The vector v with the given magnitude and the same direction as u. magnitude direction v = 4 u =< 1, 1>
=4/[tex]\sqrt2{^{2} }[/tex] i + 4/[tex]\sqrt2{^{2} }[/tex] j
What is vector?Vector, in physics, a quantity that has both magnitude and the direction. It is a typically represented by an arrow whose direction is the same as that of the quantity and whose length is proportional to the quantity’s magnitude. Although vector has magnitude and direction, it does not have the position. That is, as long as its length is not changed, vector is not altered if it is displaced parallel to itself.
In contrast to vectors, ordinary quantities that have a magnitude but not a direction are called the scalars. For example, displacement, velocity, and acceleration are vector quantities, while the speed (the magnitude of velocity), time, and mass are scalars.
To qualify as a vector, a quantity having magnitude and direction must also obey certain rules of the combination.
Therefore,
A vector a with given magnitude in the direction of b, is given by:
(||a||.b)/||b||
||u||=[tex]\sqrt{1^{2}+1^{2} }= \sqrt{2^{2} }[/tex]
||v||=4
[4(1+1)]/[tex]\sqrt{2^{2} }[/tex]= 4/[tex]\sqrt2{^{2} }[/tex] i + 4/[tex]\sqrt2{^{2} }[/tex] j
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An athlete preparing for a marathon runs 21.3 miles. how many kilometers did they run?
An athlete runs 34.271 kilometer.
solution,
Here , 1 miles is equal to 1.6093 km
therefore, an athlete runs 21.3 miles
The distance measured in kilometer of athlete preparing for a marathon is given as ,
1 mile = 1.6093 km
21.3 miles = 21.3 × 1.6093 km
21.3 miles =34.271 km
Therefore an athlete preparing for a marathon runs 34.271 km.
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What is the average rate from 2.0 to 6.0 seconds in mol / l s? use 4 decimal places
The average rate from 2.0 to 6.0 seconds in mol/L is 0.004025 mol/L.
What is decomposition reaction ?Decomposition reactions are those in which a reactant undergoes reaction to form two or more products.
2AX2(g) -------> 2AX(g) + X2(g)
t1 = 2.0 s and t2 = 6.0 s
x1 = 0.0249 and x2 = 0.0088
Average rate of reaction:
Ra = ∆[x]/DeltaT = X2 - X1/t2 - t1
Ra = 0.0088 - 0.0249/6 - 2 = 0.004025 mol
Thus, the average rate is 0.004025 mol/L.
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A car with good tires on a dry road can decelerate at about 3.0 m/s2 when braking. if the car is traveling at 65 km/h, what distance is needed to stop at the red light?
By using uniform motion, the distance needed to stop at the red light is 54.36 m.
We need to know about the uniform motion to solve this problem. The uniform motion is an object's motion under acceleration. It should follow the rule
vt = vo + a . t
vt² = vo² + 2a . s
s = vo . t + 1/2 . a . t²
where vt is final velocity, vo is initial velocity, a is acceleration, t is time and s is displacement.
From the question above, we know that
a = -3 m/s²
vo = 65 km/h = 18.06 m/s
vt = 0 m/s
By using the second equation, we get
vt² = vo² + 2a . s
0² = 18.06² + 2(-3) . s
6s = 326.16
s = 54.36 m
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If the entire apparatus is immersed in water, what happens to the distance between the fringes on the screen?
The space between the screen fringes will be closed if the complete apparatus is submerged in water.
What does fringe distance mean?The space between two consecutive bright spots (maximas, when constructive interference occurs), or two consecutive dark patches, is known as the fringe width (minimas, where destructive interference occurs). All of the fringes in Young's double-slit experiment are the same length. The formula yields the fringe width. β = λD/d. Because it depends on L, the spacings between various fringes get smaller as the slit distance gets bigger. Since the space between various fringes is wavelength dependent, increasing the light's wavelength also increases that separation.
In comparison to air, water has a shorter wavelength of light. Therefore, when the device is submerged in water, the fringe width will diminish.
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A 2 meter tall vertical stack of firewood casts a 4 meter shadow on horizontal ground. what is the angle of the sun in the horizon?
The angle of the sun in the horizon would be [tex]\theta[/tex] = 26.56°
CalculationHeight of stack of firewood = 2 m
Height of the shadow of firewood = 4m
Then according to trigonometric identities,
tan[tex]\theta\\[/tex] = 2/4
[tex]\theta[/tex] = [tex]tan^{-1}[/tex](1\2)
[tex]\theta[/tex] = 26.56°
What is trigonometry?
The area of mathematics concerned with how triangles' sides and angles relate to one another as well as with the pertinent uses of any angle is called as Trigonometry. This field of study was created in the Hellenistic era in the third century BC as a result of the use of geometry in astronomical research.
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The density beyond which people cease to be nutritionally self-sufficient is called:________
Physiological nutrition is the density at which people are no longer self-sufficient in terms of nutrients.
How the body absorbs nutrients from food, how we get the energy we require, how we use nutrients, and how all of this relates to health and disease are all topics covered by nutrition physiology.
Why does physiology need nutrition?
Nutritional requirements exist in addition to daily energy requirements in order to keep the body from losing its own proteins, carbs, and lipids. Such molecules must be replenished frequently because they are constantly broken down.An organism uses food to prolong its life through some kind of biochemical and physiological process known as nutrition. It gives living organisms nourishment that can be transformed into energy and chemical building blocks.The ingestion of nourishment, meeting psychological needs, and bodily adjustment are the three purposes of food.To learn more about Physiological nutrition, visit:
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If the bar oa is rotating clockwise with a constant velocity and the collar slides freely, the direction of the reaction force on the collar will be:_______
The direction of the reaction force on the collar will be Non constrained motion direction .
What is the relationship between the magnitude of the angular velocity ω and that of the velocity v ?ω = v / r
Since the cylinder is wrapped about the string, it rolls without slipping with respect to the string. The constraint relationship to assure this kind of motion can be obtained by considering the relative velocity of the point on the cylinder that is in contact with the string with respect to the string it should be zero.
The velocity of the center of the cylinder,
v = dy (t) / dt, r and the rotation rate of the cylinder, ω
We have to first find the velocity of the contact point relative to the center of the cylinder. Since this ignores the translational motion of the entire cylinder with respect to the ground, we then need to add back in the cylinder's center of mass velocity to find the velocity of the contact point with respect to the ground.
So, v (contact) = ωr - v where,
ω is the angular velocity
v is the linear velocity
r is the radius
ω = v / r
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Why is it important to center an object you are analyzing in the field of view of the microscope before switching to a higher power lens?
As magnification increases, field diameter decreases and objects at the periphery will no longer be in the visible field.
What is Lens ?A lens is a piece of transparent material that is typically round in shape with two polished surfaces that are either convex (bulging) or concave on one or both sides (depressed). The curves almost always have a constant radius of curvature since they are spherical.
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I need some serious help, i do not understand this question!!
An Alaskan rescue plane traveling 47 m/s
drops a package of emergency rations from
a height of 179 m to a stranded party of
explorers.
The acceleration of gravity is 9.8 m/s^2
Where does the package strike the ground
relative to the point directly below where it
was released?
Answer in units of m.
The position where the package strikes the ground is 136.3m.
Time of motion of the package
Use the following kinematic equation;
h = vt + ¹/₂gt²
179 = 47t + ¹/₂(9.8)t²
179 = 47t + 4.9t²
4.9t² + 47t - 179 = 0
solve the quadratic equation using formula method;
a = 4.9, b = 47, c = -179
t = 2.9 seconds
Horizontal distance traveled by the packageX = vt
X = 47m/s x 2.9 s
X = 136.3 m
Thus, the position where the package strikes the ground is 136.3m.
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With an increase in strain rate, ductility ______ and tensile strength _____. a) decreases, decreases b) decreases, increases c) increases, increases d) increases, decreases
With an increase in strain rate, ductility decreases and tensile strength increases. Option b. decreases, increases is the correct answer
The ductility of materials decreases as the strain rate rises. The reason is that the material exhibits brittle behaviour. Material increases in tensile strength.
Ductility: A material's ductility refers to its capacity to withstand plastic deformation or drawing without breaking. As a result, it provides information on how "soft" or pliable the material is.
Tensile strength: Maximum load a material can bear without breaking when it is stretched, divided by the material's initial cross-sectional area.
Therefore, option b. is the correct answer for the given question
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Three liquids have densities of 1.15 g/ml, 0.79 g/ml and 0.95 g/ml. when the liquids, which do not mix, are poured into a graduated cylinder, the liquid at the top is the one with a density of:________
The liquid at the top is the one with a density of 0.79 g/ml.
The matter with most density will stay at the bottom of the graduated cylinder. So when comparing the three given densities of 1.15 g/ml, 0.79 g/ml and 0.95 g/ml, the lowest density is 0.79 g/ml.
Density is nothing but weight of the matter. So basically the lighter one stays at top.
Therefore, the liquid at the top is the one with a density of 0.79 g/ml.
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Clutch a cart starts at x = 2.0 m and travels towards the origin with a constant speed of 2.0 m/s. what is it the exact cart position (in m) 2.0 seconds later?
When the cart travels towards the origin, the magnitude of its exact position reduces with time.
The cart will be at -2 m (origin) 2s later.
What is it the exact cart position (in m) 2.0 seconds later?
When the cart travels towards the origin, the magnitude of its exact position reduces with time.
The formula of speed is given as
S = d/t ................. (1)
Where S = speed of the cart,
d = distance covered by the cart over a certain time.
t = time taken to cover the distance.
Where d the subject of the equation,
d = St ................. (2)
Given: S = 2.0 m/s, t = 2.0 s
Substitute into (2)
d = 2(2)
d = 4 m.
From the above, the cart covered a distance of 4 m in 2s.
The exact position of the cart = Initial position - distance covered
x' = x - d ............ (3)
Where x' = exact position of the cart 2s later,
x = initial position of the cart, and
d = distance covered by the cart in 2.0 s
Given: x = 2.0 m, d = 4 m.
Substitute into (3)
x' = 2.0 - 4
x' = -2 m.
Therefore the cart will be at -2 m (origin) 2s later.
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Ice is put in a cooler to cool the contents. to speed up the cooling process, the ice can be?
Crushing increases the ice's surface area. Additionally, cooling from ice happens as a result of convection, which is proportional to area. Thus, breaking up the ice expedites the cooling process.
What is cooling process?When precise and consistent temperature control inside a process is necessary, this sort of cooling is used. Because they can offer cooling capacity independent of variations in the ambient temperature, heat load, and flow needs of the application, chillers are frequently employed to remove heat from a process.
It's important to properly regulate the heat load in many industrial operations. Different components of the whole application might need to be cooled.
Major locations for cooling include:
Direct product cooling
During the molding process, plastic
milling metal products
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Conceptual, human, and technical skills are important to which managerial level?
Conceptual abilities are essential for top managers, but they are less important for mid-level managers and are not necessary for first-level managers. The value of these talents will increase as we go up the managerial ladder.
What is the difference between basic and technical skills?In general, conceptual abilities refer to the capacity to deal with ideas and concepts. Whereas technical skills are concerned with objects and human skills with people, conceptual skills are concerned with the capacity to work with ideas.
These are intellectual abilities, human abilities, and technological abilities. A manager's conceptual talents enable him or her to see the complete organisation as well as deal with ideas and the links between abstract notions. Human skills, also known as human connection skills, need communication and attention to interpersonal interactions.
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A long, straight metal rod has a radius of 5. 00cm and a charge per unit length of 30. 0nC/m. Find the electric field (c) 100cm from the axis of the rod, where distances are measured perpendicular to the rod's axis
The electric field at 100cm is 5.39 x 10² N/C.
We need to know about the electric field to solve this problem. The electric field is the area affected by electric force. The magnitude of electric field at a distance from long infinite length and constant charge per unit length is given by
E = λ / (2πε₀d)
From the question above, we know that
λ = 30 nC/m
λ = 30 x 10¯⁹ C/m
d = 100 cm = 1 m
By substituting the given parameter, we get
E = λ / (2πε₀d)
E = 30 x 10¯⁹ / (2π . 8.85 x 10¯¹² . 1)
E = 5.39 x 10² N/C
Hence, the electric field at 100cm is 5.39 x 10² N/C.
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Two rocket ships approach a space station at 80% of the speed of light from opposite directions. each pilot observes the other ship approaching at __ the speed of giht
Two rocket ships approach a space station at 80% of the speed of light from opposite directions. each pilot observes the other ship approaching at 0.98 c the speed of light.
What do you understand by speed of light ?Speed of light, the rate at which light waves move through various substances. Specifically, the speed of light in a vacuum is presently calculated to be 299,792,458 meters per second. One of nature's basic constants is the speed of light.
American physicist Albert Michelson used an eight-sided spinning mirror system to conduct his research in the mountains of Southern California during the 1920s and produced one of the earliest accurate calculations of light's velocity.
It is given that
[tex]V_{AB} =\frac{V_{A} +V_{B}}{1+\frac{V_{A} V_{B} }{c^{2} } } \\V_{AB} =\frac{.8c+0.8c}{1+\frac{.8cX.8c}{c^{2} } } \\V_{AB} = 0.98c m/s[/tex]
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A beam of blue light in air is incident on a glass plate. will the beam transmitted through the glass plate emerge parallel to the incident beam?
If the top and bottom surfaces of the glass plates are parallel to each other, the incident and emergent beam will be parallel to each other no matter the wavelength (colour) of beam.
CASE 1 : The surface in which the beam is incident is parallel to the surface from which the beam is emitted. In this case, the incident and emergent ray are always parallel to each other no matter the wavelength (colour) of beam.CASE 2 : The surface in which the beam is incident is not parallel to the surface from which the beam is emitted. In this case, the incident and emergent ray are not parallel to each other.Refractive index is the lights bending ability when moving from one medium to another. Refractive index varies with colours but not angle of incidence and emergence.
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A particle has an acceleration of 6.14 m/s2 for 0.300 s. at the end of this time the particle's velocity is 9.41 m/s. part a what was the particle's initial velocity? express your answer to thr
The initial velocity of particle is 7.568 m/s
Given:
acceleration = a = 6.14 m/s2
time = t = 0.300 s
final velocity = v = 9.41 m/s
To Find:
initial velocity = u
Solution: Velocity is the prime indicator of the position as well as the rapidity of the object. It can be defined as the distance covered by an object in unit time.
v = u + at
u = v - at = 9.41 - 6.14*0.3
u = 7.568 m/s
Hence, the initial velocity of particle is 7.568 m/s
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Changing the wavelength of a light wave also changes its:_____.
a. direction
b. frequency
c. brightness
d. speed
Answer:
frequency
Explanation:
speed of light = constant = wavelength * frequency
changing WL or F will change the other
use the diagram to answer the following physics questions:
i. where is the velocity zero?
ii. where is the velocity positive?
iii. where is the velocity negative?
iv. where is the fastest velocity?
v. where is the acceleration positive?
vi. where is the acceleration negative?
vii. where is the acceleration zero?
(if you could explain that would be great! thank you so much :) )
Answer:
i. Point A
ii. None
iii. All points
iv. F
v. None
vi. All
vii. None
Explanation:
i. Not quite sure if I'm interpreting the diagram right, but from the second the ball is released, it will start accelerating. Point A is where the velocity will be closest to 0 but not necessarily 0 as it will have started accelerating downwards.
ii. Assuming standard directions for vectors, the velocity is positive at none of the points as the ball is travelling in a downwards direction.
iii. Since the ball is always travelling downwards, its direction and therefore velocity is a negative number at all points in this diagram.
iv. The ball is accelerating as it falls so the further or the longer it falls, the faster its velocity, therefore in this diagram, it is fastest at point F.
v and vi. Assuming same direction principles as ii and iii (as acceleration and velocity are both vectors), acceleration is always downwards, therefore it is positive at no points, and negative at all of them.
vii. Acceleration due to gravity is always constant, so unless the ball is not moving (being held by the boy), acceleration is not 0 at any of the points.
Hope this helped!
Infrared radiation has wavelengths ranging from about 800 nm to 1 mm. What is the corresponding frequency of radiation of a wavelength of 970 nm?.
The corresponding frequency of infrared radiation of a wavelength of 970 nanometer (nm) is 3 x 10^14 Hertz.
The relation between the frequency and wavelength of a radiation is as follows:
c = f x λ
Here c = speed of light = 3 x 10^8 m/s
So, the frequency of a given wavelength can be calculated by applying the above formula,
Putting λ = 970 nm = 970 x 10^-9 m
3 x 10^8 m/s = f x 970 x 10^-9
f = 3 x 10^14 Hz.
Hence, the corresponding frequency of radiation of a wavelength of 970 nm is 3 x 10^14 Hertz.
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If you want to add 5 calories of heat to 1 gram of water, how will the temperature change?
Answer:
It will increase to 5ᵒC.
Explanation:
What two principal factors affect the force of air resistance on a falling object?.
First, it depends on the cross-sectional/frontal area of the falling object, that is the amount of air the object must plow through as it falls. Second, it depends on the speed of the falling object.
When an object is dropped through the air, it usually faces air resistance. Air resistance is caused by collisions between the object's leading air and surface molecules. Several variables determine the actual degree of air resistance the object faces. The object's speed and the frontal area of the object are the two predominant factors that have a direct effect on the amount of air resistance. Increased speeds cause an increase in air resistance. Increased cross-sectional areas lead to increased air resistance.
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What is the highest speed during the motion.
Answer: 20mm/s
Explanation: Maximum displacement in shortest time....
Can and object have a negative position and a positive velocity? Or vice versa, a positive position and a negative velocity? Explain your reasoning, do not just give a simple sentence answer.
In a first order decomposition, the constant is 0.00702 sec-1. what percentage of the compound has decomposed after 7.1 minutes?
The percentage decomposed in the first order reaction is 69.8%.
What percentage of the compound has decomposed after 7.1 seconds?Given: rate constant, k = 0.00702 sec -1
time, t = 7.1 s
Since the reaction is first order, we calculate using the formula below:
[A] = [A]₀ [tex]$$e^{(-kt)[/tex]
Where; [A] is the final concentration
[A]₀ is the initial concentration
Finding the ratio of final and initial concentration
[A]/[A]₀ =[tex]$$ e^{(-kt)[/tex]
Substituting the values:
[A]/[A]₀ = [tex]e^{(-0.00702 * 7.1)[/tex]
[A]/[A]₀ = [tex]e^{(-0.0498)[/tex]
[A]/[A]₀ = 0.9514
Percentage decomposed = [A]/[A]₀ [tex]*[/tex] 100%
Percentage decomposed = 0.9514 [tex]*[/tex] 100%
Percentage decomposed = 95.1 %
Therefore, the percentage decomposed in the first-order reaction is 95.1 %.
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Voltage drop is a better measurement of resistance than testing static resistance because ________.
Voltage drop is a better measurement of resistance than testing static resistance because: current flow creates heat which adds to circuit resistance
The current flow or electric current is the measure of the electrons flow around a circuit. It is measured in amperes or "amps". If the current is higher the electrons flow is greater.
The course of a conventional electric current in the external circuit is directed away the positive terminal and toward the negative terminal of the battery
What is electricity?Electricity or electrical energy is the energy that occurs due to the movement of electrons in the materials that are considered conductors.
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Suppose that the marginal propensity to save (mps) equals 0.2. the value of the multiplier would be:_________
0.2 is the value of the marginal propensity to save (mps). The multiplier's value would be 5.
Briefing:
Multiplier = 1 / marginal saving propensity (MPS)
= 1 / 0.2
= 5.
What does marginal propensity mean?The percentage of an overall salary increase that a customer spends on purchasing goods and services rather than saving is known as the marginal propensity to consume (MPC) in economics.
How is marginal propensity determined?By dividing the change in consumer spending (C) by the change in disposable income (I), the MPC formula is created. Formula for the marginal propensity to consume is (C1 - C0) / (I1 - I0), where C0 is the initial amount spent by consumers.
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If an automobile gets 24.5 miles to the gallon and the cost of gasoline is $2.75 a gallon, how much will it cost to drive 975 km?
It will cost $68 to travel 975 kilometers for an automobile if the cost of gasoline is $2.75 per gallon.
This simple calculation can be explained as below calculation of the cost of driving such a distance is done by conversion of the distance into miles and multiplying such distance by $2.75.
Cost of DrivingFirst calculate the kilometers to miles.
975 kilometers is converted as 605.837 miles. Now the division of mileage of automobile will be calculated as,
Gasoline required = Distance travelled/ mileage
=605.837/24.5
=24.72 gallons of gasoline required.
Now we have to calculate the cost of gasoline.
Gasoline cost= gallons x cost per gallon
= 24.72 x 2.75
=$68
So, it is calculated that the cost of gasoline/ cost of driving is $68.0.
Hence, it would cost $68 to travel 975 kilometers for an automobile when the cost of gasoline is $2.75 per gallon.
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What is true about an object as its temperature increases?a. the object's atoms lose heat. b. the object's atoms gain kinetic and elastic potential energies. c. the object's atoms gain heat.
When temperature of an object is increases then the objects atom gain kinetic energy and elastic potential energies.
Kinetic energy- It is the energy of an object due to its motion.
Example - All moving object possesses kinetic energy due to their motion.
Elastic potential energy - it is the energy stored in a spring that has been stressed or compressed from its natural length.
Example - An Archers stretched bow.
Heat is a form of both potential and kinetic energy.
Temperature helps in thermal expansion which result in higher collision between particles. It increases the kinetic energy of the molecule.
an object as its temperature increases then the object's atoms gain kinetic and elastic potential energies.
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