vector u has a magnitude of 20 and direction of 0°.vector v has amagnitude of 40and a direction of 60°.find the magnitude and direction of the resultant
Answers
Addition of vectors:
vector u
has a magnitude of 20 and a direction of 0º with respect to the horizontal, vector v has a magnitude of 40 and a direction of 60º with respect to the horizontal.
a) Find the magnitude and direction of the resultant to the nearest whole
number.
Vector Sum:
The resultant of two vectors is simply the vector sum of the vectors. There are a handful of ways to present the resultant factor; the notation that shows the vector magnitude and direction is called the polar vector notation. An example of a vector presented in polar vector notation is
a∠θ where a is the magnitude and θis the angle that the vector makes with the horizontal axis.
Answer and Explanation:
Let's first present the vectors in rectangular vector notation.
For the vector →u of magnitude 20 and direction 0∘ to the horizontal axis, the vector is →u=^i20.
For the vector →v
of magnitude 40 and direction 60∘ to the horizontal axis, the vector is →v=^i40cos60∘+^j40sin60∘.
The resultant vector →w is the vector sum of the vectors, i.e.
→w=→u+→v
=^i20+^i40cos60∘+^j40sin60∘
=^i(20+40cos60∘)+^j(40sin60∘)
=^i40+^j20√3
For a vector ^ix+^jy, the magnitude of the vector is √x2+y2 and the direction above the horizontal axis is θ=tan−1(yx).
Let's use the formulas:
|→w|∠θ=√(40)2+(20√3)2∠tan−1(20√340)≈52.9∠40.9∘
The magnitude of the vector is about 53 units in the direction 41-degrees above the horizontal axis.
The magnitude of the resultant vector would be 60 units, and its direction will be 0°.
To find the magnitude and direction of the resultant vector when adding vectors u and v, we can use vector addition formulas:
Magnitude of the Resultant Vector (R):
R = √(u^2 + v^2 + 2uv * cosθ)
where:
u = magnitude of vector u (20)
v = magnitude of vector v (40)
θ = angle between vectors u and v (60°)
Plugging in the values:
R = √(20^2 + 40^2 + 2 * 20 * 40 * cos(60°))
≈ √(400 + 1600 + 1600)
≈ √3600
= 60
Direction of the Resultant Vector (θR):
Use the Law of Cosines to find the angle θR between the resultant vector R and vector u:
cosθR = (v^2 + R^2 - u^2) / (2 * v * R)
Plugging in the values:
cosθR = (40^2 + 60^2 - 20^2) / (2 * 40 * 60)
= (1600 + 3600 - 400) / 4800
= 1
Since cos(0°) = 1, we have θR = 0°.
So, the magnitude of the resultant vector is 60 units, and its direction is 0°.
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Related Questions
At which of the following angles will the sunlight received at a location on Earth spread out over the largest area?
90°
70°
40°
10°
Answers
The angle at which the sunlight received at a location on Earth spread out over the largest area is 10°. Last option is correct.
What is sunlight?The light coming from the Sun reaching the Earth's surface is called as Sunlight.
When the sun is overhead, the intensity is high because sun's rays are perpendicular to the earth's surface, so the energy spreads over a small area and the heat is too high in that region.
When, the angle is smaller, the sunlight will spread out over a larger area.
Thus, at 10° the sunlight received at a location on Earth spread out over the largest area. Last option is correct.
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Answer:
Expl10
anation:
Different between sound wave and water wave
Answers
Water waves shake energy over the surface of the sea, while sound waves thump energy through the body of the air. Sound waves are compression waves. They're also called longitudinal waves because the air vibrates along the same direction as the wave travels.
two identical stacked basketballs are dropped each with a mass of 0.6 kg and velocity of 4.41 m/s. what is the total momentum of the basketballs before they hit the ground? show your work.
Answers
The total momentum of the basketballs before they hit the ground is 5.292 kg·m/s.
To find the total momentum of the basketballs before they hit the ground, we need to calculate the momentum of each basketball and then add them together.
The momentum (p) of an object is given by the product of its mass (m) and velocity (v):
p = m * v
Given:
Mass of each basketball (m) = 0.6 kg
Velocity of each basketball (v) = 4.41 m/s
Momentum of each basketball:
p1 = m * v = 0.6 kg * 4.41 m/s = 2.646 kg·m/s
Since the basketballs are identical, the momentum of the second basketball will also be the same:
p2 = m * v = 0.6 kg * 4.41 m/s = 2.646 kg·m/s
Total momentum of the basketballs before they hit the ground:
Total momentum = p1 + p2 = 2.646 kg·m/s + 2.646 kg·m/s = 5.292 kg·m/s
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Someone please help me, I know I already asked a question please don't think I not smart, but
#1. How are potential and kinetic energy related?
#2. How are sounds made?
Answers
Answer:
PE is related to the ability to do work, If an item is sitting on a shelf
it has potential energy relative to its position on the floor, However, if the object were to fall it would hit the floor with a KE equal to the PE that it had sitting on the shelf.
Sounds are caused by compressional waves in the air - when a piano key is struck or a TV is turned on, then compressional waves are produced in the surrounding air due to a disturbance. The human ear recognizes the disturbed air as due to the object that created the disturbance.
What must differ between the atom of two different elements?
A. protons and neutrons in the nucleus
B. neutrons in the atom
C. electrons in the atom
D. protons in the atom
Answers
Answer:
A.protons and neutrons in the nucleus.
1.Supposed you walk 5 m south in a straight path then another 4 m on the same direction. How will you solve for the total path you have taken?
A.add the 2 distance
b. subtract the first distance to the final
c. add the two distance and divide the 2
Answers
Which of the following are equivalent to 1 Newton?
Answers
Answer:
1 kilogram meter per second squared?
Which tool should be used to measure the mass of an object?
A. graduated cylinder
B. stopwatch
C. scale
D. thermometer
hurry!!
Answers
Answer:
A. Gradulated Cylinder
A graduated cylinder is a tool that should be used to measure the mass of an object, first by measuring the volume of the substance and then calculating the mass by using the density, therefore the correct answer is option A.
What is a unit of measurement?A unit of measurement is a specified magnitude of a quantity that is established and used as a standard for measuring other quantities of the same kind. It is determined by convention or regulation.
Any additional quantity of that type can be stated as a multiple of the measurement unit.
stopwatch is used to measure the time period.
scale is used to measure the length.
A thermometer is a tool used to measure the temperature.
The correct response is option A because a graduated cylinder should be used to determine an object's mass by first determining the substance's volume and then calculating the mass using a density.
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PLEASE HELP ME!
A student notices that when calcium chloride is placed in water, the test tube feels warm. What kind of reaction has taken place?
A. Combustion Reaction
B. Endothermic Reaction
C. Exothermic Reaction
D. Endergonic Reaction
Answers
Answer:
C. Exothermic Reaction
Explanation:
Let's go through the choices
A. Combustion - Combustion is a highly exothermic / redox reaction which produces light and heat (i.e basically it bursts into flames). In the description, the only reaction is that it feels warm, hence this is not the answer.
B. Endothermic - Recall that endothermic reactions absorbs heat and thus cools the surroundings thereby making test tube feel cooler. this is obviously not the case so this is not the answer.
C. Exothermic - Recall that exothermic reactions releases heat and thus causes the surroundings thereby making the test tube feel warmer (or hotter in some cases). This describes our situation so THIS IS THE ANSWER.
D. Endergonic reactions require an input of energy from an external source that is adsorbed by the reaction (for example if heat was applied by an external source). In this case, there is no mention of additional energy sources. Hence this is probably not the answer.
An egg is dropped from a treehouse and takes 1.51.51, point, 5 seconds to reach the ground. We can ignore air resistance.
What is the egg's displacement?
Answers
The egg's displacement is 122.625 m
Here, the case of dropping the egg from the treehouse is comes under freefall condition. Meaning that the motion is under Earth's gravitational acceleration only as we have to ignore air resistance. Here initial velocity is considered to be zero.
Hence, we will use s= 1/2* g*t²
s is displacement to be find out in meter
g is acceleration due to gravity = 9.81 m/s²
t is time taken by the egg to reach the ground which is given as 5 second.
Putting all the values in the given equation
s= 1/2*9.81*5*5
s= 1/2*9.81*25
s= 245.25/2
s= 122.625
So the displacement is 122.625 meter
Three resistors are placed in series. They have the following resistances: R1 = 20 ohms, R2 = 20 ohms, R3 = 10 ohms. What
current would be moved through this circuit by a 5-V power supply?
Answers
Answer:
0.10 A
Explanation:
2. A student slides a 0.75 kg textbook across a table, and it comes to rest after
traveling 1.2 m. Given that the coefficient of kinetic friction between the
book and the table is 0.34, use the work-kinetic energy theorem to find
the book's initial speed.
Answers
The book's initial speed = 2.83 m/s
The mass of the textbook, m = 0.75 kg
The final speed of the textbook, v = 0 m/s (Since it comes to rest)
The distance covered by the book, d = 1.2 m
Coefficient of kinetic friction, \(\mu = 0.34\)
The frictional force between the table and the book is calculated as:
\(f_k=-\mu mg\\\\ f_k=-0.34 \times 0.75 \times 9.8\\\\f_k=-2.499N\)
The workdone by the textbook is calculated as:
\(W = Fd\\\\W=2.499(1.2)\\\\W=2.9988J\)
According to the work-kinetic energy theorem:
Workdone by the book = Change in Kinetic energy
\(W = 0.5m(v^2-u^2)\\\\-2.9988=0.5 \times 0.75 \times (0^2-u^2)\\\\-2.99988=-0.375u^2\\\\u^2=\frac{-2.9988}{-0.375} \\\\u^2=7.9968\\\\u=\sqrt{7.9968}\\\\u=2.83m/s\)
The book's initial speed = 2.83 m/s
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If a car accelerates at a uniform 4.0 m/s, how long will it take to reach a speed of 36.0 m/s,
starting from rest?
Answers
Answer:
9s
Explanation:
v=u+at
36=0+4t
t=36-0/4
t=9s
Which image illustrates the bending of a wave as it passes into a new
Material?
A. A
B. B
C. C
D. D
Answers
Answer:
Option B.
Explanation:
The bending of a wave when it reaches the interface separating two media is called refraction of light.
In figure B, the wave initially in medium 1. Then it reaches the interface. After that it bends. It means the bending of light occurs in this case.
Hence, the correct option is (B).
The law of __________________________ says that people think of similar objects as belonging together.
Answers
Answer:
Explanation:is the law means that the police are the law
1. A 9000 kg van was stopped at a traffic light when it rear-ended with an 850 compact car moving to the east at a velocity of 5 m/sec. What would be the velocity of the entangled cars after collision?
Answers
Answer:
1.785 m/s
Explanation:
The momentum can be calculated using the expression below
M1 *V1 + M2 * V2 = (M1+M2) V3
M1= mass of van=9000 kg
M2= mass of car= 850kg
V3= velocity of entangled car
V1= Velocity of the van= 0
V2= velocity of the car= 5 m/ s
Substitute the values
(900×0) + (500×5)=( 900+500)× V3
2500=1400 V3
V3=2500/1400
V3= 1.785 m/s
Hence, velocity of the entangled cars after collision is 1.785 m/s
Charges of 7.2nC and 6.7nC are 32 cm apart. Find the equilibrium position for a -3.0nC charge.
Answers
Answer:
I don't know I'm sorry I will tell you another answer asks me
a 3 3-inch candle burns down in 12 hours. if b represents how much of the candle, in inches, has burned away at any time given in hours, t, write a proportional equation for b in terms of t that matches the context.
Answers
The proportional equation that matches the context of a 33-inch candle burning down in 12 hours is b = 2.75t.
A candle that is 33 inches long is called a 33-inch candle. Candles are a popular decorative item that is commonly used for lighting, as decoration for weddings, and parties, or to create an aromatic atmosphere. B represents the length of the candle that has burned away at any time given in hours, t.
To find the proportional equation for b in terms of t that matches the context of a 33-inch candle burning down in 12 hours, the following steps should be followed:
Identify the given informationThe length of the candle (l) = 33 inchesThe time taken for the candle to burn down (t) = 12 hours
Determine the rate of burning The rate of burning of the candle is given by l/t. Therefore, the rate of burning = 33/12 = 2.75 inches per hour.
The proportional equation for b in terms of t is given by b = rt where r is the rate of burning. Therefore, b = 2.75t.
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Which statement correctly describes the relationship between air temperature and air pressure?
-Warm air rises, creating an area of low pressure.
-Cool air sinks, creating an area of low pressure.
-Warm air sinks, creating an area of low pressure.
-Cool air rises, creating an area of low pressure.
Answers
A 7800 W lift took 10 seconds to move a 5000 N weight. How far did the lift move this weight?
Answers
Answer:
Both are moving at 30 km/h, so their speed is the same. ... enough fuel for the trip/how long it will take. 4 Weight is a force, and so is a vector. ... c At 10 seconds David's displacement is.
how much dark matter does there appear to be in the the milky way compared to luminous matter?
Answers
It is estimated that there is about six times more dark matter than luminous matter in the Milky Way.
What is Luminous?
"Luminous" refers to any type of matter that emits or reflects light, making it visible to our eyes or to telescopes. Examples of luminous objects include stars, planets, galaxies, and even artificial light sources such as light bulbs or LED screens.
Dark matter is a form of matter that does not interact with light or other forms of electromagnetic radiation, making it invisible to telescopes. Its presence is inferred through its gravitational effects on visible matter. Luminous matter, on the other hand, is matter that emits or reflects light and includes stars, gas, and dust.
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if a distance vs time graph is a vertical line, how would the velocity vs time graph look?
Answers
The sprinter's changing speed, as well as the speed of any other moving object or person, is displayed on a velocity-time graph. The slope of the graph line on a velocity-time graph is used to represent acceleration.
What is meant by acceleration?Velocity's rate of change with time, both in terms of speed and direction. A point or object going straight ahead is accelerated when it accelerates or decelerates. m/s2 is the unit of acceleration. The term "constant acceleration" refers to the pace at which a particle's velocity changes.
Which four forms of acceleration are there?Uniform Acceleration. Non uniform acceleration. Instantaneous Acceleration. The slope of the time-velocity graph determines the rate of acceleration.To know more about acceleration visit:
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a motetcycle was heading south at 90 m/s and then it turned west and went 35 m/s what is the velocity of the motercycle
Answers
A motorcycle was heading south at 90 m/s and then it turned west and went 35 m/s , the velocity of the motorcycle is 62.5 m/s. This is average velocity.
What is velocity?Velocity is the directional speed of an object in motion as an indication of its rate of change in position as observed from a particular frame of reference and as measured by a particular standard of time (e.g. 60 km/h northbound). Velocity is a fundamental concept in kinematics, the branch of classical mechanics that describes the motion of bodies.
Velocity is a physical vector quantity; both magnitude and direction are needed to define it. The scalar absolute value (magnitude) of velocity is called speed, being a coherent derived unit whose quantity is measured in the SI (metric system) as meters per second (m/s). If there is a change in speed, direction or both, then the object is said to be undergoing an acceleration.
Given
initial velocity , x=90m/s
final velocity , y=35m/s
formula for average velocity is \(\frac{1}{2}\) (x + y)
substituting the values
average velocity is 62.5m/s
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Which of the following is an example of light energy being changed to chemical energy?
Group of answer choices
A flashlight with rechargeable batteries
A solar panel that charges a battery
Food that is eaten to provide mechanical energy
Answers
Answer:
A solar panel
Explanation:
the gulf stream appears to be slowing down in velocity. what is thought to be a main driving force for this?
Answers
The main driving force thought to be behind the slowing of the Gulf Stream is believed to be climate change. As the atmosphere and oceans warm, the Gulf Stream is losing heat to the atmosphere.
What is the Gulf Stream ?The Gulf Stream is a powerful ocean current that originates in the Gulf of Mexico and flows northward along the eastern coast of the United States. It is part of the North Atlantic gyre, a system of circulating ocean currents. The Gulf Stream is an important part of the global conveyor belt, a system that helps regulate the ocean's climate by transporting warm tropical waters to cooler regions of the world. The Gulf Stream is so powerful that it is able to move more water than all of the world's rivers combined. It transports more than 100 million cubic meters of water per second and has a maximum speed of up to 5.6 km per hour.
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By starting with a falsifiable hypothesis and proceeding to gather data and ensure replicability, a scientist can contribute to the potential formation of a(n)
Answers
Answer:
theory
Explanation:
A scientist can contribute to the formation of a theory in a particular subject by conducting research along the line of that subject.
Conducting research requires the formation of a hypothesis and testing the hypothesis by conducting a relevant experiment during which data are gathered, analyzed, and interpreted in order to falsify or accept the hypothesis.
A good experiment must be replicate-able. When the same experiment is repeated by different independent researchers and the same conclusion is arrived at, this could potentially lead to the formation of a theory.
Hence, a scientist can contribute to the formation of a theory by conducting an experiment with replicability in order to test a hypothesis.
a balloon, rising vertically with a velocity of 16 feet per second, releases a sandbag at the instant it is 64 feet above the ground. assume the acceleration of the object is -32 feet per second per second. (a) how many seconds after its release will the bag strike the ground? (b) at what velocity will the bag hit the ground?
Answers
The sandbag will hit the ground with a velocity of -48 feet per second (negative sign indicates the downward direction).
(a) To determine the time it takes for the sandbag to strike the ground, we can use the equation:
h(t) = h₀ + v₀t + 0.5at²
where h(t) is the height at time t, h₀ is the initial height (64 feet), v₀ is the initial velocity (16 ft/s), a is the acceleration (-32 ft/s²), and t is the time in seconds. We want to find the time t when h(t) = 0 (when the bag hits the ground).
0 = 64 + 16t - 16t²
0 = 64 - 16t²
Now, we solve for t:
t² = 4
t = 2 seconds
The sandbag will strike the ground 2 seconds after its release.
(b) To find the velocity at which the bag hits the ground, we use the equation:
v(t) = v₀ + at
where v(t) is the velocity at time t, v₀ is the initial velocity (16 ft/s), a is the acceleration (-32 ft/s²), and t is the time in seconds.
v(2) = 16 - 32(2)
v(2) = 16 - 64
v(2) = -48 ft/s
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The molar mass of nickel (I) chromate is Blank 1 grams per mole. Please round atomic masses to the nearest whole number.
Note answer is not 175.
Answers
The molar mass of nickel (I) chromate is 234 grams per mole.
To determine the molar mass of nickel (I) chromate, we need to first determine the chemical formula of the compound.
Nickel (I) has a +1 oxidation state, while chromate has a -2 charge. Therefore, the chemical formula of nickel (I) chromate is Ni2CrO4.
To calculate the molar mass of Ni2CrO4, we need to find the atomic masses of nickel, chromium, and oxygen, and multiply them by their respective subscripts in the chemical formula. Rounding to the nearest whole number, we get:
Ni: 2 x 59 = 118
Cr: 1 x 52 = 52
O: 4 x 16 = 64
Molar mass of Ni2CrO4 = 118 + 52 + 64 = 234 grams per mole.
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Which forms of heat transfer require matter(particles) to happen? (Select all that apply)
Conduction
Convection
Radiation
None of these
Answers
Answer.
Conduction
Convection
explanation.
Heat can travel from one place to another in three ways: Conduction, Convection and Radiation. Both conduction and convection require matter to transfer heat. If there is a temperature difference between two systems heat will always find a way to transfer from the higher to lower system.
Match each term with its best description.
Metamorphic
rock
Foliation
Burial
metamorphism
Parent rock
?
?
?
?
The original rock before it
metamorphoses.
Parallel alignment of platy
grains.
A rock changed by heat,
pressure, and fluids.
A process that changes
rock because of pressure
with equal intensity from
Answers
Metamorphic rock: A rock changed by heat, pressure, and fluids.
Foliation: Parallel alignment of platy grains.
Burial metamorphism: A process that changes rock because of pressure with equal intensity from all sides.
Parent rock: The original rock before it metamorphoses.
Metamorphic rock: A rock changed by heat, pressure, and fluids. The word metamorphic means change in form. Metamorphic rocks are made by rocks that have been altered in some way. This can happen through heat, pressure, and fluids. Examples of metamorphic rocks include slate, gneiss, and marble.
Foliation: Parallel alignment of platy grains. Foliation is a term used to describe the parallel alignment of platy grains in a metamorphic rock. This is caused by pressure during metamorphism. The platy grains can be minerals like mica or clay.
Burial metamorphism: A process that changes rock because of pressure with equal intensity from all sides. Burial metamorphism is a process that changes rock because of pressure with equal intensity from all sides. This can happen when rocks are buried deep within the earth's crust.
Parent rock: The original rock before it metamorphoses. The parent rock is the original rock before it metamorphoses. This rock is changed into a metamorphic rock through the process of metamorphism.
To summarize, metamorphic rock is a rock that has been changed by heat, pressure, and fluids. Foliation refers to the parallel alignment of platy grains. Burial metamorphism is a process that changes rock because of pressure with equal intensity from all sides. The parent rock is the original rock before it metamorphoses.
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