We first observe that the particle moves in the direction of the vector
[tex](3\,\vec\imath + 4\,\vec\jmath + 3\,\vec k) - (\vec\imath - \vec k) = 2\,\vec\imath + 4\,\vec\jmath + 4\,\vec k[/tex]
so the initial velocity vector [tex]\vec v_0[/tex] is parallel to this vector. Given its initial speed is 3 at [tex]t=0[/tex], this means for some scalar constant [tex]c>0[/tex], we have
[tex]\vec v_0 = 2c\,\vec\imath + 4c\,\vec\jmath + 4c\,\vec k[/tex]
such that
[tex]\|\vec v_0\| = \sqrt{(2c)^2 + (4c)^2 + (4c)^2} = 6c = 3 \implies c = \dfrac12[/tex]
so that the initial velocity is
[tex]\vec v_0 = \vec\imath + 2\,\vec\jmath + 2\,\vec k[/tex]
Now, use the fundamental theorem of calculus to compute the velocity and position functions.
[tex]\displaystyle \vec v(t) = \vec v_0 + \int_0^t \vec a(u) \, du \\\\ ~~~~ = (\vec\imath + 2\,\vec\jmath + 2\,\vec k) + \int_0^t (2\,\vec\imath + 4\,\vec\jmath+4\,\vec k) \, du \\\\ ~~~~ = (\vec\imath + 2\,\vec\jmath + 2\,\vec k) + (2t\,\vec\imath + 4t\,\vec\jmath+4t\,\vec k) \\\\ ~~~~ = (1 +2t)\,\vec\imath + (2+4t)\,\vec\jmath + (2+4t)\,\vec k[/tex]
[tex]\displaystyle \vec r(t) = \vec r_0 + \int_0^t \vec v(u) \, du \\\\ ~~~~ = (\vec\imath - \vec k) + \int_0^t \left((1 +2u)\,\vec\imath + (2+4u)\,\vec\jmath + (2+4u)\,\vec k\right) \, du \\\\ ~~~~ = (\vec\imath - \vec k) + ((t+t^2)\,\vec\imath + (2t+2t^2)\,\vec\jmath + (2t+2t^2)\,\vec k) \\\\ ~~~~ = (t^2+t+1)\,\vec\imath + (2t^2+2t)\,\vec\jmath + (2t^2+2t-1)\,\vec k[/tex]
An empty parallel plate capacitor is connected between the terminals of a 16.7-v battery and charges up. the capacitor is then disconnected from the battery, and the spacing between the capacitor plates is doubled. as a result of this change, what is the new voltage between the plates of the capacitor?
A car has two horns, one emitting a frequency of 199 hz and the other emitting a frequency of 203 hz. what beat frequency do they produce?
The beat frequency produced by two horns emitting frequencies of 199 Hz and 203 Hz is 4 Hz.
The question is regarding the production of beat frequency when two horns with different frequencies sound together. The two horns have frequencies of 199 Hz and 203 Hz, respectively.
To calculate the beat frequency, you subtract the smaller frequency from the larger frequency:
fbeat = |f1 - f2|
fbeat = |203 Hz - 199 Hz|
fbeat = 4 Hz
This means that the beat frequency produced by the two car horns is 4 Hz.
given current spacecraft technology, which of the objects in the table do you think it would be possible for you to travel to in your life-time?
A 170-lb man carries a 10-lb can of paint up a helical staircase that encircles a silo with radius 15 ft. if the silo is 40 ft high and the man makes exactly two complete revolutions, how much work is done by the man against gravity in climbing to the top? ft-lbs
The work is done by the man against gravity in climbing to the top with a 10 lb can of paint up a helical staircase that encircles a silo with a radius of 15 ft. If the silo is 40 ft high and the man makes exactly four complete revolutions is 670lb-ft.
What is Work done?
When an external force moves an object over a distance, at least a portion of that force must be exerted in the direction of the displacement .
Physics refers to this as work. If the force acting along the path is constant, the amount of work can be calculated by multiplying the length of the path by the force's component.
Formally, W = fd means that the work is equal to the force f times the length d. If the force is applied at an angle to the displacement, the work is W = fd cos.
Given:
The mass of man, m = 170 lb,
The mass of the can, M = 10 lb,
Calculate the work done y the following formula,
W = [tex]\int\limits^4_0 {170 -1 / 10y} \, dy[/tex]
Here W is work done
Integrate the above equation, and we get,
W = 670 lb ft.
Therefore, work is done by the man against gravity in climbing to the top with a 10 lb can of paint up a helical staircase that encircles a silo with a radius of 15 ft. If the silo is 40 ft high and the man makes exactly four complete revolutions is 670 lb ft.
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What is a correct way to measure wavelength
Bats can detect small objects such as insects that are of a size on the order of a wavelength. if bats emit a chirp at a frequency of 69.3 khz and the speed of sound waves in air is 330 m/s, what is the smallest size insect they can detect? give your answer in mm (millimeters)
How does natural selection result in adaptations in a species
What real-world examples show no work begin done? Can you think of examples other than resisting the force of gravity?
Answer:
Explanation:
The work done is defined as the product of force in the direction of displacement and the displacement.
Work done = force x displacement x Cos Ф
Where, Ф be the angle between force and the displacement vectors.
Work may be positive, negative or zero depending on the values of angle Ф.
The work done is zero when force is zero or displacement is zero or angle Ф is 90 degree.
So, when we apply a force on a body and body does not displace, then the work done is zero.
An elephant can hear sound with a frequency of 15 hz. what is the wavelength of this wave if the speed of sound in air is 343 m/s?
The wavelength of a sound wave with a frequency of 15 Hz and a speed of sound in air of 343 m/s is approximately 22.87 meters.
Explanation:To calculate the wavelength of the sound wave, we can use the formula:
Speed of sound (v) = wavelength (λ) x frequency (f)
Given that the frequency of the sound wave is 15 Hz and the speed of sound in air is 343 m/s, we can substitute these values into the formula to solve for the wavelength:
343 m/s = λ x 15 Hz
Dividing both sides of the equation by 15 Hz, we get:
λ = 343 m/s / 15 Hz = 22.87 meters (rounded to two decimal places)
Therefore, the wavelength of the sound wave is approximately 22.87 meters.
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A hot-air balloon plus cargo has a mass of 326 kg and a volume of 2310 m3 on a day when the outside air density is 1.22 kg/m3. the balloon is floating at a constant height of 9.14 m above the ground.
A cello string 0.75 m long has a 220 hz fundamental frequency. find the wave speed along the vibrating string. answer in units of m/s.
What are three benefits of being assertive and what are three tips to help you develop an assertive style of communication? (Site 1)
¿Cuál es la velocidad promedio de un hombre que camina 70m con una rapidez de 1m/s y luego corre 70m con una rapidez de 3m/s?
A cyclist is going in the positive x-direction at 9m/s. A car initially at rest, accelerates for the first 10 seconds, then it goes with a constant velocity. If the car reaches the cyclist after 15 seconds from the moment the car started moving, find: (a) The acceleration of the car during the first 10 seconds, (b) The velocity of the cyclist with respect to the car when the car reaches the cyclist
When a rocket is traveling toward a mountain at 100 m/s, the sound waves from this rocket's engine approach the mountain at speed v. if the rocket doubles its speed to 200 m/s, the sound waves from the engine will now approach the mountain at speed?
Answer:
The sound waves from the engine will approach the mountains at the same speed, no matter if the speed of the rocket is 100m/s or 200 m/s.
Explanation:
The sound wave is a property of the air, which means that the speed of the object producing sound does not matter to the sound of the waves, that is, they are always going to be the same.
So the sound waves from the engine will approach the mountains at the same speed, no matter if the speed of the rocket is 100m/s or 200 m/s.
Calculate the energy transferred when 4.6g of ice is melted at 0.0c
The energy transferred when 4.6g of ice is melted at 0.0C can be calculated using the formula Q = mLf, where Q is the heat needed to melt the ice, m is the mass of the ice, and Lf is the latent heat of fusion of water. Substituting the given values, we find that 1536.4 Jules of energy gets transferred.
Explanation:To calculate the energy transferred when ice is melted, we use the formula Q = mLf, where Q is the heat necessary to melt the ice, m is the mass of the ice, and Lf is the latent heat of fusion of the substance (the energy needed to change the substance from solid to liquid state without changing its temperature). For water, Lf is 334 kJ/kg. So, to find the energy needed to melt 4.6g of ice we rearrange the formula and find: Q = (4.6/1000 kg) x 334,000 J/kg = 1536.4 J. Therefore, 1536.4 Jules of energy gets transferred when 4.6g of ice melts at 0.0C.
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Having landed on a newly discovered planet, an astronaut sets up a simple pendulum of length 1.38 m and finds that it makes 441 complete oscillations in 1090 s. the amplitude of the oscillations is very small compared to the pendulum's length. what is the gravitational acceleration on the surface of this planet? answer in units of m/s 2 .
In Figure 18.8 the grounding wire is removed first, followed by the rod, and the sphere is left with a positive charge. If the rod were removed first, followed by the grounding wire, would the sphere be left with a charge? Account for your answer.
If the charged rod is removed before the grounding wire, the sphere will not retain a net charge because any excess charge will flow back to ground. Only if the grounding wire is removed while the rod is still present does the sphere retain an excess charge.
Explanation:If the grounding wire is removed after the charged rod is taken away, the sphere would be left with no net charge. This is because during the process of charging by induction, if the rod is removed first, any excess charge on the sphere would have the opportunity to redistribute evenly across its surface. Since the sphere was initially neutral and the grounding wire is still connected, the excess charge would flow to the ground, effectively bringing the sphere back to a neutral state.
On the other hand, as described in your references, if the grounding wire is removed first while the charged rod is still present, the sphere retains an excess of electrons. This happens because by breaking the ground connection while the sphere is still influenced by the nearby positive charge of the rod (which repels the electrons), the redistributed electrons are trapped on the sphere, thus leaving the sphere negatively charged. When the positive rod is finally removed, the sphere remains negatively charged because the extra electrons have no path to escape.
Explain how your battery works. What are some possible materials you could use to make your battery?
What happens when a person’s immune system is very weak?
a) The patient’s blood is unable to clot so he or she must take medication.
b) The patient is able to fight off more infections than normal.
c) The patient is unable to fight the infections a healthy person could resist.
d) The patient is unable to take antibiotics and must get a flu shot.
When a person's immune system is very weak, their body may be unable to fight off pathogens and diseases that a healthy immune system can resist. This can lead to increased risk of illness and vulnerability to infection.
(Option C)
Explanation:Immunodeficiency occurs when the immune system is not working properly, generally because one or more of its components are inactive. As a result, the immune system may be unable to fight off pathogens or cancers that a normal immune system would be able to resist. Immunodeficiency may occur for a variety of reasons.
The body's immune system would not be able to fight off pathogens like bacteria with fewer white blood cells. This can increase the risk of illness in HIV patients.
The person's immune system would not be able to distinguish self and non-self. This would make the person very vulnerable to infection.
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What can you infer from the fact that although CFC's have been banned, refrigerators and aerosol cans are still being sold?
Researcher must have found environmentally safer replacements for CFCs. That might be the reason aerosol cans and the refrigerators are still being sold. In aerosol cans liquefied petroleum gas is being popularly used in place of dangerous CFCs. Same is being done in refrigerators and other devices. The aerosol cans no longer hurt the ozone layer. Infact they have reduced the waste as they can be recycled now and has long life.
H e l p.. I have no idea what any of this is, what is the first step of the hydrogen fusion process
Two small objects each with a net charge of +q exert a force of magnitude f on each other: we replace one of the objects with another whose net charge is +4q: the original magnitude of the force on the +q charge was f; what is the magnitude of the force on the +q charge now?
You use energy to heat your home. what ultimately happens to the energy that you pay for in your heating bill?
The heat energy that you pay for in your heating bill releases and goes to the atmosphere.
Where heat energy goes?The heat energy that are used for warming of houses is releases and goes to the atmosphere and become a part of that atmosphere.
So we can conclude that the heat energy that you pay for in your heating bill releases and goes to the atmosphere.
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Energy paid for in your heating bill is converted into thermal energy to heat your home, distributing through power lines or pipelines. Some of the energy is lost to the environment, while the rest maintains a warm home temperature. Continuous payment is necessary to compensate for ongoing heat loss.
When you pay for energy to heat your home, you are essentially purchasing thermal energy to maintain a comfortable temperature inside. Here's a step-by-step explanation of what happens to the energy:
Generation: The energy you pay for is generated by power plants, which may use fossil fuels, nuclear energy, or renewable sources. This energy is then converted into electrical or thermal energy.Distribution: This energy is distributed through power lines or pipelines to your home.Use in Heating: Inside your home, energy is converted by your heating system into thermal energy (heat). This heat is then transferred to the air and materials in your home to maintain a warm temperature.Heat Transfer: Some of this thermal energy is inevitably lost to the outside environment due to heat transfer. The remaining energy stays within your home, ensuring a comfortable living space.Energy Dissipation: Over time, the thermal energy dissipates, balancing out with the environmental temperature unless continuously supplied.This process explains why you continuously pay for heating during colder months – it compensates for the continuous loss of heat to the outside environment.
How much heat is required to melt 86.5 g of ice at its melting point?
The range of audible frequencies is from about 20.0 hz to 2.00×104 hz . what is range of the wavelengths of audible sound in air? the speed of sound in air is 344 m/s.
what is an advantage of using coal power over solar power to generate electricity
Answer:
Coal power can be generated at night
Explanation:
An advantage of using coal power over solar power to generate electricity is Reliable Fuel.
Compared to solar power or wind energy, coal is a reliable, predictable, and dependable fuel. While it may not be at the forefront of national energy production, it can provide invaluable backup service and highly reliable fuel.
What is coal power ?"Coal-fired power plants burn coal to make steam and the steam turns turbines (machines for generating rotary mechanical power) to generate electricity." Many industries and businesses have their own power plants, and some use coal to generate electricity for their own use and mostly in combined heat and power plants.
What is solar power ?"Solar power works by converting energy from the sun into power." There are two forms of energy generated from the sun for our use – electricity and heat. Both are generated through the use of solar panels, which range in size from residential rooftops to 'solar farms' stretching over acres of rural land.
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A semiconductor can be made by adding atoms of other elements to
a.
aluminum.
b.
steel.
c.
silicon.
d.
zinc.
If you live in Earth's Northern Hemisphere, you expect the length of days to change from short in the winter to longest around the summer solstice, June 21st. This is because?
the guy on the up is jason todd
hope this helps:)
When a pendulum with a period of 2.00000 s in one location (g = 9.80 m/s2) is moved to a new location from one where the period is now 1.99863 s. what is the change in acceleration (in m/s2) due to gravity at its new location?