Find the signal energy of each of these signals. (a) x[n]=2δ[n]+5δ[n−3] (b) x[n]=u[n]/n (c) x[n]=(−1/3)
n
u[n] (d) x[n]=cos(πn/3)(u[n]−u[n−6]) (e) x[n]=n(−1.3)
n
(u[n]−u[n−6]) (f) x[n]=2(u[n+2]−u[n−3])−3tri(n/3)
Answers
The signal energy for the given signals are as follows:
Signal energy of (a) is 29.
Signal energy of (b) is 0.
Signal energy of (c) is 9/8.
Signal energy of (d) is 7.
Signal energy of (e) is 133.4066... (rounded to four decimal places)
The signal energy is the sum of the square of each point of the signal. That is, for a discrete-time signal x(n), the signal energy E is given by
E = ∑x(n)² over all possible values of n.
Thus, to find the signal energy of each of these signals, we need to calculate the square of each point and sum up all of the values.
Let's look at each signal separately and calculate their signal energies:
a) x[n] = 2δ[n] + 5δ[n-3]
E = ∑x(n)² over all possible values of n
= (2² + 5²)
= 4 + 25
= 29
b) x[n] = u[n]/n
As n tends to infinity, the signal x[n] approaches zero. Hence, the signal energy is zero.
c) x[n] = (-1/3)^n u[n]
E = ∑[(-1/3)^n u[n]]²
= ∑[(1/9)^n u[n]]
= (1/(1 - 1/9))
= 9/8
d) x[n] = cos(πn/3)[u[n]-u[n-6]]
The signal x[n] is non-zero for 0 ≤ n ≤ 6.
Hence, the signal energy is given by
E = ∑[cos(πn/3)[u[n]-u[n-6]]]²
= ∑[cos²(πn/3)][u[n]-u[n-6]]
= 7
e) x[n] = n(-1.3)^n[u[n]-u[n-6]]
The signal x[n] is non-zero for 0 ≤ n ≤ 6.
Hence, the signal energy is given by
E = ∑[n(-1.3)^n[u[n]-u[n-6]]]²
= ∑n²(-1.3)^2n[u[n]-u[n-6]]
= 133.4066... (rounded to four decimal places)
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Related Questions
the time it takes for a college student to travel between her home and her college is uniformly distributed between 40 and 90 minutes. refer to exhibit 6-2. the probability that her trip will take exactly 50 minutes is
Answers
For the continuous probability distribution probability at any constant value is 0. Because the interval width is 0 in that case. There must always be an interval to calculate the probability in case of a uniform distribution.
Continuous probability distribution: A probability distribution in which the random variable X can take on any (continuous) value. Since there are an infinite number of values that can be assumed by X, the probability that X will take a given value is zero.
For the probability distribution of continuous distributions in this problem each constant value is 0.
P[x= 50] = 0
P(the journey will take exactly 50 minutes) = 0
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Why would you be surprised if hockey puck started moving without being hit? Why would you be surprised if a fast moving
puck suddenly stopped in the middle of the ice without being touched?
Please use scientific explanations.
Answers
Answer:
id be scared because this thing is moving by its self at an alarming rate
Explanation:
HELP!
Noble gases are the ____________________.
A. most reactive of all elements
B. least consistent of all elements
C. most consistent of all elements
D. least reactive of all elements
Answers
Answer: Most consistent of all elements (if consistency here denotes stability)
if not, then the answer will be (D)
Explanation:
Nobel gasses have full outermost electron shells which means that they are very stable and do not need to lose, gain, or share electrons to gain stability. So they do not react with other elements to form ionic or covalent bonds
fraction that occurs in gases and liquids is called what
plzz help meeeee
Answers
Answer:
it is called fluid friction.
What will be the final temperature when 100 g of 25˚C water is mixed with 75 g of 40˚C water?
Answers
Answer:
trick to this answer in this question
How many minutes are each half in soccer ?
Answers
An object of mass m is projected horizontally from the top of a building. The object's initial velocity is v, its initial height is H, and it travels a horizontal distance D before striking the ground. Let t represent the time that the object is a projectile.
Write two equations that relate the quantities v, H, D, t, and fundamental constants
Write a single equation that expresses D in terms of v, H, fundamental constants, and NOT time
Answers
A) The equations relating v, H, D, t are H = 1/2 g t² and v = D/t.
B) The equation expresses D in terms of v, H, fundamental constants, and not time is D = v √(2H/g).
Velocity of the object is represented as v.
Initial height is H
Horizontal distance travelled is D.
Time of the object in a projectile is t.
A) From the equations of kinematics, we can write,
H = 1/2 g t²
v = D/t
where,
g is acceleration due to gravity
B) From the two equations above, we have,
t = D/v ---(1)
H = 1/2 g t² ---(2)
Putting (1) in (2),
H = 1/2 g t² = 1/2 g (D/v)²
D = v √(2H/g)
Thus, the required equations are explained.
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an ink-jet printer steers charged ink drops vertically. each drop of ink has a mass of 10-11 kg, and a charge due to 751896 extra electrons. it goes through two electrodes that gives a vertical acceleration of 104 m/s2. the deflecting electric field is mv/m.
Answers
The deflecting electric field is 0.83mv/m
Acc. to the newtons 2nd law - there is an acceleration when a force acts on an object.
F = ma (equation 1)
where
F is force
m is mass of object
a is acceleration
Electric field intensity- it is defined as force experienced by a unit positive charge placed at that point.
it is denoted by E = F/q
where
F is force
q is the charge
F = Eq (equation2)
from 1 and 2 equation we get
ma = Eq
E = ma /q
Charge on the drop of ink.is q.
(e is the charge on an electron.)
so,
q = 751896×e
q = 751896×1.6 ×⁻¹⁹
q = 12.03 ×10⁻¹⁴
m = 10⁻¹¹kg
a = 10⁴ m/s²
using above values
E = ma /q
E = 10⁻¹¹×10⁴/12.03 ×10⁻¹⁴
E = 0.83mv/m
The deflecting electric field is 0.83mv/m
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what does a blue shift in light from stars indicate?
Answers
Answer:
If a star is moving towards the earth, its light is shifted to higher frequencies on the color spectrum (towards the green/blue/violet/ultraviolet/x-ray/gamma-ray end of the spectrum). A higher frequency shift is called a "blue shift".
Explanation:
It just means that the entire spectrum is shifted up in frequency.
If you know the answer please answer the following question down in the picture below.
Answers
Answer:
the answer is C
I hope I helped (◍•ᴗ•◍)❤
i dont understand pojectile motion can someone help with this
Answers
When thrown from the balloon, the sandbag has a constant horizontal/forward velocity. As the text puts it, "the sandbag continues forward as if it had not been dropped." What this means is that the sandbag has no acceleration in the horizontal plane of motion, so it moves in this direction at a constant speed. So for any time \(t\), the horizontal velocity is given by
\(v_x(t) = 12\dfrac{\rm m}{\rm s}\)
In the vertical plane of motion, the sandbag has no vertical velocity until it's released and allowed to fall. As it's falling, however, the sandbag is being pulled down by gravity and is accelerating with magnitude \(g=9.8\frac{\rm m}{\mathrm s^2}\), so its vertical/downward velocity at time \(t\) is given by
\(v_y(t) = -gt\)
So, after 3 seconds have passed, the sandbag has horizontal velocity \(v_x = 12\frac{\rm m}{\rm s}\) and vertical velocity \(v_y = -g(3\,\mathrm s) = -29.4\frac{\rm m}{\rm s}\). If the question is specifically asking about speed you would just ignore the negative signs.
A football player threw a football with a velocity of (3.0 m/s x + 5.0m/s y). How far did it travel horizontally?
Answers
The horizontal distance travelled by the football is 3.1 m.
What is the angle of projection of the ball?
The angle of projection of the football is calculated as follows;
tan ( θ ) = Vy / Vx
where;
Vy is the velocity of the ball in the vertical directionVx is the velocity of the ball in the horizontal directiontan ( θ ) = 5 / 3
tan ( θ ) = 1.667
θ = arc tan (1.667)
θ = 59⁰
The resultant velocity of the ball is calculated as follows;
v = √ (Vx² + Vy²)
v = √ (3² + 5²)
v = 5.83 m/s
The horizontal distance travelled by the football is calculated as follows;
x = v² sin(2θ) /g
where;
v is the resultant velocityg is acceleration due to gravityθ is the angle of projection of the ballx = [ (5.83)² sin(2 x 59) /9.8 ]
x = 3.1 m
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how many wavelengths thick is a 1/2 mm thumbnail
how many wavelengths thick is 100 micrometer thick hair
Answers
The amount of wavelength of light thick is the thumbnail x/y.
Given:
Wavelength of light= x
Thickness of thumbnail= y
The amount of wavelength thick the thumbnail is x/y
What is wavelength?
Wavelength is the distance between identical points (adjacent peaks) in adjacent cycles of a waveform signal propagated in space or along a wire. In wireless systems, this length is usually given in meters (m), centimeters (cm), or millimeters (mm).To know more about wavelength, click the link given below:
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The energy (E) of photon depends upon its wavelngth 'λ' , Planck's constant ' h ' and velocity
' c'. Derive the formula for energy using dimensional analysis
Answers
The formula for energy of a photon in terms of its wavelength, Planck's constant, and the speed of light is:
E = (hc)/λ
We can use dimensional analysis to derive the formula for energy of a photon in terms of its wavelength, Planck's constant, and the speed of light.
A photon's energy can be written as:
E = f × h
where
f is the frequency of the photon and h is Planck's constant.
We know that the frequency of a photon is related to its wavelength and the speed of light by the following equation:
f = c/λ
where c is the speed of light and λ is the wavelength.
Substituting this expression for f into the equation for energy, we get:
E = (c/λ) × h
Now let's check the dimensions of each term in this expression using brackets [] to represent dimensions:
[c/λ] = [L/T] / [L] =\([T^{-1} ]\)
[h] = [\(M L^2 T^{-1}\)]
Therefore, the dimensions of the product (c/λ) × h are:
\([T^{-1} ] \times [M L^2 T^{-1} ] = [M L^2 T^{-2} ]\)
This is the dimension of energy (which can be expressed as\([M L^2 T^{-2} ]).\)
Therefore, we can conclude that the formula for energy of a photon in terms of its wavelength, Planck's constant, and the speed of light is:
E = (hc)/λ
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When Abner weighs himself at home in the morning, he sees that he weighs 500 N. Abner carries his scale with him to an office building. While taking the elevator up to the top floor he stands on the scale, and notices that the scale reads 400 N. What was the elevator's y-acceleration when he read the scale? (take the +y-direction to be upward) (a) 2.0 m/s2 (c) 1.5 m/s2 (e) 1.0 m/s2 (b) -2.0 m/s? (d) -1.5 m/s2 (1) -1.0 m/s
Answers
The y-acceleration is -1.96 m/s2, or approximately -1.5 m/s2.
To find the elevator's y-acceleration, we can use the equation F = ma, where F is the force, m is the mass, and a is the acceleration. In this case, the force is the difference between Abner's weight at home and his weight on the elevator, or 500 N - 400 N = 100 N. The mass is Abner's mass, which we can find by dividing his weight by the acceleration due to gravity (9.8 m/s2), or 500 N / 9.8 m/s2 = 51.02 kg. Plugging these values into the equation, we get:
100 N = 51.02 kg * a
Solving for a, we get:
a = 100 N / 51.02 kg = 1.96 m/s2
Since the elevator is moving upward, but Abner's weight is decreasing, this means that the elevator is accelerating downward. Therefore, the y-acceleration is -1.96 m/s2, or approximately -1.5 m/s2.
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If you were to make a three-dimensional model of magnetic force using a magnet and magnetic field lines, which two characteristics might your model have
Answers
Answer:
- the Magnetic field lines will spread out of the north end of the magnet.
- the magnetic fields will three-dimensional and resemble a bubble.
Explanation:
- Usually, when drawing magnetic field lines, we start outwardly from the North pole to the South Pole. This same direction is also prevalent on the Earth due to the fact that the Earth functions as a giant magnet. Thus, one characteristic of the model is that the Magnetic field lines will spread out of the north end of the magnet.
- Another thing is that Magnetic field forces are usually driven as a result bubble like configuration which affects the objects that are in such a configuration. Thus, another characteristic of the model is that the magnetic fields will three-dimensional and resemble a bubble.
Slove these problem physics
Answers
Answer:
element name = neon
no of proton = 10
no. if neutron = 9
atomic no. = 10
atomic weight = 20.17179u
it lies in group 18 and period 2
it is nonmetal because it is a noble gas .
hope this helped you ☺️
A solid will float in a liquid if it is less dense than the liquid, and sink if it is more dense than the liquid. If the density of seawater is 1.025 g/mL, which types of plastics would definitely float in seawater? JUSTIFY your answer.
Answers
Explanation:
Plastics with a density less than or equal to 1.025 g/mL will float in seawater, while plastics with a density greater than 1.025 g/mL will sink.
Here are some examples of plastic densities:
Polyethylene terephthalate (PET) has a density of approximately 1.38 g/mL, so it will sink in seawater.
Polypropylene (PP) has a density of approximately 0.9 g/mL, so it will float in seawater.
High-density polyethylene (HDPE) has a density of approximately 0.95 g/mL, so it will float in seawater.
Polystyrene (PS) has a density of approximately 1.05 g/mL, so it will sink in seawater.
Based on the above examples, we can see that plastics such as polypropylene and high-density polyethylene will definitely float in seawater, while others such as polyethylene terephthalate and polystyrene will definitely sink. Other types of plastics with densities close to 1.025 g/mL may float or sink depending on their exact density and the conditions of the water, such as temperature and salinity.
What can be said of the size of the event horizon for a 10Msun black hole?
-larger than that of a 1Msun black hole.
-smaller than that of a 1Msun black hole.
-the same size as for a 1Msun black hole (because the escape velocity for both is the speed of light).
Answers
The event horizon of a black hole is the boundary beyond which nothing, not even light, can escape its gravitational pull. The size of the event horizon is directly related to the mass of the black hole.
Specifically, the Schwarzschild radius formula can be used to determine the size of the event horizon, which is given by Rs = 2GM/c^2, where Rs is the Schwarzschild radius (event horizon radius), G is the gravitational constant, M is the mass of the black hole, and c is the speed of light. For a 10Msun black hole, the event horizon will be larger than that of a 1Msun black hole. This is because the mass term (M) in the formula directly affects the event horizon size. When comparing a 10Msun black hole to a 1Msun black hole, the 10Msun black hole has 10 times the mass, which will result in a correspondingly larger event horizon. The escape velocity for both black holes is indeed the speed of light, but their event horizons will differ in size due to the variation in mass.
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What is the objects average velocity?
Answers
Answer:
answer should be 10 because the line goes from (0,0) then to (1,10) and so on
Line segment gj is a diameter of circle l. angle k measures (4x 6)°. circle l is inscribed with triangle g j k. line segment g j is a diameter. line segments g k and k j are secants. angle k has a measure of (4 x 6) degrees. what is the value of x? 21 24 32 44
Answers
The value of x in the given right triangle in a semicircle is determined as 21.
What is the measure of a triangle in a semicircle?The triangle in a semicircle is always a right angle triangle.
From the figure shown, we can say that the triangle G J K is right triangle and m<K = 90degrees.
Given that m<K = 4x + 6, we will can use the following equation to find the value of x as shown:
4x + 6 = 90
4x = 90 - 6
4x = 84
x = 21
Thus, the value of x in the given right triangle in a semicircle is determined as 21.
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An object of mass M₁ travels in a circular path of radius R on a horizontal table. The object is attached to a string that passes through a hole in the center of the table. An object of mass M₂ is attached to the other end of the string and hangs vertically under the table, which produces a force on M₁. All frictional forces are considered to be negligible. Which quantity or quantities must be measured to determine the tangential speed required to keep the system in equilibrium?
Answers
Answer:
M₁, M₂, R
Explanation:
Draw free body diagrams for both masses.
M₁ has three forces: tension force T towards the center, gravity force M₁g downwards, and normal force N upwards.
M₂ has two forces: tension force T upwards and gravity force M₂g downward.
Sum the forces on M₁ in the centripetal direction.
∑F = ma
T = M₁ v² / R
Sum the forces on M₂ in the y direction.
∑F = ma
T − M₂g = 0
T = M₂g
Substitute:
M₁ v² / R = M₂g
Solve for v:
v² = (M₂ / M₁) g R
v = √((M₂ / M₁) g R)
Therefore, to calculate the velocity, both masses need to be known, as well as the radius of circular path.
A baseball pitcher can throw a 132 km/h (82 mph) curve ball that
rotates about 6.0×102 rpm. What is the angular velocity of the
thrown ball? The pitcher's throwing motion lasts about 0.15 s, and
the moment of inertia of the ball is 8.0x10-5 kg-m?. What average
torque did the pitcher exert on the ball?
If someone can please solve this right now it’ll be a big help!!
Answers
Answer:
To determine the angular velocity of the thrown ball, we can use the formula:
Angular velocity (ω) = (2π * n) / 60
where ω is the angular velocity, n is the rotation rate in revolutions per minute (rpm), and 2π is a conversion factor. The average torque exerted by the pitcher on the ball is approximately 3.35 × 10^-2 N·m.
Explanation:
Given that the rotation rate is 6.0 × 10^2 rpm, we can calculate the angular velocity:
ω = (2π * 6.0 × 10^2) / 60 = 20π rad/s ≈ 62.83 rad/s
Therefore, the angular velocity of the thrown ball is approximately 62.83 rad/s.
To calculate the average torque exerted by the pitcher on the ball, we can use the formula:
Torque (τ) = moment of inertia (I) * angular acceleration (α)
The moment of inertia of the ball is given as 8.0 × 10^-5 kg·m², and the time taken for the throw is 0.15 s. To find the angular acceleration (α), we can use the formula:
Angular acceleration (α) = change in angular velocity / time
Since the ball starts from rest (0 rad/s) and reaches an angular velocity of 62.83 rad/s in 0.15 s, the change in angular velocity is:
Change in angular velocity = 62.83 rad/s - 0 rad/s = 62.83 rad/s
Now, we can calculate the angular acceleration:
α = (Change in angular velocity) / time = 62.83 rad/s / 0.15 s ≈ 418.87 rad/s²
Finally, we can calculate the average torque:
τ = I * α = 8.0 × 10^-5 kg·m² * 418.87 rad/s² ≈ 3.35 × 10^-2 N·m
Therefore, the average torque exerted by the pitcher on the ball is approximately 3.35 × 10^-2 N·m.
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What is Accenture doing for sustainability?
Answers
By calculating carbon emissions reduction and sustainability index improvement, the Accenture MyNav Green Cloud Advisor incorporates sustainability when moving client data centers to the cloud.
The availability of computer system resources without the user having to manage them directly is referred to as cloud computing. The network of remote servers located on the internet in this instance aids in the management and storage of the data.
Mynav Green Cloud Advisor is essential since it aids businesses in creating cloud solutions that may be utilized to lower carbon emissions.
As cloud solutions are essential to businesses, Accenture MyNav Green Cloud Advisor integrates sustainability.
reduces the expense of transportationcreates a design that is appropriate and aids the customer in becoming more sustainable.by reconfiguring factories so that carbon emissions may be easily measuredestablishes sustainable guidelines for disposing of outdated technology.by implementing creative business techniques to reduce the cost of transportationby creating new regulations for removing outdated technologies.To learn more about Accenture and sustainability from given link
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I NEED HELP ASAP!! PLEASE
A skydiver falling towards Earth and is traveling at 19 m/s opens her parachute. She slows to a speed of 3 m/s The whole process takes only 2 seconds . What is her acceleration ? Explain why this acceleration is positive or negative
Answers
Answer:
Acceleration = -3m/s²
Explanation:
Given the following data;
Initial velocity = 19m/s
Final velocity = 3m/s
Time = 2secs
To find the acceleration;
In physics, acceleration can be defined as the rate of change of the velocity of an object with respect to time.
This simply means that, acceleration is given by the subtraction of initial velocity from the final velocity all over time. Mathematically, acceleration is given by the equation;
\(Acceleration (a) = \frac{final \; velocity - initial \; velocity}{time}\)
Substituting into the equation, we have;
\(a = \frac{3 - 9}{2}\)
\(a = \frac{-6}{2}\)
Acceleration = -3m/s²
The value for her acceleration is negative because she is decelerating i.e her final velocity is lower than her initial velocity.
A ball bouncing eventually coming to a stop A. Open system B. Closed system C. Isolated system
Answers
Given:
A ball bouncing eventually comes to stop.
To find:
What kind of a system is this?
Explanation:
An open system is a system where the free exchange of matter and energy with the surroundings takes place.
A closed system is where only the energy of the system is shared with the surrounding. In these kinds of systems, the exchange of matter does not take place.
An isolated system is where neither matter nor energy is exchanged between the system and the surrounding.
When a ball is bouncing, it gradually loses its kinetic energy to the surroundings and eventually comes to stop. But the mass of the ball remains the same. Thus this is a closed system.
Final answer:
The given system is a closed system.
Therefore the correct answer is option B.
What is the probability of rolling a 6 on a number cube?
Answers
I was researching something for some teaching resources when I came across the phrase "six-sided number cube" on the AP Statistics website, which is a sort of Martian-like description of what we call a die in English.
With six numbers, there are 63 potential combinations. In general, the formula shown below can be used to determine how many combinations are possible given a set of n elements: 2n – 1 is the number of combinations with n elements. The equation then reads as follows for 6 elements. 6 elements could be combined in 720 different ways using the formula 6*5*4*3*2. If you have the option, you can alter the order of the components in a way that uses less of each.
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A 15 kg wagon with frictionless wheels carrying a 5 kg mass is moving at a speed of 3.75 m/s when it reaches another frictionless wagon of mas 15 kg. This wagon is attached to a spring of negligible mass which has a spring constant of 250 N/m. The other end of the spring is fixed to the wall. Upon impact the two wagons stick together and compress the spring. Determine the distance the wagons travel until the spring is fully compressed.
Answers
The distance the wagons travel until the spring is fully compressed is 2 × xmax = 3.42 m. To solve this problem, we need to apply the principle of conservation of momentum and conservation of energy.
Initially, the momentum of the system is given by:
p1 = (15 kg + 5 kg) × 3.75 m/s = 75 kg m/s
After the collision, the two wagons stick together and move as one unit, with a combined mass of 30 kg. Let v be the common velocity of the two wagons after the collision. Then, the momentum of the system is given by:
p2 = 30 kg × v
According to the principle of conservation of momentum, p1 = p2. Therefore, we have:
75 kg m/s = 30 kg × v
which gives:
v = 2.5 m/s
Now, let's consider the energy of the system. Initially, the kinetic energy of the system is given by:
K1 = (1/2) × (15 kg + 5 kg) × (3.75 m/s)² = 421.875 J
After the collision, the energy of the system is stored in the compressed spring. The potential energy of a spring is given by:
U = (1/2) × k × x²
where k is the spring constant and x is the displacement of the spring from its equilibrium position. At maximum compression, the displacement is xmax, and the potential energy is:
Umax = (1/2) × 250 N/m × xmax²
According to the principle of conservation of energy, the initial kinetic energy of the system is converted to potential energy of the spring at maximum compression. Therefore, we have:
K1 = Umax
which gives:
xmax = sqrt(2 × K1 / k) = 1.71 m
Therefore, the distance the wagons travel until the spring is fully compressed is 2 × xmax = 3.42 m.
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A radioactive chemical has a decay rate of approximately 5% per year. Suppose that this chemical is released into the atmosphere each year for 15 yr at a constant rate of 1 lb per year. How much of this chemical will remain in the atmosphere after 15 yr? The amount of chemical remaining in the atmosphere is lbs.
Answers
After 15 years, approximately 0.319 lb (or 0.319 pounds) of the radioactive chemical will remain in the atmosphere.
The decay rate of the chemical is approximately 5% per year, which means that each year, 95% of the chemical will remain after decay. This can be expressed as a decay factor of 0.95.
Since the chemical is released into the atmosphere at a constant rate of 1 lb per year for 15 years, we can calculate the amount remaining using the formula:
Remaining amount = Initial amount * Decay factor^Number of years
In this case, the initial amount is 1 lb, the decay factor is 0.95, and the number of years is 15. Plugging these values into the formula, we get:
Remaining amount = 1 lb * (0.95)^15
Calculating this expression, we find:
Remaining amount ≈ 0.319 lb
After 15 years, approximately 0.319 lb of the radioactive chemical will remain in the atmosphere. The decay rate of 5% per year gradually reduces the amount of chemical present, resulting in a relatively small fraction remaining after 15 years.
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a traveler first drives 21.0 km east, then 28.8 km southeast, and finally 10 km south. what is the magnitude
Answers
The magnitude of the traveler's displacement is approximately 39.5 km.
To find the magnitude of the traveler's displacement, we can combine the individual displacements in a vector sum.
The first leg of the journey is a displacement of 21.0 km east. We can represent this as a vector in the positive x-direction: (21.0 km, 0 km).
The second leg of the journey is a displacement of 28.8 km southeast. We can break down this displacement into its x and y components. The southeast direction is a combination of east and south. The angle between the southeast direction and the positive x-axis is 45 degrees. Using trigonometry, we can find the x and y components:
x-component = 28.8 km * cos(45°) = 20.4 km
y-component = 28.8 km * sin(45°) = 20.4 km
So, the second displacement can be represented as a vector: (20.4 km, -20.4 km).
The third and final leg of the journey is a displacement of 10 km south. We can represent this as a vector in the negative y-direction: (0 km, -10 km).
To find the total displacement, we add the individual displacements:
(21.0 km, 0 km) + (20.4 km, -20.4 km) + (0 km, -10 km) = (41.4 km, -30.4 km)
The magnitude of the displacement is given by the Pythagorean theorem:
Magnitude = √((41.4 km)² + (-30.4 km)²) ≈ 39.5 km
Therefore, the magnitude of the traveler's displacement is approximately 39.5 km.
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