Answer:
The two main factors that affect kinetic energy are mass and speed.
Explanation:
Kinetic energy is the energy that is caused by the motion. The kinetic energy of an object is the energy or force that the object has due to its motion. Your moving vehicle has kinetic energy; as you increase your vehicle's speed, your vehicle's kinetic energy increases.
Have a great day! :D
In the popular game "Angry Birds" (refer Figure), for the red bird to hit the green bird with their range 55.0 m, what should be the launch angle (with respect to the horizontal) of the slingshot if the time of flight is 2.50 s?
Answer:
Explanation:
What are we to use as gravity in this imaginary world? I will ASSUME 9.81 m/s² and assume no air resistance.
horizontal velocity component
vx = 55.0/2.50 = 22 m/s
vertical initial velocity component
(12.0 - 10.0) = 0 + vy₀(2.50) + ½(-9.81)2.50²
vy₀ = 13.0625 m/s
θ = arctan(vy₀/vx) = arctan(13.0625/22) = 30.6997225... = 30.7°
Check all true statements about nonmetals. Group of answer choices
All nonmetals are gaseous at room temperature.
Nonmetals have low melting and boiling points. ✅
Nonmetals are brittle and have a relatively low density. ✅
Nonmetals are good at thermal and electrical conduction.
Using the colored periodic table below, match the group or area to its color.
alkali metals red alkaline ✅
earth metals orange ✅
transition metals white ✅
halogens purple ✅
Nobel gasses teal✅
How many of each subatomic particle are in a neutral atom of Potassium-39? What is its mass number? Potassium is in group 1 and has the symbol "K".
protons 19 ✅
neutrons 20 ✅
electrons 19 ✅
mass number 39✅
Match the ion with its charge.
11 protons, 12 neutrons, 10 electrons = +1 ✅
Groups 17, period 2 = -1 ✅
31 protons, 39 neutrons, 28 electrons = +3✅
Group 2, period 5 = +2
Which best describes a metal such as Silver (Ag)?
Answer: Lustrous, malleable, and forms cations.
Determine if the "quoted" word(s) makes each statement True or False.
Elements that share the most characteristics are found on the periodic table in the same "horizontal period". False ✅
If matter has a higher temperature, that means there will be "more" molecular motion. True✅
If you put a balloon in a freezer, its volume would "increase". False ✅
If you put the balloon into a chamber where there is half the pressure, its volume will "double". True ✅
If you cool down a propane tank, there will be "less" pressure in it. True ✅
The average atomic mass of Aluminum (Al) is "16.00 amu".
False✅
Oxygen's atomic number is "8" therefore it has "8" protons in its nucleus. True✅
An "electron" has the same mass as a neutron. False✅
The nucleus contains "protons and neutrons", virtually all the mass of an atom.✅
Metals are found towards the left hand side of the periodic table while Nonmetals are found towards the right hand side of the periodic table.
Non metals are found towards the right hand side of the periodic table. They are not all gaseous at room temperature some nonmetals such as iodine are solid at room temperature.
Nonmetals usually have low melting and boiling points, are brittle, have relatively low density and are not good at thermal and electrical conduction.
Potassium - 39 contains 19 protons, 20 neutrons and 19 electrons. Recall that the number of protons and electrons are equal in a neutral atom.
The following is an accurate matching of the ions;
11 protons, 12 neutrons, 10 electrons = +1 - Na^+
31 protons, 39 neutrons, 28 electrons = +3 - Ga^2+
Group 2, period 5 = +2 - Sr^2+
Silver is a lustrous metal.
Elements that share the most characteristics are found on the periodic table in the same "horizontal period". FalseIf matter has a higher temperature, that means there will be "more" molecular motion. TrueIf you cool down a propane tank, there will be "less" pressure in it. TrueIf you put a balloon in a freezer, its volume would "increase". FalseIf you put the balloon into a chamber where there is half the pressure, its volume will "double". TrueThe average atomic mass of Aluminum (Al) is "16.00 amu". FalseOxygen's atomic number is "8" therefore it has "8" protons in its nucleus. TrueAn "electron" has the same mass as a neutron. FalseThe nucleus contains "protons and neutrons", virtually all the mass of an atom - True
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Answer:
If your answers are the green check marks all of them are correct
Explanation: I took the test
In a thermodynamic process, the internal energy of a system in a container with adiabatic walls decreases by 800 J. Which statement is correct
The correct statement is, the system performed 800 J of work on its surroundings.
The given parameters:
change in internal energy, ΔU = 800 JApply first law of thermodynamics;
ΔU = Q + W
where;
Q is the heat gainedW is the work done on the system by the surroundingIn adiabatic process no heat is gained or lost by the system.
Q = 0
ΔU = W (work is positive when it is done on the system by its surrounding)
If work is done by the system to the surrounding, the new equation becomes;
ΔU = - W
W = - ΔU
W = -800 J
This implies that the system performed 800 J of work on its surroundings.
"Your question is not complete, it seems to be missing the following information";
In a thermodynamic process, the internal energy of a system in a container with adiabatic walls decreases by 800 J. Which statement is correct?
a. The system lost 800 J by heat transfer to its surroundings.
b. The system gained 800 J by heat transfer from its surroundings.
c. The system performed 800 J of work on its surroundings.
d. The surroundings performed 800 J of work on the system.
e. The 800 J of work done by the system was equal to the 800 J of heat transferred to the system from its surroundings.
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As a bicycle pump inflates a tyre, it pressure rises from 30 kPa to 40 kPa at constant temperature of 30 °C. By assuming the air acts as an ideal gas, calculate the work done per mol of the air.
A. -80.35 J
B. 80.35 J
C. -811.93 J
D. 811.93 J
(please show calculation)
can use this formula W=nRT ln(p1/p2)
Answer:
B.-80.35 J
i dont know the calculation
A 67 kg soccer player uses 5100 kJ of energy during a 2.0 h match. What is the
average power produced by the soccer player?
The average power produced by the soccer player is 710 Watts.
Given the data in the question;
Mass of the soccer player; [tex]m = 67kg[/tex]Energy used by the soccer player; [tex]E = 5100KJ = 5100000J[/tex]Time; [tex]t = 2.0h = 7200s[/tex]Power; [tex]P =\ ?[/tex]
Power is simply the amount of energy converted or transferred per unit time. It is expressed as:
[tex]Power = \frac{Energy\ converted }{time}[/tex]
We substitute our given values into the equation
[tex]Power = \frac{5100000J}{7200s}\\\\Power = 708.33J/s \\\\Power = 710J/s \ \ \ \ \ [ 2\ Significant\ Figures]\\\\Power = 710W[/tex]
Therefore, the average power produced by the soccer player is 710 Watts.
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Jimmy walks to school by traveling 2.0 miles east and 3.0 miles north from his starting point. What are the magnitude and direction of Jimmy's displacement with respect to his original position?
Answer:
3.6 miles at 56.3 degrees north of east.
Explanation:
If you draw a diagram to calculate Jimmy's displacement, you end up with a triangle.
To solve for the magnitude of Jimmy's displacement with respect to his original position, we need to use the Pythagorean Theorem formula.
Pythagorean Theorem Formula = a^2 + b^2 = c^2
Step by Step to solve for the magnitude of Jimmy's displacement:
1) a^2 + b^2 = c^2
2) 2.0^2 + 3^2 = c^2
3) 4 + 9 = c^2
4) 13 = c^2
5) To find what "c" equals to we need to find the square root of 13.
6) √13 = 3.6 | c = 3.6 miles
To solve for the direction of Jimmy's displacement with respect to his original position, we need to use the following formula:
tan^-1 ∅ (3/2)
tan^-1 ∅ (1.5)
∅ = 56.309° north of east
Therefore, your answer is 3.6 miles at 56.3 degrees north of east.
Example 4.16
An object of mass 3 kg rests on a plane. The coefficient of static friction and that of kinein
friction are given by Hs = 0.3 and pk = 0.2.
The plane is inclined at angle o to the horizontal.
(i) Find the maximum value of 0 for which the object remains at rest on the plane.
(ii) Find the acceleration of the object if it started sliding from rest down the plane at
angle Omax to the horizontal.
(ii) How long does it take the object to move, from rest, a distance of Imetre under the
conditions of (ii).
Answer:
Explanation:
(i) μs = F/N = mgsinθ/mgcosθ = tanθ
tanθ = 0.3
θ = 16.7°
(ii) a = F/m
a = (mgsinθ - (μk)mgcosθ) / m
a = g(sinθ - (μk)cosθ)
a = 9.8(sin16.7 - (0.2)cos16.7)
a = 0.94 m/s²
(iii) s = ½at²
t = √(2s/a)
t = √(2(1)/0.94)
t = 1.5 s
what is a non-economic benefit to international trade
Answer:
non economic benefits to international trade means not being too much profit not selling too much things /items in international trade
A less than youthful 82.6 kg physics professor decides to run the 26.2 mile (42.195 km) Los Angeles Marathon. During his months of training, he realizes that one important component in running a successful marathon is carbo-loading, the consumption of a sufficient quantity of carbohydrates prior to the race that the body can store as glycogen to burn during the race. The typical energy requirement for runners is 1 kcal/km per kilogram of body weight, and each mole of oxygen intake allows for the release of 120 kcal of energy by oxidizing (burning) glycogen.
(a) If the professor finishes the marathon in 4:45:00 h, what is the professor's oxygen intake rate, in liters per minute, during the race if he metabolizes all of the carbo-loaded glycogen during the race and the ambient temperature is 21.5°C? 2.28 Read the problem statement again carefully. Is the air at standard temperature and pressure during the marathon? How would this affect the volume of 1 mol of oxygen? L/min
(b) The human body has an efficiency of 25.0%. Only 25.0% of the energy released from oxidizing glycogen is used as macroscopic mechanical energy, and the remaining 75.0% is used for body processes such as pumping blood and respiration, and then leaves the body through the skin via radiation, evaporative cooling, and other processes. What is the average mechanical power (in W) generated by the professor during the run? 197.561 What is the total energy required by the professor during the run? How efficient is the human body, and how long did the race last? W
(c) What is the change in entropy (in J/K) of the professor's body if his core temperature has risen to 38.3°C during the run and his skin temperature is at 36.0°C during the marathon? J/K
(d) What is the change of the entropy (in J/K) of the air surrounding the professor during the race if the ambient temperature remains constant at 21.5°C? J/K
A boat is headed north at a velocity of 8 km h-1. A strong wind is blowing whose pressure on the boat’s superstructure causes it to move sideways to the west at a velocity of 2 km h-1. There is also wave present that flows in a direction 30° south of east at a velocity of 5 km h-1. What is the velocity of the boat?
The velocity of the boat moving at the given conditions is 5.97 km/h at 67⁰.
The given parameters;
velocity of boat northwards, = 8 km/hvelocity of the boat westwards, = 2 km/hvelocity of the wind, = 5 km/h 30° south of eastThe resultant vertical velocity of the boat is calculated as;
[tex]v_y = 8 \ - \ 5 sin(30)\\\\v_y = 8 - 2.5\\\\v_y = 5.5 \ km/h[/tex]
The resultant horizontal velocity of the boat is calculated as;
[tex]v_x = -2 \ + 5cos(30)\\\\v_x = 2.33 \ km/h[/tex]
The resultant boat velocity is calculated as follows;
[tex]v = \sqrt{v_x^2 + v_y^2} \\\\v = \sqrt{2.33^2 + 5.5^2} \\\\v = 5.97 \ km/h[/tex]
The direction of the velocity;
[tex]\theta = tan^{-1} (\frac{v_y}{v_x} )\\\\\theta = tan^{-1}(\frac{5.5}{2.33} )\\\\\theta = 67 \ ^0[/tex]
Thus, the velocity of the boat moving at the given conditions is 5.97 km/h at 67⁰.
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A very bouncy mushroom can be modeled as mass of 30g(the mushroom cap) on top of a spring(the mushroom stalk) when spring constant 20 N/m. A bird of mass 50g lands on the mushroom gently so that its velocity is zero when it lands. Questions are in the image.
The motion of the bouncy mushroom can be described as a simple
harmonic motion, SHM.
a) The equilibrium height of the mushroom is 0.024525 m below its initial heightb) The frequency of resulting oscillation is 0.5 Hzc) The maximum compression of the mushroom 0.03924 md) The equation that describes the oscillation of the mushroom as a function of time is; [tex]\underline{x(t) = 0.014715 \cdot cos(0.5\cdot t)}[/tex]Reasons:
The given parameters are;
Mass of the mushroom cap, m = 30 g = 0.03 kg
Mass of the bird = 50 g = 0.05 kg
The spring constant, K = 20 N/m
a) The equilibrium height of the mass spring system, is given as follows;
F = -K·x
[tex]x = \dfrac{F}{K}[/tex]
The applied force, F = The weight of the bird
∴ F = (0.05 kg) × 9.81 m/s² = 0.4905 N
[tex]x = \dfrac{0.05 \, kg \times 9.81 \ m/s^2}{20 \, N/m} = 0.024525 \, m[/tex]
The equilibrium height of the mushroom is 0.024525 m below its initial height.
b) The frequency of oscillation of a spring, ω, is given as follows;
[tex]\omega = \sqrt{\dfrac{K}{m} }[/tex]
Therefore;
[tex]\omega = \sqrt{\dfrac{20 \, N/m }{80 \, kg} } = \dfrac{1}{2} \, Hz[/tex]
The frequency of resulting oscillation, ω = [tex]\dfrac{1}{2} \, Hz[/tex] = 0.5 Hz
c) The applied force, F = The weight of the bird and the mushroom cap
F = (0.03 kg + 0.05 kg) × 9.81 m/s² = 0.7848 N
[tex]x = \dfrac{0.7848 \, N}{20 \, N/m } = 0.03924 \, m[/tex]
The maximum compression of the mushroom = 0.03924 m
d) The motion of the mushroom is a Simple Harmonic Motion, SHM.
The equation of a SHM as a function of time is; x(t) = A·cos(ω·t + Φ)
For the mushroom, we have;
The amplitude, A = 0.03924 m - 0.024525 m = 0.014715 m
Ф = The phase angle
When t = 0, cos(ω × 0 + Φ) = 1
cos(Φ) = 1
Ф = arcos(1) = 0
The equation is therefore;
x(t) = 0.014715·cos(0.5·t)
Equation of the oscillation of the mushroom is; [tex]\underline{x(t) = 0.014715 \cdot cos(0.5\cdot t)}[/tex]
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Alicia is naturally rather shy and is graduating from college. She will need to find a job, so she is starting to go on job websites and work on her
resume. She knows she should network, but it sounds a little intimidating. What is the BEST advice for Alicia?
ОА. If she is not comfortable networking, she will never find a job.
ОВ. The majority of jobs are found through networking, so she should really try it.
OC. Networking is overrated, so she can skip that part of the job search process.
OD If she is naturally shy, she probably has really poor social skills and should work on that.
Answer:
OB and i have no reasoning
the push up is dynamic or static
Answer:
Dynamic exercises
Explanation:
please.
I mark u brainliest answer
Answer:
destroy
Explanation:
cuz if anyhow throw rubbish, it will affect/destroy the world environment
Answer:
bathing regularly 2pollute 3 throwing waste in land water water pollution
a=100m/s2
Vi=10m/s
T=10sec
Vf?
Answer:
v=u+at
v= 10+100×10
v = 10+1000
v = 1010 m/s
PLZ HURRY
When you hold a racquet and swing your arm toward the ball, there are two kinds of resistance working against your muscles—the ______ and the ______.
A.
racket, air
B.
air, ball
C.
ball, net
D.
air, racket
Answer:
It should just be A
Explanation:
I dont see the difference between these 2 but ill choose A and update you
Answer:
A: racket, air
Explanation:
At a construction site, a 68.0 kg bucket of concrete hangs from a light (but strong) cable that passes over a light friction-free pulley and is connected to an 85.0 kg box on a horizontal roof (see the figure (Figure 1)). The cable pulls horizontally on the box, and a 46.0 kg bag of gravel rests on top of the box. The coefficients of friction between the box and roof are shown. The system is not moving.
Following are the calculation to the friction force:
Please see the diagram below for an illustration of the forces acting on objects.Therefore, m denotes the mass of a gravel bag, and M denotes the overall mass of the box.Whenever the system is stationary, the friction force on the box equals the tension in the string.The substring tension force is provided as follows:
[tex]\to T-m_{1}g=0 \\\\\to T = m_{1}g \\\\[/tex]
[tex]= (68\ kg) (9.81 \ \frac{m}{s^2} ) (\frac{ 1\ N}{ 1\ kg \cdot \frac{m}{s^2}}) \\\\ = (68 ) (9.81 ) ( 1\ N) \\\\= 667.08\ N \\\\[/tex]
Therefore, the friction force on the box is "667 N".
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A body at higher temperature contains more heat? Is this true ?
A large water tank is 3.70 m high and filled to the brim, the top of the tank open to the air. A small pipe with a faucet is attached to the side of the tank, 0.580 m above the ground. If the valve is opened, at what speed (in m/s) will water come out of the pipe
h =(3.7 - .58)m = 3.12m
Now put PE into KE and we have to use the formula:
√2gh (g = gravity and h = height) therefor:
√2 x 9.8 x 3.12
= 7.82m/s
I hope this helps!
What is the momentum of a 3 kg bowling ball moving at 3 m/s?
.
O 1 kg. m/s
O 3 kg. m/s
O 6 kg. m/s
O 9 kg • m/s
Explanation:
p = mvp denotes momentumm denotes massv denotes velocity→ p = 3 kg × 3 m/s
→ p = 9 kg.m/s
Option D is correct.
the temperature of ice will rise until melting state select true or false
Answer:
True
Explanation:
I have learned that in grade schoolI have known that for quite awhile now alsoDavid and Fiona want to know about how mass affects the motion of an object. David uses three objects with masses of 2 kg, 3 kg, and 8 kg, writes out his procedure, and records his observations on the force needed to move the objects. Fiona is investigating three different objects using observation. What is the difference in the way they approached this question?
A. Only Fiona gathered evidence from her investigation.
B. David used scientific articles for evidence.
C. David's observations can be replicated by repeating his procedure.
D. Fiona's observations can be replicated by observing different objects.
Answer: the answer is D if its not i'm really sorry
Eric drops a 2.20 kg water balloon that falls a distance of 45.08 m off the top of a
building. What is the kinetic energy at the bottom?
Answer:
972 J
Explanation:
At the bottom, all the gravitational potential energy was converted into kinetic energy. If you calculate the GPE, its value will be the same that the KE at the bottom. The GPE can be calculated this way:
GPE = mass×gravity×heigth
GPE = 2.2×9.8×45.08 ≈ 972
Astone has a mass of 200 grams. When it is immersed in a measuring cylinder of water,the water rises 100 ml.What is the density of the stone
Answer:
2 g/mLExplanation:
The density of a substance can be found by using the formula
[tex]d = \frac{m}{v} \\ [/tex]
m is the mass
v is the volume
From the question
m = 200g
v = 100 mL
We have
[tex]d = \frac{200}{100} = 2 \\ [/tex]
We have the final answer as
2 g/mLHope this helps you
An electron is held up against the force of gravity by the attraction of a fixed proton some distance above it. How far above the electron is the proton
5.08 m
Explanation:
The weight of the electron is being counteracted by the attractive electrostatic force exerted by the proton above it. We can write the force equation as follows:
[tex]m_eg = k_e\dfrac{Q_pQ_e}{r^2}[/tex]
where the Q's are the charges of the proton and electron, r is the distance between the particles, g is the acceleration due to gravity, [tex]m_e[/tex] is the mass of the electrons and [tex]k_e[/tex] is the Coulomb constant. So solving for r, we get
[tex]r^2 = k_e\dfrac{Q_pQ_e}{m_eg}[/tex]
Taking the square root of r^2, we then get the distance as
[tex]r = \sqrt{k_e\dfrac{Q_pQ_e}{m_eg}}[/tex]
The values are given as follows:
[tex]m_e = 9.11×10^{-31}\:\text{kg}[/tex]
[tex]g = 9.8\:\text{m/s}^2[/tex]
[tex]Q_p = Q_e = 1.60×10^{-19}\:\text{C}[/tex]
[tex]k_e = 8.99×10^9\:\text{N-m}^2\text{/C}^2[/tex]
Putting in all of these values in our equation for r,
[tex]r = \sqrt{\dfrac{(8.99×10^9\:\text{N-m}^2\text{/C}^2)(1.60×10^{-19}\:\text{C})^2}{(9.11×10^{-31}\:\text{kg})(9.8\:\text{m/s}^2)}}[/tex]
[tex]\:\:\:\:\:= 5.08\:\text{m}[/tex]
A camera takes a properly exposed photo at f/5.6 and 1/250 s. What shutter speed should be used if the lens is changed to f/4.0?
a.1/65 s
b.1/125 s
c.1/250 s
d.1/500 s
e.1/1000 s
The shutter speed that should be used if the lens is changed to f/4.0 is; Choice D: 1/500 s.
The relationship between the shutter speed and the focal ratio is an inverse relationship.
Ratio of Areas = 5.6²/4²
A1/A2 = 1.96 = 2Since; T1A1 = T2A2
T2 = T1(A1/A2)T2 = 250 × 2 = 500 secondsIn essence; when the focal ratio is reduced as in this case; from f/5.6 to f/4.0; the shutter speed is increased.
Ultimately, the shutter speed of the camera in discuss increases to; 1/500 s.
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When an alpha particle is emitted from an unstable nucleus, what happens to the atomic number of the nucleus
Answer:
The answer to your question is the number decreases by 4.
Explanation:
I hope this helps and have a great day!
A double-pane glass window is 60.0 cm x 90.0 cm and has 3.00-mm window panes. If the temperature difference between inside and outside is 24.0 K, how far apart should the panes be to have a heat loss of 4.09 W? Assume there is air in the gap.
The distance between the glass to have the given heat loss is 2.54 m.
The given parameters:
dimension of the window, = 60 cm by 90 cmtemperature, T = 24 Kheat lost, Q = 4.09 Wthermal conductivity of glass, k = 0.8 W/mKThe area of the glass window is calculated as follows;
[tex]A = 0.6 \times 0.9\\\\A = 0.54 \ m^2[/tex]
The distance between the glass is calculated as follows;
[tex]Q = \frac{KA \Delta T}{\Delta x} \\\\\Delta x = \frac{kA \Delta T}{Q} \\\\\Delta x = \frac{0.8 \times 0.54 \times 24 }{4.09} \\\\\Delta x = 2.54 \ m[/tex]
Thus, the distance between the glass to have the given heat loss is 2.54 m.
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which of the following statements describes a perfectly inelastic collision
Answer: An ice hockey player picks up a trophy as he slides past it.
Two pool balls colliding precisely inelastically and rebounding off one another is an example. So, the correct option is A.
What is an Inelastic collision?Inelastic collisions are those in which the total kinetic energy is lower after the impact than it was before. The stick is travelling quickly in the direction of the ball before to the contact. The stick comes to a stop following the accident. It transfers some of its kinetic energy to the cue ball, which rolls forward.
The type of collision mentioned in the given example is known as an inelastic collision is one in which the system's momentum is preserved but its kinetic energy is not. In a ballistic pendulum, an example of an inelastic collision. Dropped ball of clay is another illustration of an inelastic collision.
Thus, the correct option is A.
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#SPJ7
Your question is incomplete, most probably the complete question is:
Which of the following statements describes a perfectly inelastic collision?
A. Two billiard balls bounce off of each other,
B. A car crashes into a tree and rebounds in the other direction,
C. A wad of chewing gum is thrown and sticks to a moving truck,
D. Two ice skaters hit each other and fall over in opposite directions,
A 30.0-g object moving to the right at 20.5 cm/s overtakes and collides elastically with a 13.0-g object moving in the same direction at 15.0 cm/s. Find the velocity of each object after the collision. (Take the positive direction to be to the right. Indicate the direction with the sign of your answer.)
Let m₁ and m₂ be the masses of the two objects, and v₁ and v₂ their initial velocities. So
m₁ = 30.0 g = 0.0300 kg
m₂ = 13.0 g = 0.0130 kg
v₁ = + 20.5 cm/s = 0.205 m/s
v₂ = + 15.0 cm/s = 0.150 m/s
and we want to find v₁' and v₂', the final velocities of either object after their collision.
Momentum is conserved throughout the objects' collision, so that
m₁v₁ + m₂v₂ = m₁v₁' + m₂v₂'
where v₁' and v₂' are the first and second object's velocities after the collision.
Kinetic energy is also conserved, so that
1/2 m₁v₁² + 1/2 m₂v₂² = 1/2 m₁(v₁')² + 1/2 m₂(v₂')²
or
m₁v₁² + m₂v₂² = m₁(v₁')² + m₂(v₂')²
From the first equation (omitting units), we have
0.0300 • 0.205 + 0.0130 • 0.150 = 0.0300 v₁' + 0.0130 v₂'
0.0810 = 0.0300 v₁' + 0.0130 v₂'
81 = 30 v₁' + 13 v₂'
From the second equation,
0.0300 • 0.205² + 0.0130 • 0.150² = 0.0300 (v₁')² + 0.0130 (v₂')²
0.00155 ≈ 0.0300 (v₁')² + 0.0130 (v₂')²
1.55 ≈ 30 (v₁')² + 13 (v₂')²
Solving both equations simultaneously gives two solutions, one of which corresponds to the initial conditions. The other yields
v₁' ≈ + 0.172 m/s
and
v₂' ≈ + 0.227 m/s
