Answers
Givens.
• 14.91 meters North.
,• 4.40 meters East.
First, make a diagram to visualize the vectors and the resultant displacement.
In the figure, the purple vector d represents the resultant displacement, which horizontal component is 4.40m and its vertical component is 14.91m.
Let's use the following formula to find the resultant.
[tex]d=\sqrt[]{(y_{})^2+(x)^2}[/tex]Where y = 14.91 and x = 4.40.
[tex]\begin{gathered} d=\sqrt[]{(14.91m)^2_{}+(4.40m)^2} \\ d=\sqrt[]{222.31m^2+19.36m^2} \\ d=\sqrt[]{241.67m^2} \\ d\approx15.55m \end{gathered}[/tex]Therefore, the magnitude of the resultant displacement is 15.55m.
But, the resultant displacement refers to the vector, which is the following
[tex]d=(4.4i+14.91j)m[/tex]
Related Questions
A proton traveling vertically upward (out of the page) experiences a magnetic force directed North. The direction of the magnetic field is_________.Group of answer choicesdown (into the page)SouthEastWest
Answers
To find:
The direction of the magnetic force.
Explanation:
The direction of the magnetic field or a magnetic force on a charged particle is given by the right-hand rule. It states that when the thumb, middle finger, and index finger are held in such a way that they are perpendicular to each other if the thumb is pointing in the direction of the positive charge and the middle finger is pointing in the direction of the magnetic force then the index finger will point in the direction of the magnetic field.
Thus applying this rule we find that the index finger will be pointing to the east.
Final answer:
Thus the direction of the magnetic field is east.
determine the distance that light travels in a year.How long does it take light to travel 10 km? how long does it take sound to travel 10 km? How long does it take light to travel from the moon to earth?
Answers
The speed of light is equal to 300000 km/s.
Let's find how many seconds there are in a year:
1 year = 365 days = 365 * 24 hours = 365 * 24 * 60 minutes = 365 * 24 * 60 * 60 seconds
Now, multiplying this amount of time by the speed of light, we have the distance traveled by the light in one year:
distance = speed * time
distance = 300000 * 365 * 24 * 60 * 60
distance = 9,460,800,000,000 km
Now, the time needed for a distance of 10 km is:
distance = speed * time
10 = 300000 * time
time = 10/300000
time = 3.33 * 10^-5 seconds
The speed of sound is about 1225 km/h.
So, for a distance of 10 km, we have:
10 = 1225 * t
t = 10/1225
t = 0.008163265 hours
t = 29.39 seconds
The distance from moon to Earth is 384,400 km, so the time needed is:
384400 = 300000 * t
t = 384400/300000
t = 1.2813 seconds
Hello, is it possible to help me solve this question? -A 475-gram ball is traveling horizontally at 12.0 m/s to the left when it is suddenly struck horizontally by a bat, causing it to reverse direction and initially travel at 8.50 m/s to the right. If the bat produced an average force of 1275 N on the ball, for how long (in milliseconds) was it in contact with the ball
Answers
Change in momentum = ΔP
ΔP = F t
Where:
F= force
t = time
Pf - Pi = Ft
M vf - m vi = F t
m= mass = 475 g = 0.475 kg
t = M vf - M vi / F
t = M (vf-vi) / f
Replacing:
t = 0.475 ( 8.50 - (-12 ) )/ 1275 = 0.0076 s = 7.64 ms
A sled and rider with a combined weight of 70.0 kg are at rest on the top of a hill 11.0 m high. (Enter your answers in J.) Assuming there is no friction, what would the total energy be on sliding halfway down the hill?answer with:___ J
Answers
We know that at the top of the 11 m hill the sled and rider are at rest, which means that all the energy at this point is potential energy; the potential energy is given by:
[tex]U=mgh[/tex]Plugging the values given we have:
[tex]\begin{gathered} U=(70)(9.8)(11) \\ U=7546 \end{gathered}[/tex]Hence at the top of the hill the total energy is 7546 J.
Now, from conservation of energy and since there is no friction, we know that at any point of the motion the total energy is the same as the starting energy.
Therefore, the total energy halfway the hill is 7546 J.
Note: At this point we would expect the potential energy to be half of what it was at the top of the hill and the other half will be kinetic energy; nonetheless the total energy, which is the sum of the kinetic and potential energy, has to remain the same as the initial energy.
Find the capacitance of a parallel-plate capacitor made of two 4.0 cm x 4.0 cm metal plates if the plates are separated by 5.0 mm.Group of answer choices2.8x10-10 F1.0x10-6 F2.8x10-12 F2.0x10-5 F
Answers
Given the area is:
A=4.0 cmx4.0 cm
The seperation distance is d=5.0 mm
The capacitance is :
[tex]\begin{gathered} C=\frac{\epsilon_oA}{d} \\ \Rightarrow C=8.85\times10^{-12}\frac{4.0\times10^{-2}\times4.0\times10^{-2}}{5\times10^{-3}} \\ \Rightarrow C=2.83\times10^{-12}F \end{gathered}[/tex]Thus the answer is
[tex]2.8\times10^{-12}F[/tex]In a smartphone, how many megabytes (MB) are there in thirty-one gigabytes (GB) of memory?
Answers
We know that for each Gb there are 1000 Mb, thus in 31 Gb there will be 31000 Mb.
If a microwave is determined to use 840 W of power on a 120 V circuit, how many amperes does it need to run?
Answers
ANSWER:
7 amperes
STEP-BY-STEP EXPLANATION:
Given:
Power (P) = 840 W
Voltage (V) = 120 V
We can calculate the current value as follows:
[tex]\begin{gathered} I=\frac{P}{E} \\ \\ \text{ We replacing:} \\ \\ I=\frac{840}{120} \\ \\ I=7\text{ A} \end{gathered}[/tex]Therefore, the number of amperes is 7
A) show the forces acting on the block in a labelled sketch when the surface is tilted. Treat the cylinder as a point.B) what is the maximum angle the rough surface can make with the horizontal before the cylinder topples over give answer to nearest degree
Answers
Given:
Diameter, d = 20 cm
Height, h = 40 cm
Mass, m = 10 kg
Given that the surface is slowly inclined to the horizontal, let's find the following:
• (A) Show the forces acting on the block in a labelled sketch when the surface is tilted. Treat the cylinder as a point.
The forces acting on the block are sketched below:
• (B) What is the maximum angle the rough surface can make with the horizontal before the cylinder topples over give answer to nearest degree.
The normal force (N) = 0 at the time the cylinder topples.
Before the the cylinder topples, tnet = 0
Apply the formula:
[tex]mg\sin \theta\ast\frac{h}{2}-mg\cos \theta\ast\frac{d}{2}=0[/tex]Rewrite the equation for θ:
[tex]\begin{gathered} \sin \theta h=\cos \theta d \\ \\ \frac{\sin\theta}{\cos\theta}=\frac{d}{h} \\ \\ \tan \theta=\frac{d}{h} \\ \\ \theta=\tan ^{-1}(\frac{d}{h}) \end{gathered}[/tex]Where:
d = 20 cm
h = 40 cm
We have:
[tex]\begin{gathered} \theta=\tan ^{-1}(\frac{20}{40}) \\ \\ \theta=\tan ^{-1}(0.5) \\ \\ \theta=26.57\approx27^0 \end{gathered}[/tex]Therefore, the maximum angle the rough surface can make with the horizontal before the cylinder topples over is approximately 27 degrees.
Solve using a system of linear equationsA motorboat takes 3 hours to travel 108 miles going upstream. The return trip takes 2 hours going downstream. What is the rate of the boat in still water and what is the rate of the current? Rate of the boat in still water=( )mi/h Rate of the current=( )mi/h
Answers
Let's use the constant motion equation: d = v*t, to express the equation for each case. But first, let's find the speed.
[tex]v=\frac{d}{t}=\frac{108mi}{3hr}=36\cdot\frac{mi}{hr}[/tex]The speed going upstream is 36 mi/hr.
[tex]v=\frac{108mi}{2hr}=54\cdot\frac{mi}{hr}[/tex]The speed going downstream is 54 mi/hr.
Observe that the distance traveled is the same.
Once we have the speed for each case, we can form the following system of equations.
[tex]\begin{gathered} x-y=36 \\ x+y=54 \end{gathered}[/tex]The first equation represents the difference between the motorboat speed in still water (x) and the rate of the current (y).
The second equation represents the addition between these two rates x and y. One equation represents the situation where the speeds are in opposite direction, and the other one represents when the
If you throw a 0.3 kg ball straight up with an initial speed of 32 m/s, how fast will it be moving when it’s 20 m above the release point? Round your answer to the nearest tenth and include the appropriate unit.
Answers
Given:
The mass of the ball, m=0.3 kg
The initial speed of the ball, u=32 m/s
The height, h=20 m
To find:
The speed of the ball when it is at a height of 20 m.
Explanation:
The ball will be moving under the influence of acceleration due to gravity which is directed downwards.
From the equation of motion,
[tex]v^2=u^2-2gh[/tex]Where v is the final velocity of the ball and g is the acceleration due to gravity.
On substituting the known values,
[tex]\begin{gathered} v^2=32^2-2\times9.8\times20 \\ \implies v=\sqrt{32^2-2\times9.8\times20} \\ =25.1\text{ m/s} \end{gathered}[/tex]Final answer:
The velocity of the ball when it is 20 m above the releasing point is 25.1 m/s
Which is MOST responsible for Earth’s seasons?
A.tilt of the Earth on it’s axis
B.The effect of mountains and large bodies of water
C.Earth’s changing distance to the moon
D.Earth’s changing distance from the sun
Answers
The MOST responsible for Earth’s seasons is A. tilt of the Earth on it’s axis
A season is a period of the year that is distinguished by special climate conditions. The four seasons are spring, summer, fall, and winter Earth's axis of rotation is tilted 23.4 degrees with respect to the plane of Earth's orbit around the Sun. This tilt causes our yearly cycle of seasons
When the earth's axis points towards the sun, for that hemisphere there will be summer and When the earth's axis points away there will be winter for that hemisphere .
hence , correct answer will be
A. tilt of the Earth on it’s axis
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A ramp outside a building is 8 m long. One end of the ramp is 2 m higher thanthe other end. What is the mechanical advantage of the ramp?A. 4B. 6C. 1/4D. 1/8
Answers
Given that the slope of the ramp is L = 8 m
The height of the ramp is h = 2 m
We need to calculate the mechanical advantage of the ramp.
The mechanical advantage of the ramp can be calculated by the formula
[tex]\text{Mechanical advantage =}\frac{L}{h}[/tex]Substituting the values, the mechanical advantage will be
[tex]\begin{gathered} \text{Mechanical advantage =}\frac{8}{2} \\ =4\text{ } \end{gathered}[/tex]Thus, the correct option is A. 4
A train accelerates uniformly from rest to a velocity of 40 m s^-1, in 5 seconds.a)Find the acceleration of the train during the 5 seconds.b) Find the distance travelled by the train during the 5 seconds.
Answers
Answer:
a) 8 m/s²
b) 100 m
Explanation:
The acceleration of the train can be calculated as
[tex]a=\frac{v_f-v_i}{t}[/tex]Where vf is the final velocity, vi is the initial velocity, and t is the time. Replacing vf = 10 m/s, vi = 0 m/s, and t = 5 s, we get:
[tex]a=\frac{40\text{ m/s - 0 m/s}}{5\text{ s}}=\frac{40\text{ m/s}}{5\text{ s}}=8\text{ m/s}^2[/tex]Then, the distance traveled can be calculated using the following equation
[tex]x=v_it+\frac{1}{2}at^2[/tex]Replacing vi = 0 m/s, t = 5 s, and a = 8 m/s², we get
[tex]\begin{gathered} x=(0\text{ m/s\rparen\lparen5 s\rparen + }\frac{1}{2}(\text{ 8 m/s}^2)(5\text{ s\rparen}^2 \\ x=0\text{ m + }\frac{1}{2}(8\text{ m/s}^2)(25\text{ s\rparen} \\ x=0\text{ m+100 m} \\ x=100\text{ m} \end{gathered}[/tex]Therefore, the distance traveled by train was 100 m.
I need help answering these questions using my experiment results. I will send you the results
Answers
Answer:
(a) It changed
(b) It changed
(c) It changed
(d) It changed
Explanation:
For each parameter, we get:
(a) the final velocity of the ball.
The velocity is equal to the distance over time. Since the distance is always 10 m, the velocity will depend on the time. So, when the time is greater, the final velocity is smaller.
In this case, we can see that for each angle, we get different times, so, the angle affects the final velocity of the ball.
(b) work
The work can be calculated as:
W = Fdcosθ
Where F is the force, d is the distance and θ is the angle between them. When we change the angle of the incline, we affect the angle of the Force and the displacement, so the work changes.
(c) initial potential energy
The potential energy depends on the initial height, if the height is greater, the potential energy is greater. So, when the angle of the incline change, the height change, so the potential energy change
(d) final kinetic energy
The kinetic energy depends on the final velocity, if the final velocity is greater, the kinetic energy is greater. Since the final velocity changes with the angle, the kinetic energy also changes with the angle.
How high should you be if you want to drop a tennis ball and have it hit the ground with a velocity of -25.0 mi/hr?
Answers
Data: Final velocity = 11.176m/s (or 25 mi/hr)
Firstly, we need to replace our values on the third given equation. It is convenient to use all the values on their SI units.
[tex]11.176^2=0^2-2*9.81*\Delta x\Rightarrow\Delta x=\frac{11.176^2}{-2*9.81}=-6.366m[/tex]Thus, the ball would need to be dropped from a height of 6.366m, or 20.89ft
i need help with this because my teacher wont help me
Answers
Given:
The speed of the signal is v = 1500 m/s
The time is t = 1.5 s
To find the distance traveled by signal.
Explanation:
The distance traveled by signal can be calculated by the formula
[tex]d=\frac{v\times t}{2}[/tex]On substituting the values, the distance traveled will be
[tex]\begin{gathered} d\text{ = }\frac{1500\times1.5}{2} \\ =\text{ 1125 m} \end{gathered}[/tex]Thus, the distance traveled by the signal is 1125 m
Which law of thermodynamics states that absolute zero cannot be reached? Also a hot cup of tea absorbs thermal energy from a cold room? True false
Answers
The third law of thermodynamics states that the absolute zero-temperature 0 K cannot be reached by a finite number of steps.
Thus, the answer is the third law of thermodynamics.
Also, a hot cup of tea absorbs thermal energy from a cold room. The given statement is false.
Thus, the given statement is False.
A. How many Coulombs are there in one fundamental/elementary charge?B. How many electrons are there in one coulomb of negative charge?
Answers
(A). The number of Coulombs in one fundamental charge of an electron is,
[tex]1e\text{ = 1.}6\times10^{-19}\text{ C}[/tex](B). The charge in terms of the number of electrons is,
[tex]q=ne[/tex]where q is the net charge, e is the fundamental charge and n is the number of electrons,
For the net charge of q = 1 Coulomb, the number of electrons is,
[tex]\begin{gathered} 1\text{ C=n}\times1.6\times10^{-19}\text{ C} \\ n=\frac{1}{1.6\times10^{-19}} \\ n=0.625\times10^{19} \\ n=6.25\times10^{18}\text{ } \end{gathered}[/tex]Thus, the number of electrons in the 1 Coulomb of charge is,
[tex]6.25\times10^{18}[/tex]
One coulomb (1 C) is equal to approximately 6.24 x 10 18 elementary charges. Thus, an elementary charge is approximately 1.60 x 10 -19 C.
The unit of electrical charge quantity in the International System of Units is the coulomb. Coulomb is the SI unit of electric charge which is equal to the amount of charge transported by a current of one ampere in one second. It can be also, a property of a matter due to which electrical and magnetic effects are produced. It is denoted by C. Mathematically, 1 Coulomb = 1 Ampere × 1 second.
To illustrate the magnitude of 1 Coulomb, an object would need an excess of 6.25 x 1018 electrons to have a total charge of -1 C. And of course, an object with a shortage of 6.25 x 1018 electrons would have a total charge of +1 C. The charge on a single electron is -1.6 x 10 -19 Coulomb.
Charge on an electron(e)= 1.6∗10^−19 C approximately.
By quantization property of charge(Smallest unit is e),
Charge (Q) = 1C where n-number of electrons.
Electron (e) = 1.6× 10^-19
A number of electrons (n) =?
Q= ne
1 C = n × 1.6×10^-19 C
n = 1/(1.6×10^-19)
Which gives, n= 6.25*10^18 electrons
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A jet plane has a maximum deceleration rate of -7.30 m/s/s. It touches down on a runway with a speed of 122 m/s. From the instant it touches the runway, what is the minimum time needed before it comes to rest??
Answers
The maximum time needed before the jet plane that has a maximum deceleration of -7.30 m/s² comes to rest is 16.71 seconds.
What is time?Time can be defined as an ongoing and continuous sequence of events that occur in succession, from past through the present, and to the future.
To calculate the maximum time needed for the jet to come to rest, we use the formula below.
Formula:
t = (v-u)/a........... Equation 1Where:
t = Maximum time needed for the jet to come to restv = Final speedu = Initial speeda = Maximum deceleration of the jetFrom the question,
Given:
v = 0 m/s (to rest)u = 122 m/sa = - 7.30 m/s²Substitute these values into equation 1
t = (0-122)/(-7.3)t = -122/7.3t = 16.71 secondsHence, the maximum time needed is 16.71 seconds.
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Solve the inequality for x. Show each step of the solution.10x>9(2x-8)-20
Answers
Given,
[tex]10x>9(2x-8)-20[/tex]On simplifying the above equation,
[tex]\begin{gathered} 10x>18x-72-20 \\ \Rightarrow10x>18x-92 \\ \Rightarrow10x-18x>-92 \\ \Rightarrow-8x>-92 \end{gathered}[/tex]On further simplifying,
[tex]\begin{gathered} 8x>92 \\ \Rightarrow x>\frac{92}{8} \\ \Rightarrow x>11.5 \end{gathered}[/tex]Thus on solving the given inequality, we get, x>11.5
A 87 kg person sits at rest at the top of a 51m high amusement park ride. How much energy does the person have at this point
Answers
We will calculate potential energy, in this case, using the next formula
[tex]PE=\text{mgh}[/tex]where m is the mass, g is the gravity and h is the height
in our case
m=87 kg
g=9.8 m/s^2
h=51m
we substitute
[tex]PE=87(9.8)(51)=43482.6J[/tex]ANSWER
The energy is 43482.6J
Two positive charges of 10 C are separated by 12 meters. What is the force between the charges?
Answers
In order to calculate the force between the charges, we can use the formula below:
[tex]F=K\cdot\frac{q_1\cdot q_2}{d^2}[/tex]Where F is the force (in Newtons), K is the Coulomb constant (K = 9 * 10^9), q1 and q2 are the charges (in Coulombs) and d is the distance between them (in meters).
So, for q1 = q2 = 10 C and d = 12 m, we have:
[tex]\begin{gathered} F=9\cdot10^9\cdot\frac{10\cdot10}{12^2} \\ F=\frac{900\cdot10^9}{144} \\ F=6.25\cdot10^9\text{ N} \end{gathered}[/tex]Therefore the force between the charges is 6.25 * 10^9 N.
Find the equivalent resistance of thiscircuit.R₁www400 ΩIR₂600 ΩReq = [?] 2R3www500 Ω
Answers
We are given the following information.
Resistor: R₁ = 400 Ω
Resistor: R₂ = 600 Ω
Resistor: R₃ = 500 Ω
We are asked to find the equivalent resistance of the given circuit.
Notice that the resistors R₁ and R₂ are in parallel and this parallel combination is in series with resistor R₃.
First, let us find the parallel resistance of R₁ and R₂.
[tex]R_p=\frac{R_1\times R_2}{R_1+R_2}=\frac{400\times600}{400+600}=\frac{240000}{1000}=240\;\Omega[/tex]Finally, let us find the series resistance of Rp and R₃.
[tex]\begin{gathered} R_{eq}=R_p+R_3 \\ R_{eq}=240+500 \\ R_{eq}=740\;\Omega \end{gathered}[/tex]Therefore, the equivalent resistance of the given circuit is 740 Ω.
If your favorite radio station is on the FM Dial at100 MHz (Mega Hertz) Calculate the wave length for this Radio station. Hint use the equation c = Lf, Where L is the wavelength and c is given at the top of the exam.
Answers
In order to calculate the wavelength, let's use the given formula, using c = 3 * 10^8 m/s (speed of light in vacuum) and f = 100*10^6 Hz:
[tex]\begin{gathered} 3\cdot10^8=L\cdot100\cdot10^6\\ \\ L=\frac{3\cdot10^8}{100\cdot10^6}=\frac{3\cdot10^8}{1\cdot10^8}=3\text{ m} \end{gathered}[/tex]Therefore the wavelength is 3 meters.
You and your friend are trying to push a table into a corner. You push with a force of 50 N towards towards one wall while your friend pushes at right angle towards the other wall with a force of 60 N. What is the combined force on you and your friend on the table and in which direction will it move?
Answers
The combined force on the table is 110N towards the other wall your friend pushing at.
What is net force?Objects at rest tend to stay at rest, and objects in motion tend to continue to move at the same speed and in the same direction, unless an imbalanced force is applied.
Newton's first law states: , an unbalanced force refers to a force that is not completely balanced (or canceled) by other individual forces. Unbalanced forces exist when all vertical forces (up and down) do not cancel each other and/or when all horizontal forces do not cancel each other.
Net force is defined as the sum of all forces acting on a body. Net force is the term used in systems when there are a significant number of forces.
Net force = F₁ + F₂ + F₃….+ Fₙ
if the force acting differ in their angle the,
Net force = [tex]\sqrt{a^{2} + b^{2} + 2abcos}[/tex]θ
Where, a = F₁
b = F₂
θ = angle at which force exerts
For the given case:
a = 50 N
b = 60 N
θ = 90°
cos90 = 0
So, Net force (Fₙ) = [tex]\sqrt{a^{2} + b^{2}[/tex]
Fₙ = 50 N + 60 N
Fₙ = 110N
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Which statement best describes the gravitational force of an object? (1 point)
O The object only has gravitational force when it is on the surface of a massive body, such as Earth.
O The farther away an object is, the greater its gravitational force will be.
O The greater the object's mass and the closer it is, the greater its gravitational force.
O The greater the object's mass, the less its gravitational force will be.
Answers
The attraction created by gravity is between masses. The gravitational force increases as the mass of an object increases (also called the gravity force). With an increase in the distance between masses, the gravitational pull rapidly lessens.
The gravitational force is the force that exists between two bodies regardless of whether there are any other objects in their path. Its formula isF=GMm/R²
Where, R is the object's distance from the center of the Earth and G is the gravitational constant ,M is mass of earth and m is the mass of the object.
Weight is the term for the gravitational pull that the earth has on an object. It is also equal to the product of acceleration due to gravity and mass of the object.Weight = mg, where m is an object's mass and g is its acceleration due to gravity .
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Answer:
The greater the object's mass and the closer it is, the greater the gravitational force will be.
Explanation:
im taking the test and found the answer on questions.llc, another helpful and usually reliable site
A crane used 136.65 watts of power to raise a 16.22 N object in 4.97 seconds. Through what vertical distance was the object displaced?
Answers
Given,
Power, P = 136.65 watts
Force, F = 16.22 N
Time, t = 4.97 seconds
The work done is calculated by the given formula,
[tex]W=F\times d[/tex]Now, the formula of power is given by
[tex]\begin{gathered} \text{Power = }\frac{W\text{ork done}}{\text{Time}} \\ \text{P = }\frac{F\times d}{T} \\ d=\frac{P\times t}{F} \\ d=\frac{136.65\text{ W}\times4.97\text{ s}}{16.22\text{ N}} \end{gathered}[/tex]Thus, the vertical distance is
[tex]d=41.87\text{ m}[/tex]In a reactor, if power is lost what lowers the control rods into the core to shut it down? Select one:a.hydraulicsb.peoplec.robotsd.gravity
Answers
Given:
The power is lost in a reactor
To find:
What lowers the control rods into the core to shut it down
Explanation:
Control rods are important safety features of reactors as they allow the user to control the output of the reactor. The control rods are held by electromagnetic fields.
If there is some sort of power failure or loss of signal the control rods are immediately released and fall into the reactor core because of gravity.
Hence, the correct option is gravity.
selasieKOPsBunPANTOPERE. O 11.18 m, 148.435 deg14. Given the vectors A = 50 m 10 degnorth of east and B = 100 m 80 deg south of west,find the x and y components of their sum vector A + B. (1 point)A. O(31.876 m, -89.798 m)B. (18.694 m, -130.237 m)C. O(6.913 m. -76.906 m)D. O(6.913 m, -89.798 m)E. O(31.876 m. -76.906 m)70.50
Answers
Given:
The vector A is 50 m 10 deg north of east.
The vector B is 100 m 80 deg south of west.
To find the x and y components of their sum vector A+B
Explanation:
The vectors can be represented in diagram as shown below
The x-component can be calculated as
[tex]\begin{gathered} A_x+B_x=\text{ 50 cos \lparen10}^{\circ}\text{\rparen-100 cos\lparen80}^{\circ}\text{\rparen} \\ =\text{ 31.876 m} \end{gathered}[/tex]The y-component can be calculated as
[tex]\begin{gathered} A_y+B_y=50sin(10^{\circ})-100sin(80^{\circ}) \\ =-89.798 \end{gathered}[/tex]Thus, option A is correct.
A train car with a mass of 5 kg and speed of 5 m/s is traveling to the right. Another train car with a mass of 2 kg is standing still. After the collision, the 5 kg train car is stuck to the 2 kg train car, what is their combined Final Velocity?
Answers
From the Law of Conservation of Linear Momentum, we have:
[tex]m_1v_1+m_2v_2=m_1v_1^{\prime}+m_2v_2^{\prime}[/tex]If the two particles have the same velocity after the collision, then v₁'=v₂'.
Let v be equal to the final velocity of the particles. Then:
[tex]\begin{gathered} m_1v_1+m_2v_2=m_1v+m_2v \\ \\ \Rightarrow m_1v_1+m_2v_2=(m_1+m_2)v \end{gathered}[/tex]Since v is unknown, isolate it from the equation:
[tex]v=\frac{m_1v_1+m_2v_2}{m_1+m_2}[/tex]Replace the data to find the value of v:
[tex]\begin{gathered} m_1=5kg \\ v_1=5\frac{m}{s} \\ \\ m_2=2kg \\ v_2=0 \\ \\ \Rightarrow v=\frac{(5kg)(5\frac{m}{s})+(2kg)(0)}{5kg+7kg}=\frac{25kg\frac{m}{s}}{12kg}=2.08333...\frac{m}{s} \end{gathered}[/tex]Therefore, the combined final velocity of both train cars is approximately 2.1m/s.