Potassium and gold cathodes are used in a photoelectric-effect experiment. For each cathode, find: The threshold frequency. The threshold wavelength. The maximum electron ejection speed if the light has a wavelength of 210 nm . The stopping potential if the wavelength is 210 nm . Throughout this problem, be sure to use 6.63×10−34J⋅s for Planck's constant.A) The threshold frequency of potassium in hertz.B) The threshold frequency of gold in hertzC) The threshold wavelength of potassium in nanometers.D) The threshold wavelength of gold in nanometers.
Answers
A. The threshold frequency of potassium is 2.29 × 10¹⁵ Hz.
B. The threshold frequency of gold is 1.09 × 10¹⁵ Hz.
C. The threshold wavelength of potassium is 539 nm.
D. The threshold wavelength of gold is 284 nm.
To find the threshold frequency, we use the equation E = hf, where E is the work function (energy required to remove an electron), h is Planck's constant, and f is the frequency of the incident light. Setting E equal to the energy of a photon with the minimum frequency required to remove an electron (the threshold frequency), we can solve for f.
For potassium, the work function is 2.3 eV or 3.69 × 10⁻¹⁹ J. Plugging this value into the equation gives us:
3.69 × 10⁻¹⁹ J = (6.63 × 10⁻³⁴ J⋅s) f
f = 2.29 × 10¹⁵ Hz
Similarly, for gold with a work function of 4.81 eV or 7.72 × 10⁻¹⁹ J, we get:
7.72 × 10⁻¹⁹ J = (6.63 × 10⁻³⁴ J⋅s) f
f = 1.09 × 10¹⁵ Hz
To find the threshold wavelength, we can use the equation λ = c/f, where λ is the wavelength, c is the speed of light, and f is the frequency. Plugging in the threshold frequencies we just found, we get:
For potassium, λ = (3 × 10⁸ m/s)/(2.29 × 10¹⁵ Hz) = 539 nm
For gold, λ = (3 × 10⁸ m/s)/(1.09 × 10¹⁵ Hz) = 284 nm
To find the maximum electron ejection speed, we use the equation KE = hf - Φ, where KE is the kinetic energy of the ejected electron, Φ is the work function, and f is the frequency of the incident light. Solving for KE and converting to speed, we get:
For a wavelength of 210 nm, the frequency is f = (3 × 10⁸ m/s)/(210 × 10⁻⁹ m) = 1.43 × 10¹⁵ Hz
For potassium, Φ = 3.69 × 10⁻¹⁹ J, so KE = (6.63 × 10⁻³⁴ J⋅s) (1.43 × 10¹⁵ Hz) - 3.69 × 10⁻¹⁹ J = 9.14 × 10⁻¹⁹ J
The speed of the ejected electron is v = sqrt(2KE/m), where m is the mass of the electron. Plugging in the values, we get:
v = √[(2 × 9.14 × 10⁻¹⁹ J) / (9.11 × 10⁻³¹ kg)] = 6.14 × 10⁶ m/s
For gold with a higher work function of 7.72 × 10⁻¹⁹ J, we get a lower maximum speed of 4.43 × 10⁶ m/s.
Finally, to find the stopping potential, we use the equation eVstop = hf - Φ, where e is the charge of an electron and Vstop is the stopping potential. Solving for Vstop, we get:
For a wavelength of 210 nm and potassium, Φ = 3.69 × 10⁻¹⁹ J, so:
Vstop = [(6.63 × 10⁻³⁴ J⋅s) (1.43 × 10¹⁵ Hz) - 3.69 × 10⁻¹⁹ J] / (1.60 × 10⁻¹⁹ C)
= 1.12 V
For gold with a higher work function of 7.72 × 10⁻¹⁹ J, we get a higher stopping potential of 2.08 V.
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Related Questions
a central concept in quantum mechanics is that both matter and are alternate forms of the same entity and therefore both exhibit dual characteristics of particles and of . this model allows a better understanding of the behavior of tiny particles such as electrons.
Answers
Answer:
energy, waves
Explanation:
In quantum mechanics, a central concept is that both matter and energy are alternate forms of the same entity and therefore both exhibit dual characteristics of particles and of waves.
Matter can be defined as anything that has mass and is able to occupy space.
Thus, any physical object or substance that is found on Earth is typically composed of matter.
Similarly, energy is highly affected by the mass of a any physical object or substance just like matter,
Hence, both energy and matter are known to be made up of atoms and as a result of this fact, exhibit dual characteristics of particles and of waves.
A wave can be defined as a disturbance in a medium that progressively transports energy from a source location to another location without the transportation of matter.
In conclusion, this central concept makes it easier for us to better understand the behavior of tiny particles such as electrons.
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The adjacent figure shows a solid 'S' of weight 15N connected to a thread and put on an inclined plane. 1) a-Is the weight of solid 'S' a contact force or a force acting from a distance? b- List the characteristics of the weight of solid 'S'. Thread Inclined plane c- Represent the weight of solid 'S' by a vector. Choose a convenient scale. 2) a- Name the other forces acting on solid 'S' and indicate their types. b- Represent each force by a vector without respecting a scale. c- List the characteristics of each of the above forces. (Without the magnitude) 3) The thread is cut and solid 'S' moves as shown in the adjacent figure a- Name the new force that acts on solid 'S' and indicate its type. b- List the characteristics of this force.(scale 1cm-1.3N). Thread Inclined plane Solid 'S' Solid 'S'
Answers
Answer:
Here is answer
Explanation:
a) The weight of the solid 'S' is a contact force because it acts on the solid 'S' through physical contact with the ground.
b) The characteristics of the weight of solid 'S' are:
It acts in the downward direction.
It is a gravitational force that is exerted by the Earth on the solid 'S'.
It is equal to the mass of the solid 'S' multiplied by the acceleration due to gravity (W = m*g).
c) The weight of solid 'S' can be represented by a vector as shown below:
[asy]
unitsize(1cm);
draw((0,0)--(0,15),Arrow(6));
label("$W$", (0,7.5), W);
[/asy]
a) The other forces acting on solid 'S' are the normal force exerted by the inclined plane on the solid 'S' and the frictional force exerted by the inclined plane on the solid 'S'. The normal force is a contact force, while the frictional force is also a contact force.
b) These forces can be represented by vectors as shown below:
[asy]
unitsize(1cm);
draw((0,0)--(0,15),Arrow(6));
label("$W$", (0,7.5), W);
draw((0,0)--(15sqrt(2)/2,15/2),Arrow(6));
label("$N$", (7.5sqrt(2),7.5), NE);
draw((0,0)--(-15sqrt(2)/2,-15/2),Arrow(6));
label("$F_f$", (-7.5sqrt(2),-7.5), SW);
[/asy]
c) The characteristics of these forces are:
The normal force acts perpendicular to the surface of the inclined plane.
The frictional force acts in the opposite direction to the direction of motion or intended motion of the solid 'S'.
The magnitude of the normal force is equal to the weight of the solid 'S', but in the opposite direction.
The magnitude of the frictional force depends on the coefficient of friction between the solid 'S' and the inclined plane, as well as the normal force.
a) The new force acting on solid 'S' is the gravitational force, which is a force acting from a distance.
b) The characteristics of the gravitational force are:
It acts in the downward direction.
It is a force that is exerted by the Earth on the solid 'S'.
Its magnitude can be represented by the vector shown below (using a scale of 1 cm to represent 1.3 N):
[asy]
unitsize(1cm);
draw((0,0)--(0,-1.3),Arrow(6));
label("$W$", (0,-0.65), S);
[/asy]
which of the following is true of inertia
a) it is a property of motion
b) it is measured by weight
Answers
Answer:
it is a property of motion
Which quantity is a vector quantity?
А.
acceleration
B.
mass
C.speed
D.
volume
Answers
Answer:
acceleration .......
Mr. Thompson hangs a small weight from a spring, which expands and contracts a few times before resting at equilibrium. Which forces are primarily in action?
A The normal force of the weight pulls down on the spring, while the frictional force of the spring pulls up on the weight.
B. The force of gravity on the weight is pulling down on the spring, while the elastic force of the spring pulls up on the weight.
C. The elastic force of the weight pulls down on the spring, while the normal force of the spring pulls up on the weight.
D. The frictional force of the weight pulls down on the spring, while the gravitational force of the spring pulls up on the weight.
Copyright 2022 Illuminate Education,
Answers
Answer:
The acceleration of an object is based on the force applied. An object continues its motion until an unbalanced force is applied.
Explanation:
So B
When will you attract the sun more,
today at noon or tonight at midnight
Answers
What two factors are a part of thermohaline circulation
Answers
Answer:
These deep-ocean currents are driven by differences in the water's density, which is controlled by temperature (thermo) and salinity (haline). This process is known as thermohaline circulation.
Explanation:
The fastest human ever recorded was Usain Bolt at 43 km/h. If a white tail
deer can run 3 km in 3 minutes and 45 seconds, how many km/h faster would Usain Bolt need to run to catch a deer?
Please show work! Will mark brainliest!
Answers
Deer 3km/3.75min because 45sec/60sec = .75min
All we need to do is convert
3km/3.75min * 60min/1h = 48km/h
Usain bolt 43km/h - deer 48km/h
= 5km/h
A hemispherical tank is full of oil (density = 50 pc). It has a diameter of 10 ft. Find the work done in Ib-ft in pumping all the liquid out of the tank
Answers
The work done in pumping all the liquid out of the tank is 2500π lb-ft.
Work done calculationThe potential energy of an object is given by the formula:
PE = mgh
Given:
Density of oil = 50 lb/ft^3
Diameter of the tank = 10 ft ( r = 5 ft)
To calculate the work done, we need to find the mass of the oil and the height it is lifted. Let's start by finding the mass:
Volume of oil in the tank:
The volume of a hemisphere = (2/3) * π * (r^3)
Volume = (2/3) * π * (5^3) = (2/3) * π * 125 = 250π/3 ft^3
Mass of the oil:
Mass = Volume * Density = (250π/3) * 50 lb
Now, we need to find the height of the tank. For a hemisphere, the height is equal to the radius (5 ft).
Finally, we can calculate the work done:
Work = PE = mgh = (250π/3) * 50 lb * 5 ft
Work = (250π/3) * 50 * 5 lb-ft
= 2500π lb-ft
So, the work done in pumping all the liquid out of the tank is approximately 2500π lb-ft.
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a stone is thrown straight up. when it reaches its highest point,
Answers
The velocity of the stone will be zero and the acceleration due to gravity will be maximum when it reaches its highest point.
When the stone is thrown up, it goes on moving against gravity and then at some point, it will lose its upward velocity and eventually come to rest for a moment. This is the highest point of the motion of the stone. At this point, the velocity of the stone will be zero and the acceleration due to gravity will be maximum. The acceleration due to gravity is the maximum at the highest point because, at this point, the direction of the velocity changes from upward to downward. At this point, the velocity and acceleration of the stone are both zero.
In conclusion, the highest point of a stone thrown straight up is the point where the velocity of the stone will be zero and the acceleration due to gravity will be maximum.
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The three types of meteorites come from different parts of their parent bodies. Stony-iron meteorites are rare because.
Answers
The three different types of meteorites originate from various locations on their parent bodies. Because only a small portion of a parent body contains both stone and iron, stony-iron meteorites are uncommon.
What makes stony-iron meteorites uncommon?Pallasites were most likely formed in a relatively small area within these differentiated asteroids, which may account for their scarcity. Only about 45 known pallsites exist among the many thousands of identified meteorites.
More than 95% of meteorites that are seen to crash to Earth are made of stone. The two types of them are chondrites and achondrites. The majority of both types also contain metallic iron in small, dispersed grains, but silicate minerals make up the majority of both.
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Someone plz help I’ll give the right answer branliest
Answers
Answer:
the one that is clicked in the photo I think is right
A psychiatrist will establish privacy guidelines with clients near the end of their second diagnostic visit
Answers
The given statement, "A psychiatrist will establish privacy guidelines with clients near the end of their second diagnostic visit is ethical violations in clinical psychology" is false. It is unethical in clinical psychology for a psychiatrist to set privacy rules with a patient at the conclusion of their second diagnostic appointment.
The area of psychology known as clinical psychology deals with diagnosing and treating mental disorders and aberrant behavior. In clinical psychology, psychiatrists employ a variety of therapies including behavior therapy, developmental therapy, and psychoanalytic therapy.
The Ethics Code has eleven principles, including guidelines for addressing moral dilemmas, competence, interpersonal relationships, privacy and confidentiality, public statements and advertising, record-keeping and fees, education and training, research and publishing, evaluation, and treatment. Clinical psychology ethics breaches include:
chance of receiving improper satisfaction.the therapeutic hold's letting go.Intrapsychic conflicts are brought on by the patient and therapist's dialogue.Learn more about Psychology here:
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The complete question is, "A psychiatrist will establish privacy guidelines with clients near the end of their second diagnostic visit is ethical violations in clinical psychology. True or False"
Substance de compones at a rate proportional to the amount of A prosent. It is found that a tb of A will reduce to 4 lb in 38 hr. Anar how long wil there be only 16 2 There will be 1 to left?
Answers
The substance will be reduced to 1/16 of A present, that is 1 lb, in 95 hours.
Let the initial amount of A present be X lb. The rate of decomposition of A is proportional to the amount of A present. Therefore, the rate of decomposition = k * X where k is the proportionality constant. We know that 1 lb of A will reduce to 4 lb in 38 hours. So, the rate of decomposition = X/38.
Also, the rate of decomposition = k * X. Comparing both the equations, k = 1/38. Therefore, the rate of decomposition = X/38A substance will reduce to 1/16 of A present i.e., X/16. Using the equation for the rate of decomposition, we get, X/16 = (1/38)*X*(t). Simplifying, we get t = 95 hrs. Hence, the substance will be reduced to 1/16 of A present, that is 1 lb, in 95 hours.
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You are on a skateboard not moving when your friend throws you a basketball and you catch it. The 0.50kg basketball was going 5 m/s when you catch it. You weigh 55kg with the skateboard. After you catch the basketball you, the basketball, and the skateboard are moving.
a. What is your mass with the basketball and skateboard?
b. What is your new velocity after you catch the basketball?
Answers
Answer:
a. Your mass with the basketball is 55.5 kg
b. Your new velocity is 0.045 m/s
Explanation:
We first add your weight and the basketballs weight to get 55.5 kg.
Then to find b. we use the equation: v final = (m1 * v1) / (m1 +m2)
So m1 is the basketball which is 0.5 kg and v1 is 5 m/s. So the top half is (0.5 * 5)
The bottom half is just our weights added together.
Answer:
a) 55.5 kg
b) .045 m/s
Explanation:
Using conservation of momentum, we can set the initial momentum of the skateboard-person-basketball system equal to the final momentum of the skateboard-person-basketball system.
m1 = skateboard + person = 55 kg
m2 = basketball = .50 kg
v1_i = 0 m/s
v2_i = 5 m/s
Solve for v_f (same as v1_f or v2_f since the system is moving together -- assuming perfectly inelastic collision).
m1v1_i + m2v2_i = m1v1_f + m2v2_f
m1v1_i + m2v2_i = v_f (m1 + m2)
Substitute known values into the equation.
(55)(0) + (.5)(5) = v_f (55 + .5)
2.5 = v_f (55.5)
v_f = .045 m/s
Your new velocity after catching the basketball is .045 m/s.
When a solid is heated, it emits electromagnetic radiation known as ________________. an example of such radiation is the element of a stove top burning bright red.
Answers
Answer:
I think the answer is thermal radiation
Ramu,the gardener,is trying to pull out weeds. however,he has to apply great force.why do you think he has to apply to much force?
Answers
Answer:
Roots are basically hooked into the ground?
Explanation:
Maybe you could comment here the choices if it's multiple choice.
True or False: You walk across a carpet and accumulate a net negative charge on the soles of your shoes. When you touch your sister with your finger and give her a small zap, the charge that accumulated on your finger is due to charging by contact.
Answers
Answer:
True
Explanation:
Charging by conduction occurs when a charged conductor comes in contact with an uncharged conductor, leading to the sharing of charges between both conductors. Contact charging leads to a sharing and distribution of the same type of charges on the two conductors.
In this case, your entire body is charged by the sole of your feet coming in contact with the charged carpet on the floor, leading to a charge buildup all over your body.
suppose one speaker is driven at 569 hz and the other at 559 hz. what is the beat frequency in hz? the average frequency in hz? please write your answers with integers.
Answers
When one speaker is driven at 569 Hz and the other at 559 Hz, the beat frequency is 10 Hz and the average beat frequency is 564 Hz.
The beat frequency is equal to the difference between the two frequencies.
Beat frequency = \(569 Hz - 559 Hz = 10 Hz\)
So the beat frequency is 10 Hz.
The average frequency is equal to the sum of the two frequencies divided by two.
The average frequency is calculated as follows
Average frequency = \((569 Hz + 559 Hz) / 2 = 564 Hz\)
So the average frequency is 564 Hz.
Therefore, the beat frequency is 10 Hz while the average frequency is 564 Hz when one speaker is driven at 569 Hz and the other at 559 Hz.
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Students in a science class were provided with this image and asked to identify which color of light would refract the most if white light was passed through a prism?which student below identified the correct color of light with the proper justification?
Answers
The identification of the correct color of the light with the proper justification would be by student 4: violet, because it has the highest frequency, therefore the correct answer is option D.
What is Wavelength?It can be understood in terms of the distance between any two similar successive points across any wave for example wavelength can be calculated by measuring the distance between any two successive crests.
As given in the problem, students in a science class were provided with this image and asked to identify which color of light would refract the most if white light was passed through a prism.
Student 4 would correctly identify and justify violet as the appropriate hue of the light since it has the greatest frequency, making option D the right response.
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HELP!!!
Which of the following statements is true about magnets?
A. The molecules of the atom are unaligned
B. The orientation of atoms does not affect a magnet
C. The north pole is stronger than the south pole
D. The molecules of the atom are all aligned
Giving brainliest to the correct answer! (If both are correct I'll give whoever answered correctly 1st brainliest!)
Answers
Answer:
Explanation:
A is not correct. That means that D is since they offer exactly the opposite meanings.
C is rubbish. One pole could not be stronger than the other. Heaven help us if touched the stronger pole.
B the very point of a magnet is that it does matter how the atoms are orientated.
Question 4 (2 points)
Your friend just challenged you to a race. You know in order to beat him, you must run 50 meters within 60 seconds in an eastern direction.
What does your average velocity need to be to win the race? (2 points)
5 meters per second, east
Оа
Ob
.83 meters per second, east
Ос
1.2 meters per second, east
Od
3000 meters per second, east
Answers
Answer:
0.83m/s,east
Explanation:
velocity=d/t
v=50/60
v=0.83m/s,east
which is denser: an object that has a density of 1000 kg/m3 or one that has a density of 1 g/cm3?
Answers
Density is a measure of how much mass is contained within a given volume. An object with a density of 1000 kg/m³ is denser than an object with a density of 1 g/cm³.
Density is a measure of how much mass is contained within a given volume. The formula for density is mass divided by volume (ρ = m/V). In the metric system, density is commonly expressed in kilograms per cubic meter (kg/m³) or grams per cubic centimeter (g/cm³).
Comparing the given densities, we can see that 1 g/cm³ is equivalent to 1000 kg/m³ since there are 1000 grams in a kilogram and 1 cubic meter is equal to 1,000,000 cubic centimeters. Therefore, the object with a density of 1000 kg/m³ has a higher mass per unit volume compared to the object with a density of 1 g/cm³.
This means that for the same volume, the object with a density of 1000 kg/m³ contains more mass, making it denser than the object with a density of 1 g/cm³. In simpler terms, if you were to compare objects of the same size, the object with the higher density would feel heavier because it has more mass packed into the same amount of space.
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help asap please!
calculate the answer to the correct number of significant digits.
-3.22 x 5.1
Answers
a negative charge, -q, has a mass, m, and an initial velocity, v, but is infinitely far away from a fixed large positive charge of q and radius r such that if the negative charge continued at constant velocity it would miss the center of the fixed charge by a perpendicular amount b. but because of the coulomb attraction between the two charges the incoming negative charge is deviated from its straight line course and attracted to the fixed charge and approaches it. find the closest distance the negative charge gets to the positive one
Answers
Answer:
The closest distance the negative charge gets to the positive charge is given by the expression:
r = (k * q^2) / (m * v^2)
Explanation:
To find the closest distance the negative charge gets to the positive charge, we can analyze the motion of the negative charge under the influence of Coulomb's attraction.
Given that the negative charge is initially moving with a constant velocity and would miss the center of the fixed positive charge by a perpendicular distance of b, we can consider the perpendicular distance b as the impact parameter.
The motion of the negative charge can be treated as a projectile motion with the Coulomb force acting as a centripetal force. As the negative charge approaches the positive charge, the Coulomb force causes it to deviate from its straight-line path and approach the positive charge.
The closest distance the negative charge gets to the positive charge occurs when the centripetal force due to Coulomb's attraction is equal to the gravitational force acting on the negative charge.
Using the equation for Coulomb's force, we have:
k * (q^2) / r^2 = m * (v^2) / r
Simplifying and rearranging the equation, we get:
r = (k * q^2) / (m * v^2)
Note that this expression assumes the motion occurs in a straight line and the interaction is purely Coulombic. In reality, the motion of the negative charge may be more complex due to other forces and factors.
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What is the velocity of a dropped object after it has fallen for 5 s?
Answers
Answer:
Height and Velocity Functions
Explanation:
Multiply the height by 2, and divide the result by the object's acceleration due to gravity. If the object fell from 5 m, the equation would look like this: (2*5 m)/(9.8 m/s^2) =1.02 s^2.
Marvin sells luxury cars at a dealership. He earns a 7% commission on his total weekly sales. This week, Marvin sold a $95,000 Benz and an $80,000 BMW. How much commission did he earn this week?
Answers
Answer:
5600 + 6650 = 12250
Explanation:
Two people, Micah and Lyra, with different near points are equally close to an object. Both inspect the object through the same magnifier by holding the lens close to the eye. Micah's near point is located farther away from his eye than Lyra's near point is located relative to her eye. Micah will experience a larger magnification for which of the following reasons?
When the object is located at his near point, the angular size of the object is smaller for Micah than for Lyra.
Micah sees a larger image than Lyra sees.
Micah can see the image clearly from a larger distance than Lyra can.
Lyra can see the image clearly from a larger distance than Micah can.
The angular size of the image relative to the angular size of the object at the near point is greater for Micah than for Lyra.
Answers
Micah will experience a larger magnification is because the angular size of the object is smaller for Micah than for Lyra.
Why angular size of the object is smaller for Micah than for Lyra?
The magnification produced by a magnifier is given by the formula:
M = (25cm/f) + 1, where f is the focal length of the magnifier.
The magnification is larger when the focal length is smaller. However, in this case, both Micah and Lyra are using the same magnifier, so the focal length is the same for both of them.
The near point is the closest distance at which an object can be brought into focus by the eye. The near point varies from person to person, and it depends on the elasticity of the lens and the shape of the eye. In this case, Micah's near point is located farther away from his eye than Lyra's near point is located relative to her eye. This means that Micah's eye has less ability to focus on close objects than Lyra's eye.
When an object is located at the near point, the image formed on the retina is at its maximum size.
The angular size of the object is given by the formula:
θ = tan⁻¹ (s/d), where s is the size of the object and d is the distance between the object and the eye.
Since Micah's near point is farther away than Lyra's near point, the distance d is larger for Micah. This means that the angular size of the object is smaller for Micah than for Lyra.
When Micah uses the magnifier to inspect the object, the magnification will be larger because the angular size of the object is smaller.
This is because the magnification is proportional to the ratio of the angular size of the image to the angular size of the object.
Since the angular size of the object is smaller for Micah, the angular size of the image produced by the magnifier will be larger, resulting in a larger magnification for Micah.
Therefore, the correct reason why Micah will experience a larger magnification is because the angular size of the object is smaller for Micah than for Lyra when the object is located at his near point.
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When the object is located at his near point, the angular size of the object is smaller for Micah than for Lyra, for which reason Micah will experience a larger magnification.
The statement that is correct for the given question is "When the object is located at his near point, the angular size of the object is smaller for Micah than for Lyra."
Micah and Lyra are two people with different near points but are equally close to an object.
Both inspect the object through the same magnifier by holding the lens close to the eye. In this context, magnification is the ratio of the size of the image seen through the magnifier to the size of the object when viewed directly.
The distance between the object and the lens must be greater than the focal length of the lens to create a virtual image. Micah's near point is located farther away from his eye than Lyra's near point is located relative to her eye.
So, Micah will experience a larger magnification for the reason that when the object is located at his near point, the angular size of the object is smaller for Micah than for Lyra.
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find the angle between the vectors. u = (2, 3, 0), v = (3, −2, 1)
Answers
Therefore, the angle between vectors `u` and `v` is 90°.
To find the angle between two vectors, we can use the formula:
`cos(θ) = (u . v) / (||u|| ||v||)`
Where u and v are vectors, `.` is the dot product of vectors and || || is the magnitude of a vector.θ is the angle between the two vectors.
In this problem, we need to find the angle between vectors `u` and `v`.
We have the following vector
s:u = (2, 3, 0) and v = (3, −2, 1)
Let's find the dot product of vectors `u` and `v`.u .
v = 2 × 3 + 3 × (−2) + 0 × 1
= 6 − 6 + 0
= 0
Let's now find the magnitudes of vectors `u` and `v`.||u|| = √(2² + 3² + 0²) = √(13) and
||v|| = √(3² + (−2)² + 1²)
= √(14)
Now, we can use the formula to find the angle between vectors `u` and `v`.cos(θ) = (u . v) / (||u|| ||v||)cos(θ)
= 0 / (√(13) × √(14))cos(θ)
= 0θ
= cos⁻¹(0)θ
= 90°
The angle between the vectors u = (2, 3, 0) and v = (3, −2, 1) is 90 degrees.
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Flossie blew a tire 5 minutes into the second leg, up to that point she had traveled 10 km making her speed 2 km/m. It took 2 minutes to fix her tire. Flossie had to finish within 2 minutes in order to stay even with the evil Mabel. If Flossie had 8 km left what speed will she need to win?
Answers
Answer:
4km/m
Explanation:
She was going at 2km/m, so 2 kilometers per minute. She has 2 minutes therefore she needs to double her rate to 4 kilometers per minute.