed of train = 34.5 m/s
Frequency of sound = 215 Hz
speed of sound = 341 m/s
when the train is approaching:
[tex]f1 = f[/tex]ₓ [tex]\frac{V}{V-Vt}[/tex]
[tex]f1 = 215[/tex]ₓ [tex]\frac{341}{341 + 34.5}[/tex]
f₁ = 239.2 Hz
Hence, when the train is approaching then the frequency is 239.2 Hz.
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A jumbo jet must reach a speed of 360 km/h on the runway for takeoff. What is the lowest constant acceleration needed for takeoff from a 1.80 km runway
The lowest constant acceleration needed for takeoff from a 1.80 km runway is 2.8 m/s².
To find the answer, we need to know about the Newton's equation of motion.
What's the Newton's equation of motion to find the acceleration in term of initial velocity, final velocity and distance?The Newton's equation of motion that connects velocity, distance and acceleration is V² - U²= 2aSV= final velocity, U= initial velocity, S= distance and a= accelerationWhat's the acceleration, if the initial velocity, final velocity and distance are 0 m/s, 360km/h and 1.8 km respectively?Here, S= 1.8 km or 1800 m, V= 360km/h or 100m/s , U= 0 m/sSo, 100²-0= 2×a×1800=> 10000= 3600a
=> a= 10000/3600 = 2.8 m/s²
Thus, we can conclude that the lowest constant acceleration needed for takeoff from a 1.80 km runway is 2.8 m/s².
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A worker pushing a 35.0-kg wooden crate at a constant speed for 12.0 m along a wood floor does 350 J of work by applying a constant horizontal force of magnitude F on the crate. (a) Determine the value of F. (b) If the worker now applies a force greater than F, describe the subsequent motion of the crate. (c) Describe what would happen to the crate if the applied force is less than F.
If the force is increased, the crate will become accelerated while if the force is decreased, the crate will decelerate.
How do we obtain the force?Recall that the force is the product of mass and acceleration. Now we know that work is done when the force applied moves a distance. Since the velocity is constant;
W = Fs
F= W/s
F = 350 J/ 12.0 m
F = 29.2 N
If the force is increased, the crate will become accelerated while if the force is decreased, the crate will decelerate.
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The current in a wire is 3 a . calculate the charge that flows through the wire in 1 minute
The charge of the wire is 180 C.
What is a charge?The term charge is defined as the product of the current and the time taken. Thus we can write that;
Q = It
Q = charge
I = current
t = time
Hence;
Q = 3 A * 1 * 60 s = 180 C
Thus the charge of the wire is 180 C
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A cylindrical metal rod has a resistance R . If both its length and its diameter are tripled, its new resistance will be:
The new resistance will be 9R
A longer wire should have a higher electrical resistance than a wire with a bigger cross section, and vice versa. The electrical resistance of a wire should also be affected by the material from which it is formed.
The resistance of a wire is R = ρL/A. The volume of a wire is LA. If L increases by 3, then A must decrease by 3 in order for the volume to remain constant. If L increases by 3 and A decreases by 3, then L/A increases by 9 .
Hence the new resistance will be 9R
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Please help :/
Two objects have the same center point of the circle, but are located at different positions away from the center point. Each object is moving with uniform circular motion. Which would describe the tangential speed of the objects?
A) both objects would have the same tangential speed
B) the object with the smaller radius has a faster tangential speed
C) the object with the larger radius has a faster tangential speed
D) both objects would have oscillating tangential speeds
C. The object with the larger radius has a faster tangential speed.
What is tangential speed?
Tangential speed is the linear component of the speed of any object which is moving along a circular path.
v = ωr
where;
ω is angular speedr is the radius of the circular pathIf both object the same center point, they will have the same angular speed but different tangential speed due to their location from the center point.
Thus, the object with the larger radius has a faster tangential speed.
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What is the formula for the moment of inertia of the person/single particle rotating in a circle? (Give these values with a subscript of 1, e.i. I1 = ) What is this value of the moment of inertia when the person is on the edge of the merry-go-round?
Moment of inertia of single particle rotating in circle is I1 = 1/2 (m*r^2)
The value of the moment of inertia when the person is on the edge of the merry-go-round is I2=1/3 (m*L^2)
Moment of Inertia refers to:
the quantity expressed by the body resisting angular acceleration.It the sum of the product of the mass of every particle with its square of a distance from the axis of rotation.The moment of inertia of single particle rotating in a circle I1 = 1/2 (m*r^2)
here We note that the,
In the formula, r being the distance from the point particle to the axis of rotation and m being the mass of disk.
The value of the moment of inertia when the person is on the edge of the merry-go-round is determined with parallel-axis theorem:
I(edge) = I (center of mass) + md^2
d be the distance from an axis through the object’s center of mass to a new axis.
I2(edge) = 1/3 (m*L^2)
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The box resting on the inclined plane above has a mass of 20kg. The incline sits at a 30o angle. Find the friction force between the box and the incline if the box does not slide down the incline.
The friction force between the box and the incline if the box does not slide down the incline will be 0.577
The force preventing sliding against one another of solid surfaces, fluid layers, and material components is known as friction. There are several kinds of friction: Two solid surfaces in touch are opposed to one another's relative lateral motion by dry friction.
Given the box resting on the inclined plane above has a mass of 20kg and the The incline sits at a 30 degree angle
We have to find the friction force between the box and the incline if the box does not slide down the incline
Since the frictional force F₁ must equal or exceed gravitational force F₂ down the incline:
F₁ = F₂
μmgcosΘ = mgsinΘ
μ = (mgsinΘ)/(mgcosΘ)
μ = tanΘ
μ = 0.577
Hence the friction force between the box and the incline if the box does not slide down the incline will be 0.577
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:The resistance created by the box's friction with the incline The slope will be 0.577 if the box doesn't descend.
Friction is the force that prevents solid surfaces, fluid layers, and material constituents from sliding past one another. Different types of friction exist. Dry friction opposes the relative lateral motion of two touching solid surfaces.
Given that the 20-kg box lying on the inclined plane above and the incline's 30 degree inclination
If the box does not slide down the incline, we must determine the friction force between them.
Given that the gravitational force F2 down the gradient must be equal to or greater than the frictional force F1,
F₁ = F₂
If mgcosx = mgsinx
equals (mgsinx)/(mgcosx)
μ = tanx
μ = 0.577
Therefore, if the box does not slide down the incline, the friction force between the box and the incline will be 0.577.
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