The tension in the string is 0.344 Newton, if the mass of the ball is 4.5 gm and the charge on the ball is 5 μc in an electric field of 6×10⁴ N/C.
Mass of the ball, m = 4.5 gm = 4.5 × 10⁻³ kg
Weight of the ball, w = 4.5 × 10⁻³ × 9.81 = 44.145 × 10⁻³ N = 0.044 N
Charge on the ball, q = 5 μC = 5 × 10⁻⁶ C
Intensity of electric field, E = 6×10⁴ N/C
Downward force on the ball due to charge, F = qE
F = 5 × 10⁻⁶ × 6×10⁴ = 0.3 N
Total downward force = 0.3 + 0.044 = 0.344 N
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What are the magnitude and direction of the electric force on an electron in a uniform electric field of strength 3075 N/C that points due east?
The magnitude of electric force on an electron is calculated to be 4.92 × 10⁻¹⁶ N and the direction is due west.
The electric field strength facing straight east is E = 3075 N/C.
The magnitude of the charge on an electron is q = e = 1.6 × 10⁻¹⁹ C
In a uniform electric field with a strength of 3075 N/C and a direction of straight east, we are asked to determine the size and direction of the electric force acting on an electron. Due to the electron's negative polarity charge. The electric force acting on the electron in the electric field will therefore move in the opposite direction of the electric field. So, the direction of the electric force on the electron will be due west.
Calculating the strength of the electric force acting on the electron in the electric field is also required of us. As a result, we can use the following formula to describe the electric force acting on a charged particle in a consistent electric field:
F = q E = 1.6 × 10⁻¹⁹ × 3075 = 4920 × 10⁻¹⁹ N = 4.92 × 10⁻¹⁶ N
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A projectile is fired with an initial speed of 500m/sec at an angle of elevation of 45o. How high overhead with the projectile be when it is 5 km downrange?
Initial velocity: 500 m/s Height: 19.6 m
Therefore, the y-direction motion equation is:
19.6/4.9 =t 2 t 2 =4 t=2s, where s=ut+ 1/2 at 2 19.6=0+ 1/2 9.8t 2
Consequently, the x-direction is the equation of motion.
s=ut+ 1/2 at 2
s=500×2=1000m
where u=5000m/s, t=2s, and a=0
Thus, it hits the earth at a distance of 1000 metres from the base of the cliff.
Why does velocity matter?
The motion's rate and direction are measured vectorially via this. Simply said, velocity is the rate of movement in a specific direction. As an illustration, think of the speed of a car driving north on a highway or the speed at which a rocket takes off.
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an electric charge with charge q is placed in an electric field with field magnitude e. due to the field, the charge experiences a force f. if the charge is doubled and the field tripled, how much force is then exerted on the charge?
If the charge is doubled and the field tripled, the force has increased by a factor of 6.
The electric force experienced by a charge q in an electric field E is given by Coulomb's law:
f = q X E
where q is the charge and E is the electric field magnitude.
If the charge is doubled to 2q and the electric field magnitude is tripled to 3E, the force experienced by the charge becomes:
f' = 2q X 3E
= 6q X E
So, the new force experienced by the charge is 6 times the original force. This means that the force has increased by a factor of 6.
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activity 3 response: as an investigation of scientific question b, consider an object that is not the human body, but that also has a consistently higher temperature than the environment. describe how its thermal energy content should change with time. how would you expect the temperature of the object to change with time? how is it able to stay at a hotter temperature than the surroundings, even though heat is constantly flowing?
The thermal energy content of the object should decrease over time as heat is transferred from the object to the environment.
What is thermal energy?Thermal energy is the energy that is generated from the movement of molecules in a material. It is a form of kinetic energy, or energy that is being moved. Thermal energy is generated from the heat of the sun and is the main form of energy that powers the Earth’s climate system.
As heat flows from the object to the surrounding environment, the object will cool down until it reaches the same temperature as the environment. This is because the thermal energy content of the object is determined by the temperature of the object and the temperature of the environment is lower than the temperature of the object.
To stay at a hotter temperature than the surroundings, the object must constantly absorb more heat than it releases. This can be done through processes such as conduction and convection, where the object will absorb heat from its surroundings. Additionally, the object can also absorb heat from the sun or other sources of heat. As long as the object is absorbing more heat than it is releasing, it will remain at a higher temperature than the environment.
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a positively charged test particle is placed midway between two fixed, identical positively charged source particles. part a is the test particle in a stable or unstable equilibrium at that location?
a) The test particle is in a stable equilibrium regardless of dimensionality.
b) The test particle is in stable equilibrium if these particles are constrained to one dimension and in unstable equilibrium if the particles can move in at least two dimensions.
c) The test particle is in stable equilibrium if these particles are constrained to one or two dimensions and in unstable equilibrium if the particles can move in three dimensions.
d) The test particle is in an unstable equilibrium regardless of dimensionality.
b) The test particle is in stable equilibrium if the moving particles can only travel in one dimension, and in unstable equilibrium if they can move in at least two dimensions.
In this case, the dimensionality of the system affects the test particle's stability. The test particle will be in a stable equilibrium if the system is limited to one dimension. The test particle is in this case equally far from the two source particles, and as a result, each of them exerts electrostatic forces on it that are equal and opposing and cancel one another out. As a result, the test particle doesn't move from its place.
The test particle, on the other hand, is in an unstable equilibrium if the system exists in two or more dimensions.
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Miguel threw a baseball a distance of 40 meters. It hit the ground in 5 seconds.
The velocity of the baseball is: 8 m/s
What is velocity?It is a physical quantity that indicates the displacement of a mobile per unit of time, it is expressed in units of distance per time, for example (miles/h, km/h).
The formula and procedure we will use to solve this problem is:
v= x/t
Where:
x = volumet = timev = velocityInformation about the problem:
x = 40 mt= 5 sv = ?Applying the velocity formula we get:
v= 40 m/5 s
v= 8 m/s
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Suppose you are testing the hypotheses H0: π = 0.25 and Ha: π < 0.25 and the observed statistic, pˆ is equal to 0.30 with a sample size of 100.
a. If you are using a proportion as your statistic, where do you expect your null distribution to be centered?
b. If you are using a count as your statistic, where do you expect your null distribution to be ce
a. If you are using a proportion as your statistic, you expect your null distribution to be centered at 0.25.
b. If you are using a count as your statistic, you expect your null distribution to be centered at n * π = 25, where n is the sample size.
The null hypothesis H0: π = 0.25 states that the population proportion (π) of a binary outcome is equal to 0.25. The observed statistic, pˆ, is the sample proportion, which is calculated from the sample data.
When testing the hypothesis, you would compare the observed statistic, pˆ, to the expected value under the null hypothesis, which is π = 0.25. If pˆ is significantly different from 0.25, you would reject the null hypothesis and conclude that the population proportion is not equal to 0.25.
In this case, you are counting the number of successes (e.g., the number of individuals with a certain trait) out of the sample size (n = 100) and using this count as the statistic. The expected value under the null hypothesis is n * π = 100 * 0.25 = 25.
Like in the case of using a proportion as the statistic, if the observed count is significantly different from the expected value under the null hypothesis, you would reject the null hypothesis and conclude that the population proportion is not equal to 0.25.
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Two masses m1 = 15 kg amd m2 = 25 kg are joined by connecting a rod of length 0.8 m. Determine the
distance of the CM of the system from the m1 if a.) the connecting rod is massless, and b.) the connecting
rod is a uniform rod of mass 15 kg.
(a) The center mass when the connecting rod is massless is 0.5 m.
(b) The center mass when the connecting rod has a mass of 15 kg is 0.47 m.
What is the center mass of mass m1?The center mass of m1 is calculated by applying the following formula for center of gravity.
Cm = ( m1x₀ + m2x₁ ) / ( m1 + m2 )
since we are looking for the center mass of m1, we use it as the reference point.
when the connecting rod is massless,
Cm = ( 15kg x 0 + 25kg x 0.8 m ) / ( 15 kg + 25 kg )
Cm = 0.5 m
when the connect rod has a mass of 15 kg;
Cm = ( 15 kg x 0 + 15 kg x 0.4 m + 25 x 0.8 m ) / ( 15 kg + 15kg + 25 kg )
Cm = 0.47 m
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who is going to watch the mars occupation tonight?
that's happening ?????
Could a planet with a composition similar to that of the Earth have formed around a first-generation star? Explain your answer.No. First-generation stars formed from nebulae that had only elements 1 through 5 on the periodic table, whereas Earth's core is composed primarily of iron (26 on the periodic table).
No, a planet with a composition similar to that of the Earth could not have formed around a first-generation star.
First-generation stars, also known as Population III stars, form from nebulae consisting primarily of hydrogen, helium, and a small amount of heavier elements such as carbon, nitrogen, and oxygen. The material from which these stars formed did not contain enough heavy elements to form planets like Earth.
The core of Earth, in particular, is composed primarily of iron, which was not present in the material from which first-generation stars formed. Later generations of stars, formed from nebulae enriched in heavy elements, eventually produced the material from which Earth and other terrestrial planets could form.
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6. How long does it takes a swimmer with a power output of 275 watts to accomplish
3600 J of work? If she applied a 650 N force during that time with the same power
output, how far did she swim? SHOW YOUR WORK.
It takes 13.1 seconds for a swimmer with a power output of 275 watts to accomplish 3600 J of work. If she applied a 650 N force during that time with the same power output, she would have swam up to 5.54 meters.
In physics, power is the amount of energy that is converted or delivered in a given amount of time. The unit of power is the watt, which in the International System of Units is equivalent to one joule per second. In ancient literature, power is occasionally referred to as activity. A scalar quantity is power.
We know that
power = work / time
⇒ time = work / power
= 3600 / 275 = 13.1 seconds
Thus, It takes 13.1 seconds for a swimmer with a power output of 275 watts to accomplish 3600 J of work.
We also know that
power = (force × distance) / time
⇒ distance = (power × time) / force
= (275 watts × 13.1 seconds) / 650 N
= 5.54 meters
Thus, If she applied a 650 N force during that time with the same power output, she would have swam up to 5.54 meters.
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Predict the brightness on the distant screen if the path difference is exactly one wavelength λ (or any integer d sin θ number of wavelengths)? Explain your reasoning
If the path difference is exactly one wavelength, the screen will be at maximum brightness.
The brightness on a distant screen depends on the interference of light waves. If the path difference between two light waves is an integer number of wavelengths, then the waves will be in phase and constructively interfere, leading to maximum brightness on the screen.
If the path difference is exactly one wavelength (or any integer multiple of a wavelength), the light waves will have a phase difference of zero and will reinforce each other to produce maximum brightness.
This phenomenon is known as constructive interference and occurs when the crests of two light waves coincide.
Constructive interference produces the brightest regions on the screen and is an important aspect of many optical systems and applications, including diffraction gratings, holography, and interferometry.
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What are some examples of system variables(forensics)
Lineups, photo arrays, and other identification procedures are some examples of system variables(forensics).
What are system variables(forensics)?The criminal justice system should and can control system factors. They comprise any technique used by law enforcement to access and document witness recollection, including lineups, photo arrays, and other identification processes.
The type of lineup used, the choice of "fillers," blind administration, instructions to witnesses prior to identification procedures, administration of lineups or photo arrays, and communication with witnesses after they make an identification are system variables that significantly affect the accuracy of identifications.
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When a cannon fires a cannon ball, the cannon will recoil backwards because the...
a) energy of cannon ball and the cannon is conserved
b) momentum of cannon ball and the cannon is conserved
c) energy of the cannon is greater than the cannon ball
d) Momentum of the cannon is greater than the cannon ball.
b) momentum of cannon ball and the cannon is conserved.
According to the law of conservation of momentum, when an object, such as a cannon ball, is fired from a cannon, the momentum of the system (cannon ball and cannon) remains constant before and after the firing.
This means that the total momentum of the system before firing is equal to the total momentum of the system after firing. To conserve the momentum of the system, the cannon ball moves in one direction with a certain momentum while the cannon moves in the opposite direction with an equal amount of momentum, resulting in a recoil of the cannon.
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the widest part of an ellipsoidal microorganism observed under 4x magnification spans to the 18thdivision on the ocular microscope. what is the actual size of the microorganism?
A. 12 μm
B. 18 μm
C. 72 μm
D. 180 μm
E. 216 μm
Option C. 72 μm is coorrect. The actual size of the microorganism can be calculated by multiplying the size observed under the microscope with the magnification factor.
The calculation of actual size of a microorganism observed under a microscope is a crucial step in microbiology. This is because the actual size of a microorganism is necessary to determine its classification, morphology and other characteristics.
When using a light microscope, the size of an object is determined by using the ocular micrometer, which is a scale etched onto the lens of the eyepiece. The ocular micrometer allows you to accurately measure the size of an object by comparing its size to the scale etched onto the eyepiece. The ocular micrometer is calibrated to represent a specific magnification, and the actual size of an object can be calculated by multiplying the size observed under the microscope with the magnification factor.
In this case, the microorganism was observed under 4x magnification, and the widest part of the microorganism spanned to the 18th division on the ocular microscope. Therefore, the actual size of the microorganism would be 18 * 4 = 72 μm.
It's important to note that the actual size of a microorganism may change based on the type of microscope used, the sample preparation method, and other factors. Therefore, it's essential to accurately determine the actual size of a microorganism for accurate analysis and interpretation of results.
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What is 80 °C in Fahrenheit?
In Fahrenheit, 176 degrees are equal to 80 degrees Celsius.
What is Fahrenheit?In honour of physicist Daniel Gabriel Fahrenheit, a temperature scale is named Fahrenheit. At standard air pressure, it measures temperature using water at 32°F for the freezing point and 212°F for the boiling point.
How do you calculate it?The formula is F = (C * 9/5) + 32, where F is the temperature in Fahrenheit and C is the temperature in Celsius, can be used to convert a temperature from Celsius to Fahrenheit.
It is significant to observe that there is not an equal difference between each temperature increment on the two scales. One degree Celsius is equal to 1.8 degrees Fahrenheit. As a result, a temperature change from 20°C to 21°C is similar to one from 68°F to 69.8°F.
In conclusion, translating 80°C to 176°F allows us to better appreciate its significance on the Fahrenheit scale.
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Choose the correct explanation why does the following statement make sense (or is clearly true) or does not make sense (or is clearly false):
"I've never been to space, so I've never experienced weightlessness."
This assertion is illogical. On Earth, everyone can experience weightlessness; all it takes is a sufficiently extended freefall.
What is the real name of Earth?Contrary to common opinion, Earth lacks an accepted name on a global scale. Another widespread misunderstanding of a planet's scientific name is "Terra." English speakers keep referring to the planet as Earth, including in analytical study.
Who named Earth Earth?Earth does not explicitly share a name in English with a prehistoric Roman deity, unlike other planets within the Solar System. The Anglo-Saxon term erda, which meaning ground or soil and ultimately descended from Proto-Indo European *er, was used to give the planet its name in the eighth century.
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How much charge is on each plate of a 3.00-µF capacitor when it is connected to a 16.0-V battery?
Charge on each plate of 3.00µF capacitor is 48C when it is connected to a 16.0-V battery.
The capacitors capacity to store this electrical charge ( Q ) between its plates is corresponding to the applied voltage, V for a capacitor of known capacitance in Farads. Note that capacitance C is Dependably sure and never negative.The more prominent the applied voltage the more noteworthy will be the charge put away on the plates of the capacitor.
Moreover, the more modest the applied voltage the more modest the charge. Hence, the genuine charge Q on the plates of the capacitor and can be determined as:Capacitance is the deliberate worth of the capacity of a capacitor to store an electric charge. This capacitance esteem likewise relies upon the dielectric consistent of the dielectric material used to isolate the two equal plates. Capacitance is estimated in units of the Farad (F), so named after Michael Faraday.
So,we know that charge on capacitor is equal to=capacitance×Voltage
=>Q=C×V
We have C=3.00-µF ,V=16V
=>Q=3×16
=>Q=48Columb.
Hence,charge on each plate is 48C.
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consider two identical fans, one at sea level and the other on top of a high mountain, running at identical speeds. how would you compare (a) the volume flow rates and (b) the mass flow rates of these two fans?
Two identical fans, one at sea level and another on top of a high mountain with identical speeds have:
Equal volume flow ratesDifferent mass flow rates, the one at sea level will have higher mass flow ratesVolume flow rate defines the volume of a fluid passing through a given cross sectional area per unit time. Volume flow rate can be calculated using formula:
Q = V / t
where:
Q = volume flow rate
V = volume
t = time
Mass flow rate refers to the mass of a fluid passing through a given cross sectional area per unit time. Mass flow rate can be defined by deviding the changes of fluid's mass with the change of time. Mass flow rate can be calculated using formula of:
mass flow rate = ρ x A x V
where:
ρ = density of fluid
A = cross sectional area
V = velocity
Based on both formulas, we know that volume flow rates only depends on the volume of the fluid, meanwhile mass flow rate depends on the density of fluid. As we know, the air density at sea level is higher than the top of mountain. This will cause the mass flow rate of a fan at sea level will be higher than the one on top of a high mountain.
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How to convert 2.5 centimeters to inches
The measurement of 2.5 centimeters is 0.9842 inches. One centimeter is equivalent to 0.393701 inches, and one inch is equal to 2.54 centimeters in measurement.
How much is a centimeter?A length measurement unit is the centimeter (cm). It is commonly used to measure shorter distances and is the same as 0.01 meters. It is also the metric system base unit of measurement and is used in rulers, pens, and other common household items. Because it is a part of the International System of Units (SI), it is also used in a lot of countries all over the world. 100 centimeters are equal to one meter, and 10 millimeters are equal to one centimeter.
Evaluating :Divide 2.5 by 2.54 to convert 2.5 centimeters to inches. There are 2.54 centimeters in one inch.
2.5 times 2.54 equals 0.9842 inches,
so 2.5 centimeters equal 0.9842 inches.
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What energy transformations occur at the macroscopic level?
Answer:electric
Explanation:
how much does 5 gallons of water weigh
Fresh water weights roughly 8.34 pounds per gallon, or a staggering 41.7 lbs for five gallons.
41.7 lbs.
What does "weight" mean in physics?
Weight is indeed the gravitational force that pulls objects toward the centre of the Earth. The resulting force that pulls a mass toward Earth is known as gravity. In contrast to gravitational force, which happens between any two masses, this only occurs among Earth and a mass. What is the weight called?
Weight: What Is It?
It gauges how much gravity is pulling on a body. Weight is calculated using the method w = mg. Since weight is a force.
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what is the line charge density on the wire?
The line charge density on a wire is the amount of electric charge per unit length on a wire. It is a measure of the distribution of electric charge along the length of a wire. The line charge density is calculated by dividing the total charge on the wire by the length of the wire.
In a conductor, electrons are free to move along the length of the wire, and the line charge density on the wire depends on the number of electrons and their distribution along the length of the wire. In an insulated wire, the line charge density is constant and uniform, while in a charged wire, the line charge density may vary along the length of the wire due to differences in the distribution of electrons.
The line charge density is an important concept in electromagnetism and electrical engineering. It is used to calculate the electric field and potential along a wire, as well as to determine the force between two charged conductors. Understanding the line charge density is important for the design and analysis of electrical circuits and systems, as well as for the study of fundamental electromagnetism phenomena.
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The quantity of electric charge present on a wire per unit length is known as line charge density. It is a measurement of the way electric charge is distributed along a wire's length.
Why would someone use the Wire app?With the aid of Wire, your team is able to interact and exchange information quickly, securely, and always in context. Your team can collaborate whether at the office or on the go thanks to Wire's availability on any platform and operating system.
Compared to signal, is wire safer?Neither has a serious security weakness, but both contain some flaws. As a person, it's likely impossible to find a safer app than Signal, which is fantastic for daily use. Businesses should seriously consider Wire, on the other hand.
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what the caused or operated by heat that has changed into different forms of energy
The caused or operated by heat that has changed into different forms of energy is known as "thermodynamics."
Thermodynamics is the branch of physics that studies the conversion of heat into other forms of energy, such as mechanical energy, electrical energy, and chemical energy. It deals with the laws that govern energy transformation and the relationships between energy, work, and heat.
Thermodynamics operates under the idea that heat is a form of energy that can be transferred from one body to another as a result of temperature differences. This transfer of heat can result in the conversion of heat into other forms of energy, such as when heat is used to produce steam that drives a turbine, generating electricity.
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a 82-kg athlete can climb 60 steps in 48 seconds. assuming the height of each step is 0.32 m, what is the average power output during the climb? (express result with no decimals followed by simplified is units)
The average power output by the athlete during the climb is equal to 321 joules per second or 321 watts.
In physics, power is defined to be work W over elapsed time t (P = W/t). Work is defined to be force F times displacement x (W = F · x). Weight is the force of gravity (Fg) and is equal to mass m times acceleration due to gravity g (Fg = m · g).
We are given that the athlete's mass is 82 kg and the acceleration due to Earth's gravity is 9.8 m/s², hence the athlete's weight is equal to 803.6 newtons. Also, the height of each of the 60 steps is 0.32 meters. The work done by the athlete then is Fg · x = 803.6 · (60 · 0.32) = 15,492.12 joules. Therefore, in 48 seconds the work done by the athlete is equal to 15,492.12 joules.
However, we haven't divide the work done by the elapsed time. The standard unit of power is watt (W — not to be confused with work W), and 1 watt is equal to 1 joule per 1 second (1 W = 1 J/s). We only need to divide the work done by 48 to get the average power output as follows:
15,492.12/48 = 321 J/s = 321 W.
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According to the big bang theory the universe began expanding about 13. 7 billion years ago and.
According to the Big Bang Theory, the universe began expanding about 13.7 billion years ago from a single, hot and dense point (aka, a singularity) in an event known as the Big Bang.
This event marked the beginning of space and time, and set in motion the expansion of the universe that continues today. Since then, the universe has been growing in size and complexity, and is now estimated to be over 13.8 billion years old.
The Big Bang Theory states that the universe was initially a very hot and dense state and has been continuously expanding and cooling ever since. This expansion is thought to be driven by the force of gravity, which pulls matter and energy together. As the universe expands, the matter and energy become more spread out, causing the temperature to drop. This cooling process has allowed for the formation of stars and galaxies, as well as the emergence of complex structures like planets, moons, and life.
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A block is pushed with a force of 15 newtons and accelerates at a rate of 3. 0 m/s2. How much force would be needed to accelerate the same block at a rate of 6. 0 m/s2?.
The force required to accelerate the given block at 6.0 m/s² is 30 N
According to the Newton's second law of motion
Force(F)= Mass(m) × Acceleration(a)
Here, Initial Force (F) = 15 Newton (N)
Initial acceleration (a) = 3.0 m/s²
Finding the mass (m) of the block from the above equation , F = m×a
Mass of the block = F/a = 5 g
Now, the force required to accelerate the given block of 5g at 6.0 m/s²
= 5g × 6.0 m/s² = 30 N
Hence, the force required to accelerate the given block of 5g at 6.0 m/s² is 30 N
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energy saving can be known as energy production and justify this statement
Energy produced from energy saved. We cannot keep producing non-sustainable resources like gas, diesel, and electricity.
How would you define energy conservation?The definition of energy conservation is the utilization of less electricity to carry out a task or achieve a goal. Homes, buildings, and manufacturing facilities that use less energy to manufacture things uses less power to heat, cool, and operate appliances and electronics.
What kind of energy is primarily produced?Any extraction of primary energy in a usable form from plant sources is considered primary energy production. This happens either during the extraction of natural resources (for instance, in coal, crude oil fields, or hydroelectric power plants) or during the production of biofuels.
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What happens when voltage-gated K+ channels open?
The potential of the membrane is shifted in a hyperpolarizing manner toward the K+ resting potential by the activating of Ion channels in cellular membranes and the resultant increase in K+ conductance.
What does the term "potential" mean?Countless noun When you refer to someone or something as having potential, you are referring to their potential to succeed or be beneficial in the future. The young man is quite talented. The school makes an effort to treat each student as an individual and to support them in realizing their full potential.
What are examples and potential?The potential advantages of the new medicine are exhilarating for doctors. The plant, according to critics, might endanger the environment. possible expansion of the institution. He could run for the office of president.
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a three-dimensional vector, →, has a magnitude of 12 units and makes angles 60° and 50° with the x- and z- axis, respectively. what is the y-component of →? A) 7.2(B) 7.0c 6.3(D 7.7(E 8.2
By the help of The directional cosines The y component is 7
The direction cosines of a vector in analytical geometry are the cosines of the angles that the vector makes with the three positive coordinate axes. They are, in essence, the contributions of each basis component to a unit vector pointing in that direction.
The directional cosines are linked to the direction or angle of a vector
[tex]\vec{a}[/tex]=[tex](a_x,a_y,a_z)[/tex] with reference to the three coordinate axes. The directional angles of [tex]\vec{a}[/tex]=[tex](a_x,a_y,a_z)[/tex] is the [tex]\alpha,\beta,\gamma[/tex] between x,y,and z ( vectors [tex]\vu{i}[/tex],[tex]\vu{j},\vu{k}[/tex])
are the vectors of [tex]\vec{a}[/tex] so the directional of cosines is
[tex]cos\theta=\frac{a_x}{||\vec{a}||}[/tex], [tex]cos\beta=\frac{a_y}{||\vec{a}||}[/tex],[tex]cos\theta=\frac{a_z}{||\vec{a}||}[/tex]
the fundamental property of cosines is :
[tex]cos^2\theta+cos^2\beta+cos^2\gamma=1[/tex]
solving for [tex]cos\beta:[/tex]
[tex]cos\beta=\sqrt{1-cos^2\(60-cos^2\ 50}[/tex]
[tex]cos\beta=0.58[/tex]
so , [tex]cos\beta=\frac{a_y}{||\vec{a}||}[/tex]
substituting[tex]{||\vec{a}||=12 \:and \:cos\beta=0.58[/tex] ,
[tex]a_y=12\times0.58[/tex]=6.96 or 7
Therefore the y component is 7
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