Answer:
Petametres; 41 Pm
Explanation:
A measurement should use units that give a number between 0.1 and 1000.
The measure that astronomers use is the light year — the distance that light travels in one year.
In those units, the distance is 4.3 light years.
We can calculate the distance in SI units.
[tex]\text{Time} = \text{4.3 yr} \times \dfrac{\text{365.25 da}}{\text{1 yr}} \times \dfrac{\text{24 h}}{\text{1 da}} \times \dfrac{\text{3600 s}}{\text{1h}} = 1.36 \times 10^{8} \text{ s}\\\\\text{Distance} = 1.36 \times 10^{8} \text{ s} \times \dfrac{2.998 \times 10^{8}\text{ m}}{\text{1 s}} = 4.1 \times 10^{16} \text{ m} = 41 \times 10^{15} \text{ m}[/tex]
In SI, we should measure the distance in petametres (1 Pm = 10¹⁵ m)
Thus, the distance to the nearest star is 41 Pm.
PLEASE HELP ME check the photo.
Answer:
1/ How do scientists determine the elements present in different stars?
KEY WORD for the main idea: Analysis of the starlight.
Answer: Scientists can identify what elements present in different stars by analysing the starlight.
Note: The "starlight" = spectral lines. Astronomers can can identify what kinds of stuff are in stars from the lines they find in star's spectrum. From spectral lines astronomers can determine not only the element, but the temperature and density of that element in the star.
..
2/ What happens to a star when the fuel for its nuclear fusion reactions is exhausted?
KEY WORD for the main idea: generate light from energy
Answer: A star generates energy through nuclear fusion; this energy is released a light and heat.
Note: The energy source for all stars is nuclear fusion. Stars spend most of their lives repetitively compressing two hydrogen atoms into a single helium atom - plus a lot of energy, which is released as light and heat. A normal star that has exhausted the nuclear fuel in its interior, its outer layers have expanded, and it has become a red giant.
....
3/ Why aren't stars and galaxies spread out evenly across the universe?
KEY WORD for the main idea: Gravitational attraction
Answer: Stars and Galaxies aren't evenly distributed uniformly throughout the universe, because of the existance of gravity.
Note: Gravity, as one of the fundamental forces of the universe, is the powerful force that glues our universe together. This is the one that causes every object in the universe to attract every other object. One of the most noticeable effects of gravity in the solar system is the orbit of the planets.
Explanation:
Hope this answer can help you. Have a nice day !
A ray in glass arrives at the glass-water interface at an angle of 48° with the normal. The refracted ray, in water, makes a 72° angle with the normal. The index of refraction of water is 1.33. Then the ray in glass is redirected so its new angle of incidence is 37°. What is the new angle of refraction in the water? Show all work. (2 points)
An electromagnetic wave of frequency 2.30 × 10^14 Hz propagates in carbon tetrachloride with a speed of 2.05 x 10^8 m/s. What is the wavelength of the wave in carbon tetrachloride? Show all work and include units of measure. (2 points)
Based on the data in the graph provided, which value is closest to the index of refraction of quartz for extreme violet light of wavelength 400 nm? (1 point)
1.44
1.53
1.56
1.67
The index of refraction of medium 1 is 2.3 and the index of refraction for medium 2 is 1.6. What is the critical angle for light traveling within medium 1 toward medium 2? (1 point)
40°
14°
44°
70°
A ray of laser light strikes a glass surface at an angle θa = 22.5° to the normal. What is the angle θb of the refracted ray? Let the index of refraction for glass nb = 1.77. (1 point)
12.7°
12.5°
31.8°
10.1°
As explained by the theory of quantum electrodynamics, light is best described as _____. (1 point)
Both a wave and particles.
A wave, not particles.
Particles, not a wave.
Match the following types of electromagnetic waves with where they exist on the electromagnetic spectrum. (2 points)
1
2
3
4
a. Radio Waves
b. Infrared
c. Gamma Rays
d. X-Rays
Describe the difference(s) between electromagnetic waves and mechanical waves. Provide an example of each in your descriptions. (2 points)
A step-down transformer providing electricity for a residential neighborhood has exactly 2750 turns in its primary. When the potential difference across the primary is 5670 V, the potential difference at the secondary is 240 V. How many turns are in the secondary? Show all work. (2 points)
A circuit has 3 resistors, all connected in parallel. Let R1 = 4.0 Ω, R2 = 3.0 Ω, and R3 = 6.0 Ω. What is the equivalent resistance of the circuit? Show all work and include units of measure.
Answer:
hope this helps
...........
Can someone please help me with this pre ap physics question?
Answer:
they will be moving east and west, or perpendicular to particles of the wave.
Explanation:
Answer:
The answer is B: Perpendicular to the particles of the wave
Explanation:
A submarine is carefully navigating its way to the seafloor. It sends out “pings”—a radar wave—as it descends to keep track of its location in relation to the ground. The wavelength of the radar as it leaves the ship is 3 cm. Which of the following could be the wavelength as the wave returns? show work
A. 2 cm
B. 3 cm
C. 4 cm
D. impossible to estimate
Answer:
D. impossible to estimate
Explanation:
According to the doppler effect, the frequency of the wave will increase.
let u be the speed of the submarine,
let the speed of sound in water be c,
let initial frequency of the sent out wave be f,
let frequency of received wave be f'
The distance occupied by the new wave will be (c - u), therefore, the new wavelenght will be (c - u)/f
Frequency = speed of sound ÷ wavelenght
therefore the new Freq f' will be
f' = cf/(c - u) which will be shorter than the initial wavelenght.
But we do not know the speed of the submarine, so we can't estimate.
A note on a piano vibrates 262 time per second. What is the period of the wave
Answer: it is period 93
Explanation:
The period of a wave, measured in seconds, is the reciprocal of its frequency. Given that a piano note vibrates at a frequency of 262 times per second, the period of the wave is approximately 1/262 or 0.00381 seconds.
Explanation:In physics, the frequency is the number of waves that pass a fixed point in a given time period. We typically measure it in hertz (Hz), which is synonymous with cycles per second. On the other hand, the period is the duration it takes for one cycle to pass, which is the reciprocal of the frequency.
Here the note on the piano is stated to vibrate (frequency) 262 times per second. Thus, to calculate the period, we take the reciprocal of the frequency i.e. 1 divided by the frequency. Hence, it's 1/262 which equals approximately 0.00381 seconds. So, the period is about 0.00381 seconds.
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Which phase of the moon will occur after "waning gibbous"?
A. full moon
B. last quarter
C. waning crescent
D. new moon
E. waxing crescent
F. first quarter
G. waxing gibbous
Answer: B. The last quarter. Half of the moon's surface will be visibly illuminated.
Answer:
B. Last Quarter
The areas in which the individual magnetic orientations of atoms line up are called
Answer:
Magnetic domains
Explanation:
The areas in which the individual magnetic orientations of atoms line up are called magnetic domains.
In most magnetic materials, atoms are arranged in such a way that the magnetic orientation of one electron cancels out the orientation of another
In magnetic domain electrons have the same magnetic orientation. This means that the individual magnetic moments of the atoms are aligned with one another and they point in the same direction.
If 20 J of work is done in 4 seconds, what is the power?
When 20 J of work is done in 4 seconds, the power is 5 watts
Power is the rate at which work is done, expressed in watts.
In this case, if 20 J of work is done in 4 seconds, the power can be calculated as follows:
Power = Work done / Time taken
Power = 20 J / 4 s
= 5 watts
Which therapy is associated with light, but not sound?
A: breaking down kidney stones
B: acoustically targeting the delivery of a drug
C: cauterizing an incision or wound
D: ablating tumors
Cauterizing an incision or wound is associated with light, but not sound.
What is Cauterization?This is a medical procedure which involves burning a part of a body to remove or close off a part of it.
It is usually done with the use of hot iron, electricity etc which makes it associated with light and not sound.
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a screen door spring has a spring constant of 188 N/m, and when stretched, exerts a 59.5 N force on the door. how far is the spring stretched?(unit=m) PLEASE HELPPPPP MEEE
Answer:0.316 m
Explanation:
The spring is stretched by 0.316 m, when force is exerted.
What is Hooke's law?If a spring is stretched from its equilibrium position, then a force with magnitude proportional to the increase in length from the equilibrium length is pulling each end.
F = kx
where k is the proportionality constant called the spring constant or force constant.
Given, a screen door spring has a spring constant of 188 N/m, and when stretched, a 59.5 N force is applied on the door.
Substitute the values, we get
59.5 = 188 x
x = 0.316 m
Thus, the spring is stretched by 0.316 m, when force is exerted.
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At one instant an electron is moving in the positive x direction along the x axis in a region where there is a uniform magnetic field in the positive z direction. When viewed from a point on the positive z axis, it subsequent motion is:
When viewed from a point on the positive z-axis (looking downward), the subsequent motion of the electron in a region with a uniform magnetic field in the positive z-direction will be in a circular path around the z-axis. This path is perpendicular to both the electron's velocity vector and the magnetic field direction.
The motion of charged particles like electrons in a magnetic field is governed by the Lorentz force equation:
F = q * (v x B)
where:
F is the magnetic force acting on the electron,
q is the charge of the electron,
v is the velocity of the electron,
B is the magnetic field vector.
Since the velocity of the electron (v) is in the positive x-direction, and the magnetic field (B) is in the positive z-direction, the cross product (v x B) will result in a force perpendicular to both the x and z axes. This force causes the electron to move in a circular path around the z-axis.
This motion is commonly referred to as circular motion in a magnetic field, and it is similar to the way charged particles move in a cyclotron or a particle accelerator. The electron will continue to move in this circular path as long as it remains in the region with the uniform magnetic field and no other forces act on it.
Hence, When viewed from a point on the positive z-axis (looking downward), the subsequent motion of the electron in a region with a uniform magnetic field in the positive z-direction will be in a circular path around the z-axis. This path is perpendicular to both the electron's velocity vector and the magnetic field direction.
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What is the law of conversation of energy?
Answer:
the law of conservation of energy states that the total energy of an isolated system remains constant; it is said to be conserved over time
Explanation:
A heat pump is to be used for heating a house in winter. The house is to be maintained at 70°F at all times. When the temperature outdoors drops to 40°F, the heat losses from the house are estimated to be 75,000 Btu/h. Determine the minimum power [Btu/h] required to run this heat pump if heat is extracted from the outdoor air at 40°F.
Answer:
[tex]\dot{W_{H} } = 4244.48 Btu/h[/tex]
Explanation:
Temperature of the house, [tex]T_{H} = 70^{0} F[/tex]
Convert to rankine, [tex]T_{H} = 70^{0}+ 460 = 530 R[/tex]
Heat is extracted at 40°F i.e [tex]T_{L} = 40^{0}F = 40 + 460 = 500 R[/tex]
Calculate the coefficient of performance of the heat pump, COP
[tex]COP = \frac{T_{H} }{T_{H} - T_{L} } \\COP = \frac{530 }{530 - 500 }\\ COP = \frac{530}{30} \\COP = 17.67[/tex]
The minimum power required to run the heat pump is given by the formula:
[tex]\dot{W_{H} } = \frac{\dot{Q_{H} }}{COP} \\[/tex]...............(*)
Where the heat losses from the house, [tex]\dot{Q_{H} } = 75,000 Btu/h[/tex]
Substituting these values into * above
[tex]\dot{W_{H} } = \frac{75000}{17.67} \\ \dot{W_{H} } = 4244.48 Btu/h[/tex]
Why is the weight of an object more on Earth than the Moon
Answer:
Due to gravity on the earth but on moon there is 1/6th of the gravity than on earth. Since the acceleration of gravity Is lesser in moon and weight is constant, the weight of an object is lesser on the surface of the moon.
Explanation:
Answer: C.
The gravitational pull of Earth is greater than that of the Moon.
Explanation: plato
When astronauts are in the International Space Station, they can breathe normally in their living areas. However, when they go on a spacewalk to work on the Space Station, to repair or replace parts, they must be in a spacesuit. Why must they have their own supply of oxygen within the spacesuit?
Astronauts must have their own supply of oxygen in their spacesuits during spacewalks due to the absence of breathable air in the vacuum of space, and to protect them from harmful solar radiation and the extreme temperatures of space. The suits also maintain positive pressure relative to the outside to prevent air from the vacuum of space from entering the suit if a leak occurs.
Explanation:Astronauts must have their own supply of oxygen within their spacesuits during spacewalks because outer space does not have an atmosphere like the Earth which contains beneficial and breathable air; instead, space is a vacuum. This absence of atmosphere leaves astronauts exposed to the direct speed and force of solar radiation which can be harmful and potentially lethal. Their spacesuits, equipped with their own oxygen supply, not only enable astronauts to breathe but also serve as a barrier to protect them from this radiation and the extreme temperatures of space. The suit also maintains a positive pressure relative to the outside, ensuring that if a leak occurs, air will flow out of the suit, not into it from the vacuum of space.
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How do scientists determine the elements present in different stars
Answer:
Thus, astronomers can identify what kinds of stuff are in stars from the lines they find in the star's spectrum. This type of study is called spectroscopy. ... From spectral lines astronomers can determine not only the element, but the temperature and density of that element in the star.
Explanation:
Scientists use spectroscopy to identify the elements present in stars by analyzing the light they emit. The distinct atomic spectra for each element acts as a fingerprint, allowing astronomers to understand a star's composition and its evolution over time.
Scientists determine the elements present in different stars by using spectroscopy to analyze the light those stars emit. Each chemical element has a unique atomic spectrum, either emitting or absorbing specific wavelengths of light, identifiable through spectroscopic techniques. By comparing the observed spectra with known spectra obtained in laboratories, astronomers can deduce the elements that make up a star. Stars primarily consist of hydrogen and helium, but the presence of heavy elements, such as iron, varies, offering insight into their composition and history.
The study of light elements like lithium, beryllium, and boron in stars, as compared to heavier ones, can illuminate the processes of stellar evolution and the creation of new stellar and planetary bodies. Information from stars' spectra, including subtle shifts due to Doppler effect adjustments for radial velocity, allows scientists to understand not only a star's chemical makeup but also its motion in space. Thus, spectroscopy is a powerful tool for uncovering the secrets of celestial bodies, from individual stars to distant galaxies.
Which factors affect the resistance of a material? Check all that apply.
length
currer
thickness
temperature
voltage
Answer: Length, thickness, and temperature
Explanation:
I did it
Resistance of a material is affected by its length, thickness, temperature, and type of material; voltage does not determine resistance.
Explanation:The factors that affect the resistance of a material include the length of the resistor, thickness of the resistor, the temperature of the conductor, and the type of material. Length affects resistance because the longer a conductor, the more collisions charges will make with its atoms, increasing resistance. The thickness of a resistor affects resistance inversely; a thicker conductor has a greater cross-sectional area, allowing more current to flow and decreasing resistance.
The temperature affects resistance because as a conductor gets hotter, the atoms vibrate faster, increasing kinetic energy and making it more difficult for the electric current to flow. Different materials also have different inherent resistances due to their atomic structures. Voltage does not affect resistance; rather, resistance determines how much voltage is required to drive a certain current through a conductor.
The permanent bar magnet is moved to the left, toward a loop of wire (as shown). The north pole of the magnet is closer to the loop, as shown. What direction will the (induced) magnetic field be in the center of the loop of wire?
The direction of the induced magnetic field will be the same as the direction of the external magnetic field.
The Direction of magnetic field:As per Felhming's right-hand rule: The direction of the magnetic field is perpendicular to the wire and is in the direction of the fingers of your right hand.
The direction of induced current in the coil is clockwise. Since the magnet is being moved away, the magnetic flux linked with the coil must be decreasing. Hence the induced magnetic field must be in the same direction as the external magnetic field.
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If a thunder clap comes 1.5 s after the lightning strike, how far away is the
strike?
Answer:
514.5 meters
1687.9921 feet
Explanation:
speed of sound = 343 m/s
1.5 (seconds) x 343 (m/s) = 514.5 meters
The distance of the lightning strike is approximately 514.5 meters or 0.5145 kilometers away, calculated by multiplying the time delay of the thunder clap (1.5 seconds) with the average speed of sound (343 m/s).
Explanation:If a thunder clap comes 1.5 seconds after a lightning strike, you can estimate the distance of the strike from your location. Since the speed of sound varies with temperature, we'll use the average speed of sound at room temperature, which is approximately 343 meters per second. To calculate the distance, you multiply the time it takes to hear the thunder (1.5 seconds) by the speed of sound (343 m/s), which equals to about 514.5 meters or roughly 0.5145 kilometers away.
how does the current in a resistor change if the voltage across the resistor is decreased by 4
According to Ohm's law, if the voltage across a resistor is decreased, the current flowing through it will decrease proportionally. This is because the current is directly proportional to the voltage while the resistance remains constant.
Explanation:The change in current flowing through a resistor, when the voltage across the resistor is decreased, can be explained using Ohm's law. According to Ohm's law, the voltage (V) across a resistor is equal to the product of the current (I) that passes through it and its resistance (R). The relationship is given by the formula V = IR.
If the voltage across the resistor is decreased, it would result in a decrease in the current through the resistor. For instance, if the voltage is decreased by 4 units, the current will drop by a factor that is equal to '4 divided by the resistance (R).' This is because current is directly proportional to voltage, maintaining a constant resistance.
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The word inverse means ____ and is an alternative word for __________ relationship.
A. same, direct
B. opposite, direct
C. opposite, indirect
D. same, indirect
Answer:
B - Opposite, and direct
The word inverse means c) opposite and is an alternative word for indirect relationship.
In mathematics, this often refers to a situation where one value increases while the other decreases, creating a contrasting effect between the two variables.
Types of Relationships: When discussing relationships between variables:
A direct relationship means that as one variable increases, the other variable also increases.
An inverse relationship, on the other hand, indicates that as one variable increases, the other decreases.
In this context, the question asks for an alternative word for inverse relationships. The correct option would be that it is an alternative word for an indirect relationship since as one variable goes up, the other goes down, highlighting the opposite effect.
The frequency of a tornado siren is 1,000 Hz. If a cyclist is moving toward the siren at 10 m/s in 15 °C air, which has a speed of sound of 340 m/s, what is the frequency that the cyclist observes?
Answer:
The frequency the cyclist observes is 1029.412 Hz
Explanation:
Here we have that the frequency is given by the relation;
[tex]f_{obs} = f_{source}\left (\frac{v \pm v_{obs}}{v \pm v_{source}} \right )[/tex]
Where:
[tex]f_{obs}[/tex] = Frequency sensed by the observer
[tex]f_{source}[/tex] = Frequency emitted by the source = 1,000 Hz
v = Velocity of sound in air
[tex]v_{obs}[/tex] = Speed of observer = + 10 m/s
[tex]v_{source}[/tex] = Speed of source = 0 m/s
Plugging in the values, we have;
[tex]f_{obs} =1000 \times \left (\frac{340 + 10}{340 + 0} \right ) = 1000 \times \left (\frac{350}{340 } \right ) = 1029.412 \ Hz[/tex]
Therefore, the frequency the cyclist observes = 1029.412 Hz.
The phenomenon described in the question is known as the Doppler Effect, used to explain why a moving observer perceives a change in frequency. Given the conditions in the problem, the cyclist would perceive the siren's frequency to be approximately 1029.4 Hz instead of 1000 Hz.
Explanation:The phenomenon described in the question relates to the Doppler Effect, which involves a change in frequency of a wave (in this case, sound) due to the relative motion between the source of the wave and the observer.
When the observer is moving towards the source of a sound, the frequency they perceive is higher than the actual frequency of the sound. This perceived frequency (f') can be calculated using the formula:
f' = f * (v + vo) / v
Where: f is the actual frequency, v is the speed of sound, and vo is the speed of the observer (cyclist).
Substituting the given values:
f' = 1000 Hz * (340 m/s + 10 m/s) / 340 m/s = 1029.4 Hz
Therefore, the cyclist will observe a frequency of approximately 1029.4 Hz.
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ASAP -Will give brainliest - Look at the graph below. Which of these lines represents the fastest moving object?
Answer:
Purple
Explanation:
They've all gone for the same amount of time, but purple is pointed the highest
pls vote me brainliest
What does it mean when energy is conserved? How are energy and work related? What are the two basic types of energy and how are they related?
kenetic and potential
What is the difference between internal hardware and software?
Internal hardware is the physical parts of a computer that you see on the outside; software is the physical parts of a computer that you see on the inside.
Internal hardware is the physical parts of a computer that you see inside the computer; software is the physical parts of a computer that you see on the outside.
Internal hardware is the programs and applications that make the computer work; software is the physical parts that help the computer work.
Internal hardware is physical parts that help the computer work; software is the programs and applications that make the computer work.
Answer:
Internal hardware is physical parts that help the computer work; software is the programs and applications that make the computer work.
Explanation:
Credit to the guy above me
The difference between internal hardware and software lies in their physical nature and functions within a computer system. Internal hardware refers to the tangible components of a computer, while software consists of the programs and applications that enable the computer to perform tasks.
The difference between internal hardware and software lies in their physical nature and functions within a computer system. Internal hardware refers to the tangible components of a computer, such as the motherboard, processor, memory, and storage devices, that are housed inside the computer's casing. These components work together to enable the computer to perform tasks.
On the other hand, software refers to the intangible programs and applications that are installed on the computer and instruct the hardware on how to perform specific tasks.
For example, the operating system (e.g., Windows, macOS, Linux) is a type of software that manages and controls the computer's hardware, allowing users to interact with the computer and run other software applications.
Applications like word processors, web browsers, and media players are also examples of software that users can install and use on their computers.
In summary, internal hardware comprises the physical components of a computer, while software consists of the programs and applications that enable the computer to perform tasks.
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Uranus is a pale green planet, with 27 satellites and several rings.
True or False
P.S what subject would this be
Hi,
All of it is true. :
Uranus is a pale green planet, with 27 satellites and several rings.
Describe each type of biotechnology:
Genetic engineering:
Cloning:
Artificial selection:
Answer:
Genetic Engineering: the direct manipulation of an organisms genes using biotechnology (ex. genetically engineering corn to be insect resistant)
Cloning: The process of producing genetically identical individuals of an organism either natually or artificially,cloning allows for the creation of multiple copies of genes, expression of genes, and study of specific genes (ex. Cloning cells for untreatable diseases)
Artificial Selection: Also known as Selective breeding it is the process by which humans use animal breeding and plant breeding to selectively develop particular phenotypic traits/ characteristics (ex. Dog breeding)
Answer:
Genetic Engineering :
Benefits
-Ability to create food that is resistant to pests, cold, and disease
-Greater food production volume and increased vitamins
Risks
-Concerns about long-term health risks
-Lack of regulation
Cloning
Benefits
-Ability to increase endangered animal populations
-Possibility of eliminating diseases and defective genes
Risks
-Shorter lifespan for cloned animals
-Greater chance of health issues for cloned animals
Artificial Selection
Benefits
-Allows for selection of desired traits
-Ability to create better versions of organisms
Risks
-Loss of genetic diversity
-Increased chance of diseases that can shorten lifespan
Explanation:
This is straight from the lesson 6.01 page 5 (FLVS)
A wheel is used to turn a valve stem on a water valve. The wheel radius is 4 inches and the axle radius is .25 inches.
a)What is the mechanical advantage of the wheel and axle?
b)How much resistance force can be overcome when an effort of 6 lbs is applied to the wheel of the water valve in this problem?
Answer:
a) Mechanical advantage of the wheel and axle is 16b) The resistance force that can be overcomed with the effort is 96lbsExplanation:
Mechanical Advantage of a wheel and axle is defined as the ratio of the load on the axle to the effort applied on the wheel. It can also be described as the ratio of the radius of the wheel (larger radius) to the radius of the axle (smaller radius).
Mechanical advantage = Load/ Effort = R/r
Given the wheel radius as 4 inches and the axle radius as 0.25 inches.
MA = R/r = 4/0.25
MA = 16
Mechanical advantage of the wheel and axle is 16
b) Using the formula Mechanical Advantage = Load/ Effort
Given MA = 16, Effort = 16lbs, Load =?
On substitution, 16 = Load/6
Load = 16*6
Load = 96lbs
The resistance force that can be overcomed with the effort is 96lbs
Please help this determines my grade! A 25 V battery is connected into a circuit with two resistors in series. One resistor has resistance 5.0 Ω and the other has resistance 7.5 Ω. What is the voltage drop across the 7.5 Ω resistor?
15 V
25 V
10 V
0 V
The answer is V=25(7.5/(7.5+5)).
This is the voltage divider equation.
I hope this helps!
Answer:
I am so sorry
Explanation:
if your still here. Have you taken the algebra 2 B unit 8 semester B exam??
The magnitude and direction exerted by two tugboats towing a ship are 1620kilograms, N35degreesW,and 1250kilograms, S50degreesW,respectively. Find the magnitude, in kilograms, and the direction angle, in degrees, of the resultant force.
Answer:
Magnitude (in kilogram) of the resultant force, [tex]|M| = 1958.53 kg[/tex]
Direction = 164.37°
Explanation:
The two forces exerted by the two tugboats are non zero vectors, therefore they can be expressed as:
For the 1620 kg tugboat in the direction N35degreesW
[tex]M_{1} = 1620 cos \theta_1 i + 1620 sin \theta_1 j\\[/tex]
The direction of the force from the positive x - axis, [tex]\theta_1 = 90 - 35 = 55^{0}[/tex]
The equation above then becomes:
[tex]M_{1} = 1620 cos 55 i + 1620 sin 55 j\\ M_{1} = (1620 * 0.57) i + (1620*0.82) j\\M_{1} = 923.4 i + 1328.4j[/tex]
For the 1250 kg tugboat in the direction S50degreesW
[tex]M_{2} = 1250 cos \theta_2 i + 1250 sin \theta_2 j\\[/tex]
The direction of the force from the positive x - axis,
[tex]\theta_2 = - (90 - 50) = - 40^{0}[/tex]
The equation above then becomes:
[tex]M_{2} = 1250 cos(-40) i + 1250 sin (-40) j\\ M_{2} = (1250 * 0.77) i - (1250*0.64) j\\M_{2} = 962.5 i - 800j[/tex]
The resultant vector will be given by:
[tex]M = M_{1} + M_{2} \\ M = 923.4 i + 1328.4j + 962.5 i - 800j\\M = 1885.9i + 528.4j[/tex]
The magnitude of the resultant is given by:
[tex]|M| = \sqrt{1885.9 ^{2} + 528.4^2 } \\|M| = \sqrt{3556618.81 + 279206.56}\\|M| = \sqrt{3835825.37} \\|M| = 1958.53 kg[/tex]
The direction will be given by :
[tex]cos \theta = \frac{a}{|M|} \\cos \theta = \frac{1885.9}{1958.53}\\cos \theta = 0.963\\\theta = cos^{-1} 0.963\\\theta = 15.63^0[/tex]
Direction = 180 - 15.63 = 164.37°