Answer:
1.14*10^-3m
Explanation:
We know that
Volume= mass/ density
But
Area x depth= mass/density
πr²*depth= mass/density
r²=m/πdp
So
r= √0.35/3.142*0.085*1000
r= 1.14*10^-3m
Draw the velocity vectors starting at the black dots and the acceleration vectors including those equal to zero. The orientation of the vectors will be graded. The location and length of the velocity vectors will be graded. The location and length of the nonzero acceleration vectors will not be graded. To draw a zero vector click at the point of its location.
Answer:
hello your question is incomplete attached below is the remaining part and the solution
Explanation:
The accelerations at points 1,2,3 is zero and this is because the velocities at points 1,2,3 are constants. attached below is the velocity vector diagram and the acceleration vectors
A paper pinwheel is spinning in the wind. Which statement is correct about the forces responsible for the rotation?
A. The perpendicular components of gravity and the force of wind are responsible for the rotation.
B. Only the perpendicular component of wind is responsible for the rotation, because gravity points downward.
C. The components of gravity and the force of wind that point through the pivot are responsible for the rotation.
D. Only the perpendicular component of gravity is responsible for the rotation, because wind points toward the pivot.
Answer:
Only the perpendicular component of gravity is responsible for the rotation because wind points toward the pivot.
Explanation:
Where on the physical activity pyramid do sedentary activities belong?
Answer:A
Explanation:
i just did the test
Answer: A.
Explanation: Edge said it was right
Use the table below to calculate the acceleration of the object. Time (s) 0.0 3.0 6.0 9.0 Velocity (m/s) 0.0 1.2 2.4 3.6
explanation
a=average velocity/average time
average velocity=0.0+1.2+2.4+3.6/4
average velocity=7.2/4
average velocity=1.8 m/s
average time=0.0+3.0+6.0+9.0/4
average time=18/4
average time=4.5 s
a= average velocity/average time
a=1.8/4.5
a=0.4 m/s²
You toss a 100-g rock in the air with a kinetic energy of 5.0 J. How much is its speed as it leaves your hand
Answer:
The speed is 10 m/s
Explanation:
Th mass if the rock = 100 g = 0.1 kg
The kinetic energy = 5.0 J
speed of the rock = ?
The kinetic energy of the rock is given by the equation
E = [tex]\frac{1}{2} mv^{2}[/tex]
where
m is the mass of the rock
V is the velocity of the rock
substituting, we have
5 = [tex]\frac{1}{2} *0.1*v^{2}[/tex]
[tex]v^{2}[/tex] = 5/0.05 = 100
v = [tex]\sqrt{100}[/tex] = 10 m/s
A 5 kg object is launched from a 35 m high cliff at an angle of 30 degrees with a speed of 100 m/s. How far from the cliff does it hit the ground
Answer:
The object will hit the ground at 882.77 m from the lunch
Explanation:
we are to find the range of the motion
What is range?
It is the distance from the point of projection to the point where the object hits the ground
R=(v^2sin2θ)/g
Given data
v= 100 m/s
θ= 30 degree
g= 9.81 m/s^2
Substituting to find the R we have
R= 100^2 *sin(2*30)/9.81
R= (10000*0.866)9.81
R= 8660/9.81
R= 882.77 m
PLEASE HELP NEED ANSWERS NOW! Time-Distance Graph
Listed in the Item Bank are some important labels for sections of the image below. To find out more information about labels, some have more details available when you click on them. Drag and drop each label to the corresponding area it identifies in the image.
Answer: I added a picture of the answer
Explanation: its right
The image of answer with labeled Time-Distance Graph is attached.
What is speed?
Speed is distance travelled by the object per unit time. Due to having no direction and only having magnitude, speed is a scalar quantity With SI unit meter/second.
What is a Distance-Time Graph?How far an object has moved in a certain amount of time is displayed on a distance-time graph. The graph that shows the results of the distance vs time analysis is a straightforward line graph.
The Y-axis represents the distance.The X-axis is used to plot time.When the object's motion is uniform, and the graph is a straight line. we can determine the object's speed at any given moment of time from the graph. The object was in the following positions when it started and stopped:
Speed = (Final Position-Initial position)/Time
Drawing a rectangle anywhere along the straight line that regulates the object's speed will reveal the slope of the line. A horizontal line on the distance-time graph indicates that an object is at rest if it is not moving.
Learn more about speed here:
https://brainly.com/question/28224010
#SPJ5
"Which gives the transverse acceleration of an element on a string as a wave moves along an x axis along the string?"
Answer:
the second derivative of y with respect to time gives the transverse acceleration of an element on a string as a wave moves along an x axis along the string
Explanation:
This is because the transverse wave movement of particles take place in direction 90° to direction of movement of the wave (x) itself, so second derivative of y with respect to time (t)is what will be required
Examples of sources of physical entropy for secure random number generation include:________
Answer:
Noise in the environment
Electrons emitted via the photoelectric effect
Explanation:
Physical entropy can be seen as a disorderliness that can be observed in a physical system. The noise in a physical system can be used for secure number generation because of its randomness.
Noise is known to have no defined pattern and hence, can be used to creates secure random key generations.
Electrons emitted via the photoelectric effect: Electrons are emitted in a random order whenever a beam of light is incident on a photoelectric material. These electrons emitted can be used for random key generations
The tidal lung volume of human breathing, representing the amount of air inhaled and exhaled in a normal breath, is 500 cm3. (Assume atmospheric pressure.)(a) What is the number of molecules of air inhaled with each human breath when the air temperature is 18.0°C?________molecules(b) If the molar mass of air is 28.96 g/mol, what is the mass of air molecules inhaled with each breath? (Assume the air temperature is 18.0°C.)(c) It has been calculated that all of the air in Earth's atmosphere could be collected into a sphere of diameter 1,999 km at a pressure of 1.00 atm. What is the mass of the air in Earth's atmosphere? (Assume the density of air used in this calculation was 1.225 kg/m3.)(d) If all 7 billion humans on Earth inhaled simultaneously, what percentage of the atmosphere would be inhaled during this process? (Assume the air temperature is 18.0°C everywhere on Earth.)
Answer:
Explanation:
Temperature of air = 18°C = 273 + 18 = 291 K .
volume = 500 cc = 0 .5 litre .
pressure = one atmosphere ( atm) .
From gas equation , we can calculate this volume at NTP as follows.
volume = .5 x ( 273 / 291 ) litre
= 0.469 litre .
In any gas at NTP , 22.4 litre contains 6.02 x 10²³ molecules
.469 litre will contain 6.02 x 10²³ x .469 / 22.4 molecules
= 126 x 10²⁰ molecules .
b )
one mole = 6.02 x 10²³ molecules
6.02 x 10²³ molecules has weight of 28.96 grams
126 x 10²⁰ molecules has weight of 28.96 x 126 x 10²⁰ / 6.02 x 10²³ grams
= .606 gram .
c )
volume of all the air in the atmosphere = volume of sphere
= 4 / 3 x π x R³
= ( 4 / 3) x 3.14 x (999.5 x 10³ )³ m³
= 4.18 x 10¹⁸ m³
density of air = 1.225 kg / m³
mass of air = 1.225 x 4.18 x 10¹⁸ kg
= 5.12 x 10¹⁸ kg
d )
volume of air inhaled by 7 billion people
= . 5 x 7 x 10⁹ litre
= 3.5 x 10⁶ m³ .
Total volume of air in atmosphere = 4.18 x 10¹⁸ m³
required percentage
= 3.5 x 10⁶ x 100 / 4.18 x 10¹⁸
= .8373 x 10⁻¹⁰ % .
g a small smetal sphere, carrying a net charge is held stationarry. what is the speed are 0.4 m apart
Complete Question
A small metal sphere, carrying a net charge q1=−2μC, is held in a stationary position by insulating supports. A second small metal sphere, with a net charge of q2= -8μC and mass 1.50g, is projected toward q1. When the two spheres are 0.80m apart, q2 is moving toward q1 with speed 20ms−1. Assume that the two spheres can be treated as point charges. You can ignore the force of gravity.The speed of q2 when the spheres are 0.400m apart is.
Answer:
The value [tex]v_2 = 4 \sqrt{10} \ m/s[/tex]
Explanation:
From the question we are told that
The charge on the first sphere is [tex]q_1 = 2\mu C = 2*10^{-6} \ C[/tex]
The charge on the second sphere is [tex]q_2 = 8 \mu C = 8*10^{-6} \ C[/tex]
The mass of the second charge is [tex]m = 1.50 \ g = 1.50 *10^{-3} \ kg[/tex]
The distance apart is [tex]d = 0.4 \ m[/tex]
The speed of the second sphere is [tex]v_1 = 20 \ ms^{-1}[/tex]
Generally the total energy possessed by when [tex]q_2[/tex] and [tex]q_1[/tex] are separated by [tex]0.8 \ m[/tex] is mathematically represented
[tex]Q = KE + U[/tex]
Here KE is the kinetic energy which is mathematically represented as
[tex]KE = \frac{1 }{2} m (v_1)^2[/tex]
substituting value
[tex]KE = \frac{1 }{2} * ( 1.50 *10^{-3}) (20 )^2[/tex]
[tex]KE = 0.3 \ J[/tex]
And U is the potential energy which is mathematically represented as
[tex]U = \frac{k * q_1 * q_2 }{d }[/tex]
substituting values
[tex]U = \frac{9*10^9 * 2*10^{-6} * 8*10^{-6} }{0.8 }[/tex]
[tex]U = 0.18 \ J[/tex]
So
[tex]Q = 0.3 + 0.18[/tex]
[tex]Q = 0.48 \ J[/tex]
Generally the total energy possessed by when [tex]q_2[/tex] and [tex]q_1[/tex] are separated by [tex]0.4 \ m[/tex] is mathematically represented
[tex]Q_f = KE_f + U_f[/tex]
Here [tex]KE_f[/tex] is the kinetic energy which is mathematically represented as
[tex]KE_f = \frac{1 }{2} m (v_2^2[/tex]
substituting value
[tex]KE_f = \frac{1 }{2} * ( 1.50 *10^{-3}) (v_2 )^2[/tex]
[tex]KE_f = 7.50 *10^{ -4} (v_2 )^2[/tex]
And [tex]U_f[/tex] is the potential energy which is mathematically represented as
[tex]U_f = \frac{k * q_1 * q_2 }{d }[/tex]
substituting values
[tex]U_f = \frac{9*10^9 * 2*10^{-6} * 8*10^{-6} }{0.4 }[/tex]
[tex]U_f = 0.36 \ J[/tex]
From the law of energy conservation
[tex]Q = Q_f[/tex]
So
[tex]0.48 = 0.36 +(7.50 *10^{-4} v_2^2)[/tex]
[tex]v_2 = 4 \sqrt{10} \ m/s[/tex]
A football is kicked from ground level with an initial velocity of 23.8 m/s at angle of 42.5° above the horizontal. How long, in seconds, is the football in the air before it hits the ground? Ignore air resistance.
Answer:
The value is [tex]t = 3.28 \ s[/tex]
Explanation:
From the question we are told that
The initial velocity is [tex]u = 23.8 \ m/s[/tex]
The angle is [tex]\theta= 42.5^o[/tex]
Generally from the projectile motion equation we know that the time of flight is mathematically represented as
[tex]t = \frac{2 * u *sin (\theta )}{ g }[/tex]
=> [tex]t = \frac{ 2 * 23.8 * sin (42.5)}{9.8 }[/tex]
=> [tex]t = 3.28 \ s[/tex]
An optical fiber made of glass with an index of refraction 1.50 that is coated with a material with index of refraction 1.30 has a critical angle of
Answer:
A critical angle of 60.1°
Explanation:
Let's say
n1 Refractive index of rarer medium
n2 Refractive index of denser medium
So using the relation
စc= Sin^ -1(n1/n2)
So
စc = Sin^-1(1.3/1.5) = 60.1°
What speed would such a block have if pushed horizontally 108 m along a frictionless track by such a laser
Hello. This question is incomplete. The full question is:
You've recently read about a chemical laser that generates a 20-cm-diameter, 25.0 MW laser beam. One day, after physics class, you start to wonder if you could use the radiation pressure from this laser beam to launch small payloads into orbit. To see if this might be feasible, you do a quick calculation of the acceleration of a 20-cm-diameter, 100 kg,perfectly absorbing block. What speed would such a block have if pushed horizontally 108 m along a frictionless track by such a laser?
Answer:
V = 0.408 m / s
Explanation:
First, it is necessary to find the radiation pressure on the surface. You will find it using the following formula:
P = P / (πr ^ 2) c
where P is the pressure and c is the speed of light in vacuum
P = 25 * 10 ^ 6 / π (0.2 / 2) ^ 2 * (3 * 10 ^ 8) = 2,652 N / m ^ 2.
Then you must calculate the force (F) and the acceleration (a). This is done through the formulas:
F = P * (πr ^ 2)
F = 2,652 * π * (0.2 / 2) ^ 2 = 0.083N
a = F / m
a = 0.083 / 100 = 0.0002129 m / s ^ 2
You can now calculate the speed.
V = √2ad
V = √2 *0.0002129 * 108
V = 0.2144 m / s
A proton accelerates from rest in a uniform electric field of 660 N/C. At one later moment, its speed is 1.30 Mm/s (nonrelativistic because v is much less than the speed of light). (a) Find the acceleration of the proton. m/s2 (b) Over what time interval does the proton reach this speed? s (c) How far does it move in this time interval? m (d) What is its kinetic energy at the end of this interval? J
Answer:
a) a = 6.31 10¹⁰ m / s² , b) t = 2.06 10⁻⁵ s , c) x = 13.39 m , d) ΔK = 1.41 10⁻¹⁵ J
Explanation:
a) Since they indicate that the speeds are non-relativistic, we can use the kinematics relations and Newton's second law
F = m a
The force in electrical is
F = qE
qE = m a
a = qE / m
we calculate
a = 1.6 10⁻¹⁹ 660 / 1.673 10⁻²⁷
a = 6.31 10¹⁰ m / s²
b) Let's use the one-dimensional kinematics relation
v = v₀ + a t
as part of rest its initial velocity is zero
v = a t
t = v / a
t = 1.30 10⁶ / 6.31 10¹⁰
t = 2.06 10⁻⁵ s
c) We use the kinematics displacement equation
x = v₀ t + ½ a t²
initial velocity is zero
x = ½ a t²
x = ½ 6.31 10¹⁰ (2.06 10⁻⁵)²
x = 1,339 10¹ m
x = 13.39 m
d) the kinetic energy is
ΔK = Kf -K₀
ΔK = ½ m v² - 0
ΔK = ½ 1.673 10⁻²⁷ (1.30 10⁶) 2
ΔK = 1.41 10⁻¹⁵ J
Joey drives his Skidoo 13 kilometres north. He stops for lunch and then drives 10kilometres south. What distance did he cover? What was his displacement?
Answer:
Total distance covered (scalar quantity) = 23 km
Displacement (vector quantity) = 3 km north from the original starting point
Explanation:
Since he drove 13 km north and then 10 km south, the total distance he cover in his drive was: 13 km + 10 km = 23 km
On the other hand, his displacement was 3 km north from where he started.
Rayna studied rats in a lab. She observed that all 50 rats in her sample preferred to eat brand A rat food and would eat brand B food only when brand A was not available. Can she correctly conclude that all rats prefer brand A rat food over brand B food? Why or why not?
Answer:
it is correct to conclude that rats prefer food A over food B
the standard deviation is zero
Explanation:
In the experiment performed when both meals are available, rats prefer food A and eat only B when no other is available.
Therefore it is correct to conclude that rats prefer food A over food B
This conclusion is correct because ours is significant with a population of 50 animals all have the same preference for which the standard deviation is zero
PHYSICS HW HELP PLS!! explain how you got it too thank you! :)
1.) F= Gm1m2/d2 for m2
2.) R= V/I for I
3.) = xd/L for d
4.) ac= v^2/r for v
5.) A= πr^2 for r
6.) vf^2= vi^2+2ax for x
Answer:
Explanation:
Can you please place the square roots in a proper manner so I may assist you?
A container of gas at 2.7 atm pressure and 133 ∘C is compressed at constant temperature until the volume is halved. It is then further compressed at constant pressure until the volume is halved again.
a) What is the final pressure (atm)?
b) What is the final temperature (C)?
Answer:
5.4atm ,66.5°c
Explanation:
Note that we are given the initial temperature to constant,
Thus PV = constant
so volume halved means pressure doubled from P1v1= p2v2
Hence P2 = 2.7*2atm = 5.4atm
next step we keep pressure constant thenV/T = constant
so volume halved means temperature also halved from V1/T1= v2/T2
Hence
T = 133/2 = 66.5°C
if abus travelling at 20m/s is subject to steady decceleration of 5m/s².how long will it take yo come to rest.
Answer:
4 seconds
Explanation:
Given:
v₀ = 20 m/s
v = 0 m/s
a = -5 m/s²
Find: t
v = at + v₀
0 m/s = (-5 m/s²) t + 20 m/s
t = 4 s
A right triangle has a hypotenuse of 37 and a leg of 10. What is the second leg of the triangle?
Answer:
The second leg of the triangle is 35.62
Explanation:
Given that
Hypotenuse = 37
A leg = 10
Based on the above information
The second leg of the triangle is
According to the Pythagorean theorem
a^2 + b^2 = c^2
where,
a and b = legs
And, the c = hypotenuse.
Now put these values to the above formula
So,
10^2 + b^2 = 37^2
b^2 = 37^2 - 10^2
b^2 = 1269
b = sqrt(1269)
b = 35 .62
Hence, the second leg of the triangle is 35.62
The other leg is 35 mm.
what is the significant contribution of Heraclitus
Explanation:
HERACLITUS ALSO SPELLED HERADEITUS, [ BORN C.540 bce, EPHESUS, ANATOLIA [ NOW SELCUK, TURKEY] - DIED C.486 ] GREEK PHILOSOPHER REMEMBERED FOR HIS COSMOLOGY, IN WHICH FIRE FORMS THE BASIC MATERIAL PRINCIPLE OF AN ORDERLY UNIVERSE . LITTLE IS KNOWN ABOUT HIS LIFE, AND THE ONE BOOK HE APPARENTLY WROTE IS LOST.
HOPE IT HELP.....❤❤Formula of velocity
Answer:
s = d/t
Explanation:
s= speed
d = distance traveled
t = time elapsed
if the DIY parachute is dropped freely from the rooftop of the building of a building and reached the ground 3s later.Upon reaching the ground,What is the (a)final velocity of DYI parachutes ?(b) Height of the rooftop?
Answer:
It depends on what the parachute is made out of.
Explanation:
What is the direction of the magnetic field at the location of the charge due to the current-carrying wire
Answer: please find the answer in the explanation.
Explanation:
The direction of the magnetic field at the location of the charge due to the current-carrying wire can be determined by using right hand rule.
The thumb points in the direction of current while the fingers curl around in the direction of the magnetic field.
The right hand rule applies to a current in a straight wire. The thumb is pointed in the direction of the current and the fingers then give the direction of the magnetic field lines.
When a rubber ball dropped from rest bounces off the floor, its direction of motion is reversed becaue
(A) energy of the ball is conserved
(B) momentum of the ball
(C) the floor exerts a force on the ball that stops its fall and then drives it upward
(D) the floor is in the way and the ball has to keep moving
(E) none of the above
Answer:In physics, energy is the quantitative property that must be transferred to an object in order to perform work on, or to heat, the object.[note 1] Energy is a conserved quantity; the law of conservation of energy states that energy can be converted in form, but not created or destroyed. The SI unit of energy is the joule, which is the energy transferred to an object by the work of moving it a distance of 1 metre against a force of 1 newton.
Common forms of energy include the kinetic energy of a moving object, the potential energy stored by an object's position in a force field (gravitational, electric or magnetic), the elastic energy stored by stretching solid objects, the chemical energy released when a fuel burns, the radiant energy carried by light, and the thermal energy due to an object's temperature.
Mass and energy are closely related. Due to mass–energy equivalence, any object that has mass when stationary (called rest mass) also has an equivalent amount of energy whose form is called rest energy, and any additional energy (of any form) acquired by the object above that rest energy will increase the object's total mass just as it increases its total energy. For example, after heating an object, its increase in energy could be measured as a small increase in mass, with a sensitive enough scale.
Living organisms require energy to stay alive, such as the energy humans get from food. Human civilization requires energy to function, which it gets from energy resources such as fossil fuels, nuclear fuel, or renewable energy. The processes of Earth's climate and ecosystem are driven by the radiant energy Earth receives from the sun and the geothermal energy contained within the earth.
Explanation:
Some forms of energy (that an object or system can have as a measurable property)
Type of energy Description
Mechanical the sum of macroscopic translational and rotational kinetic and potential energies
Electric potential energy due to or stored in electric fields
Magnetic potential energy due to or stored in magnetic fields
Gravitational potential energy due to or stored in gravitational fields
Chemical potential energy due to chemical bonds
Ionization potential energy that binds an electron to its atom or molecule
Nuclear potential energy that binds nucleons to form the atomic nucleus (and nuclear reactions)
Chromodynamic potential energy that binds quarks to form hadrons
Elastic potential energy due to the deformation of a material (or its container) exhibiting a restorative force
Mechanical wave kinetic and potential energy in an elastic material due to a propagated deformational wave
Sound wave kinetic and potential energy in a fluid due to a sound propagated wave (a particular form of mechanical wave)
Radiant potential energy stored in the fields of propagated by electromagnetic radiation, including light
Rest potential energy due to an object's rest mass
Thermal kinetic energy of the microscopic motion of particles, a form of disordered equivalent of mechanical energy
Main articles: History of energy and timeline of thermodynamics, statistical mechanics, and random processes
If the charge remains the same but the radius of the sphere is doubled, the electric flux coming out of it will be
Answer:
Explanation:
We shall apply Gauss's theorem for electric flux to solve the problem . According to this theorem , total electric flux coming out of a charge q can be given by the following relation .
∫ E ds = q / ε
Here q is assumed to be enclosed in a closed surface , E is electric intensity on the surface so
∫ E ds represents total electric flux passing through the closed surface due to charge q enclosed in the surface .
This also represents total flux coming out of the charge q on all sides .
This is equal to q / ε where ε is a constant called permittivity which depends upon the medium enclosing the charge . For air , its value is 8.85 x 10⁻¹² .
If charge remains the same but radius of the sphere enclosing the charge is doubled , the flux coming out of charge will remain the same .
It is so because flux coming out of charge q is q / ε . It does not depend upon surface area enclosing the charge . It depends upon two factors
1 ) charge q and
2 ) the permittivity of medium ε around .
Andy took a bus and then walked from his home to downtown.
For the first 16 hour, the bus drove at an average speed of 15
km/h. For the next 0.4 hours, he walked at an average speed
of 4.5 km/h. What was the average speed for the whole
journey?
Given :
Speed of bus for first 16 hours is , u = 15 km/h .
Distance he walked for next 0.4 hour is , v = 4.5 km/h .
To Find :
The average speed for the whole journey.
Solution :
Average speed is given by :
[tex]v_{avg}=\dfrac{u_1t_1+u_2t_2}{t_1+t_2}\\\\v_{avg}=\dfrac{15\times 16 + 4.5\times 0.4}{16+0.4}\\\\v_{avg}=14.74\ km/h[/tex]
Therefore , the average speed of the journey is 14.74 km/h .
Hence , this is the required solution .
a train it speed steading from 10 m/s to 20m/s in 1 minutes average speed during this time in m/s
how far does it travel while increase its speed
Explanation:
Given:
v₀ = 10 m/s
v = 20 m/s
t = 60 s
Find: v_avg and Δx
v_avg = ½ (v + v₀)
v_avg = ½ (20 m/s + 10 m/s)
v_avg = 15 m/s
Δx = v_avg t
Δx = (15 m/s) (60 s)
Δx = 900 m
Add the following vectors using head-to-tail method and verify your results using the component method.
1. Vector A has a magnitude of 4.0 cms at an angle of 30 degrees with the positive X-axis; vector B has a magnitude of 3.0 cms at 90 degrees with + X-axis; vector C has a magnitude of 5.0 cms at 120 degrees with + X-axis.
2. In addition to vectors A, B, and C in problem # 1, there is a vector D with a magnitude of 6.0 cms at an angle of 210 degrees with +X-axis.
Note: Use a graph paper to show your work for problem number 1 and 2 using the head-to-tail method.
Do the component method analysis of both of these problems using the component method of adding vectors. Show your work step by step by taking the x and y components of all the vectors; adding all the x and y components together and then finding the resultant vector magnitude and direction knowing x and y are perpendicular to each other.
Compare the results of the graphical analysis as well as the component method and find the percent error using the component method as standard result
Answer:
See attached image for the requested graphs.
Part 1 : Vector sum is about 9.4 cm long in the graph, from components: about 9.35 cm long. Percent difference = 0.5%
Part 2: Vector sum is about 7.6 cm long in the graph and from components: 7.57 cm long. Percent difference = 0.4%
Explanation:
Part 1.
The graphical addition of the three vectors A, B and C gives a vector sum of approximately 9.4 cm at an angle of about 84 degrees
The component form addition is
Ax + Bx + Cx = 3.5 + 0 + (-2.5) = 1
Ay + By + Cy = 2.0 + 3 + 4.3 = 9.3
Magnitude: [tex]\sqrt{1^2+9.3^2} \approx 9.35\,\,cm[/tex]
The percent difference is: (9.4-9.35) * 100 /9.35 = 0.5%
Part 2.
The graphical addition of the four vectors (A, B, C, and D) measures approximately 7.6 cm at an angle of about 124 degrees.
The component form addition is
Ax + Bx + Cx + Dx = 3.5 + 0 + (-2.5) + (-5.2) = -4.2
Ay + By + Cy + Dy = 2.0 + 3 + 4.3 + (-3) = 6.3
Magnitude = [tex]\sqrt{(-4.2)^2+6.3^2} \approx 7.57\,\,cm[/tex]
The percent difference is: (7.6-7.57) * 100 /7.57 = 0.4%