Assuming both billiard balls have the same mass, conservation of momentum says
[tex]m\vec v_1 + m\vec v_2 = m{\vec v_1}\,' + m{\vec v_2}\,'[/tex]
where m = mass of both billiard balls, and v₁ and v₂ = their initial velocities, and v₁' and v₂' = their final velocities. The masses are the same so the exact value of m is irrelevant. The first ball has initial speed 5 m/s and the second is at rest, so
[tex]\left(5 \dfrac{\rm m}{\rm s}\right) \, \vec\imath = {\vec v_1}\,' + {\vec v_2}\,'[/tex]
After the collision, the first ball has speed 4.35 m/s and is moving at angle of 30° below the original path, so
[tex]{\vec v_1}\,' = \left(4.35\dfrac{\rm m}{\rm s}\right)\left(\cos(30^\circ) \, \vec\imath + \sin(30^\circ) \, \vec\jmath\right) \approx \left(3.77 \dfrac{\rm m}{\rm s}\right) \vec\imath + \left(-2.18 \dfrac{\rm m}{\rm s}\right) \vec\jmath[/tex]
Then the second ball has final velocity vector
[tex]{\vec v_2}\,' \approx \left(1.23 \dfrac{\rm m}{\rm s}\right) \vec\imath + \left(2.18 \dfrac{\rm m}{\rm s}\right) \vec\jmath[/tex]
so it moves with speed
[tex]\left\|{\vec v_2}\,'\right\| \approx \sqrt{\left(1.23\dfrac{\rm m}{\rm s}\right)^2 + \left(2.18\dfrac{\rm m}{\rm s}\right)^2} \approx \boxed{2.50 \dfrac{\rm m}{\rm s}}[/tex]
at an angle of
[tex]\theta \approx \tan^{-1}\left(\dfrac{2.18}{1.23}\right) \approx \boxed{60.5^\circ}[/tex]
or about 60.5° above the original line of motion.
Part Two: Criteria, Constraints, and Prioritizations
1. Choose one sub-problem that you will investigate further and explain which one you chose here.
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2. List two realistic criteria for the sub-problem.
o
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3. Explain why it is important for these criteria to be met in order to solve the problem.
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4. List two constraints for the sub-problem.
o
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5. Explain why these constraints exist. (How do they limit solutions to the problem?)
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6. Prioritization of the criteria and constraints and an explanation supporting the decisions made based on research.
PLEASE HELP ME I DONT UNDERSTAND<333
Answer:
Usually, a solution can have several criteria and constraints. Even though all are important, some criteria are more important than others. The same holds true for constraints. But what do you do if it's impossible for a solution to cover every criterion while avoiding every constraint? In cases like this, you can use prioritization. Listing criteria and constraints based on priority shows the relative importance of each. You will need to prioritize the criteria and constraints for each sub-problem so that you can design a solution for each one individually. Prioritization can help you compare two different possible solutions. For example, the criterion that cars travel at 15 mph through the neighborhood might be a higher priority than the constraint that homeowners are only willing to spend $10,000 on this issue. If this is the case, you would want to generate solutions that also follow the priority in mind. All criteria are important, but engineers must sometimes make a trade-off, which is a compromise or change in one or more criteria or constraints so that they can be met at the same time. This is where prioritization comes in handy as it helps determine the trade-offs. A solution that is doing a better job of meeting one criterion may result in not completely meeting another criterion. Prioritization will help you choose which solution to go with.
Explanation:
I got this from quizlet :)
Which are examples of perfectly inelastic collisions? Check all that apply.
a baseball bouncing off a bat
bumper cars bumping off of each other
a cue ball hitting an eight ball and stopping
a plane landing on an aircraft carrier
rain sticking to a window
two train cars coupling together
Answer:
D. a plane landing on an aircraft carrier
E. rain sticking to a window
F. two train cars coupling together
Explanation:
which is the correct relationship among pressure, flow, and resistance?
Answer:
Flow is proportional to change in pressure and inversely proportional to resistance.
A 7.5 kg beaver dives horizontally off a 50 kg log at a speed of 4 m/s. What is the speed of the log?
Answer:
[tex]0.6\; \rm m\cdot s^{-1}[/tex], assuming that drag of the water on the log is negligible.
Explanation:
The momentum [tex]p[/tex] of an object is equal to the product of mass [tex]m[/tex] and velocity [tex]v[/tex]. That is, [tex]p = m\, v[/tex].
If the drag of water on the log is negligible, momentum of the beaver and the log, combined, would be preserved.
The momentum of the beaver and the log, combined, was initially [tex]0\; \rm kg\cdot m \cdot s^{-1}[/tex].
The momentum of the beaver right after the dive would be [tex]7.5 \; {\rm kg} \times 4\; {\rm m \cdot s^{-1}} = 30\; {\rm kg \cdot m \cdot s^{-1}}[/tex].
The sum of the momentum of the beaver and the log is conserved and should continue to be [tex]0\; {\rm kg\cdot m \cdot s^{-1}}[/tex] even after the dive. Since the momentum of the beaver is [tex]30\; {\rm kg \cdot m \cdot s^{-1}[/tex] after the dive, the momentum of the log should become [tex](-30)\; {\rm kg \cdot m \cdot s^{-1}}[/tex].
Since the mass of the log is [tex]50\; {\rm kg}[/tex], the new velocity of this log would be:
[tex]\begin{aligned}v &= \frac{p}{m} \\ &= \frac{(-30)\; {\rm kg \cdot m \cdot s^{-1}}}{50\; {\rm kg}} \\ &= (-0.6)\; {\rm m \cdot s^{-1}}\end{aligned}[/tex].
(The new velocity of the log is negative because the log would be moving away from the beaver.)
The speed of an object is the magnitude of velocity. For this log, a velocity of [tex](-0.6)\; {\rm m \cdot s^{-1}}[/tex] would correspond to a speed of [tex]|(-0.6)\; {\rm m \cdot s^{-1}| = 0.6\; {\rm m \cdot s^{-1}[/tex].
what is the necessary condition for the conservation of angular momentum
Answer:
The conservation of momentum of a system is a fundamental principle in classical mechanics. The only condition for this principle being valid is that the system should be an isolated one, i.e. It should not be acted upon by any external force.
You are pulling a child in a wagon. The rope handle is inclined upward at a 60∘ angle. The tension in the handle is 20 N.
Part A
How much work does the rope do on the wagon if you pull the wagon 200 m at a constant speed?
Answer:
2000 J
Hope you could get an idea from here.
Doubt clarification - use comment section.
S O L U T I O N:
Here we've been provided with the information i.e
Force (F) = 20N Distance (s) = 200m Angle (θ) = 60°Ans we have given to find out what is work done (W) = ?
The standard formula to calculate work done is given by,
[tex]:\implies\sf{w = f \times s \times cos \theta}[/tex]
[tex]:\implies\sf{w = 20 \times 200 \times cos60}[/tex]
[tex]:\implies\sf{w = 20 \times 200 \times \frac{1}{2} }[/tex]
[tex]:\implies\sf{w = 20 \times 100 \times 1}[/tex]
[tex]:\implies\sf{w = 2000J}[/tex]
Total work done done by rope is 2000J.When Magnesium and Fluorine react what type of bond is formed
A) Metallic
B) Ionic
C) Covalent
D) Diatomic
Answer:
hi your answer should be B
Explanation:
Hope this helps!
Answer:
ionic
Explanation:
two metals that bond are considered ionic bonds
how to calculate kinetic energy given mass and velocity
In classical mechanics, kinetic energy (KE) is equal to half of an object's mass (1/2*m) multiplied by the velocity squared. For example, if a an object with a mass of 10 kg (m = 10 kg) is moving at a velocity of 5 meters per second (v = 5 m/s), the kinetic energy is equal to 125 Joules, or (1/2 * 10 kg) * 5 m/s2.
Define "one solar day".
Answer:
the interval between transits of the apparent or mean sun across the meridian at any place.
what is the prmary source of energy inside of the earth
A horizontal force F~ is applied to a block of mass m = 1 kg placed on an inclined
at θ = 30◦ plane. The coefficients of static and dynamic friction are µs = 0.3 and µ = 0.2, respectively. Find F such that the block is moving up the slope with a constant speed.
Hi there!
To find the appropriate force needed to keep the block moving at a constant speed, we must use the dynamic friction force since the block would be in motion.
Recall:
[tex]\large\boxed{F_D = \mu N}}[/tex]
The normal force of an object on an inclined plane is equivalent to the vertical component of its weight vector. However, the horizontal force applied contains a vertical component that contributes to this normal force.
[tex]\large\boxed{N = Mgcos\theta + Fsin\theta}}[/tex]
We can plug in the known values to solve for one part of the normal force:
N = (1)(9.8)(cos30) + F(.5) = 8.49 + .5F
Now, we can plug this into the equation for the dynamic friction force:
Fd= (0.2)(8.49 + .5F) = 1.697 N + .1F
For a block to move with constant speed, the summation of forces must be equivalent to 0 N.
If a HORIZONTAL force is applied to the block, its horizontal component must be EQUIVALENT to the friction force. (∑F = 0 N). Thus:
Fcosθ = 1.697 + .1F
Solve for F:
Fcos(30) - .1F = 1.697
F(cos(30) - .1) = 1.697
F = 2.216 N
A tennis ball is dropped from a height of 3 m and bounces back to a height of
1 m after hitting the ground (s = 0).
Use the equation V^2=U^2 + 2as to calculate the velocity of the tennis
ball when it hits the ground.
The velocity of the tennis ball when it hits the ground is calculated as 4.43m/s. Details about velocity can be found below.
How to calculate velocity?The velocity of a moving object can be calculated using the equation of motion as follows:
v² = u² + 2as
Where;
v = final velocityu = initial velocitya = accelerations = distancev² = 0² + 2(9.8) (1)
v² = 19.6
v = ✓19.6
v = 4.43m/s
Therefore, the velocity of the tennis ball when it hits the ground is calculated as 4.43m/s.
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A bus accelerates away from the bus stop at 2.5 m/s2
.
The total mass of the bus and passengers is 14 000 kg.
Calculate the resultant force needed to accelerate the bus and passengers.
help pls my brain is not working
Explanation:
F=k.g m\s2
=2.5 m\s2 14000k.g
= 35000N
what is value of 2.37 in sl units
does a perfectly elastic colission conserve momentum and impulse
Answer:
A perfectly elastic collision conserves momentum and kinetic energy..
Question 17 (Essay Worth 5 points)
(02.06 HC)
Choose two spheres of Earth which interact when hot springs are formed. Use complete sentences to explain how they interact during this process
X2
= 12 Source
ус
cM
В І
U S XX T
.
Styles
Format
Font
Size
A- A -
Increase Indent
Answer:
geosphere and hydrosphere
Explanation:
please help me !! i’ll give you brainliest if you get the answer right!
Answer: 25N to the right
Explanation: 35N - 10N = 25N
Object 1 has a mass of 7.0kg and a initial velocity of 17.0 m/s. Object 2 has a mass of 8.0kg and a initial velocity of -14.0 m/s. What are the final velocitys of each object. Please show work
[tex]\\ \sf\longmapsto m1v1+m2v2=(m1+m2)v3[/tex]
[tex]\\ \sf\longmapsto 7(17)+8(-14)=(7+8)v3[/tex]
[tex]\\ \sf\longmapsto 119-112=15v3[/tex]
[tex]\\ \sf\longmapsto 15v3=7[/tex]
[tex]\\ \sf\longmapsto v3=7/15[/tex]
[tex]\\ \sf\longmapsto v3=2.1m/s[/tex]
A heavy crate is pushed across a floor at a constant velocity. Friction is present between the crate and floor. During this motion, the force of friction is _?_ the force pushing the crate forward.
Question 3 options:
less than
greater than
equal to
Answer:
less than.
Explanation: because Friction is the resistance to motion of one object moving relative to another. which means it cant be greater because how would it be greater if its pushing forward when friction is the resistance.
THANKS FOR THE POINTS :D
Learning Task 1: Define or describe the following words relat are not familiar with the word, you may ask assistance from y your answer in your notebook. 1. table 2. tennis C 3. ping-pong 4. net 5. ball 6. racket
Answer:
1.) TABLE = The table is 2.74 m (9.0 ft) long, 1.525 m (5.0 ft) wide, and 76 cm (2.5 ft) high with any continuous material so long as the table yields a uniform bounce of about 23 cm (9.1 in) when a standard ball is dropped onto it from a height of 30 cm (11.8 in), or about 77%.
2.) TENNIS = Tennis is a racket sport that can be played individually against a single opponent (singles) or between two teams of two players each (doubles). Each player uses a tennis racket that is strung with cord to strike a hollow rubber ball covered with felt over or around a net and into the opponent's court.
3.) PING-PONG = Table tennis, also known as ping-pong and whiff-whaff, is a sport in which two or four players hit a lightweight ball, also known as the ping-pong ball, back and forth across a table using small rackets. ... Spinning the ball alters its trajectory and limits an opponent's options, giving the hitter a great advantage.
4.) NET = This is stretched across the centter of the table by a cord attached to a post at either end. It measures 6ft long and the ball must pass over it for a rally to continue.
5.) BALL = The ball, which is spherical and hollow, was once made of white celluloid. Since 1969 a plastic similar to celluloid has been used. The ball, which may be coloured white, yellow, or orange, weighs about 0.09 ounce (2.7 grams) and has a diameter of about 1.6 inches (4 cm).
6.) RACKET = A table tennis racket is made up of two distinct parts - a wooden blade which incorporates the handle together with table tennis rubbers affixed to each side of the blade using water-based glue.
Explanation:
All my answers are
about the tools of the
game of tennis
how does gravitational lensing tell us about the mass of a galaxy cluster?
Answer:
Newton's universal law of gravitation predicts how mass can distort light, so we can apply Newton's law to determine the mass of the cluster. ... The lensing allows us to determine the orbital speeds of galaxies in the cluster, so that we can determine the mass of the cluster from the orbital velocity law.
Explanation:
What is the half-life of an isotope if after 30 days you have 31.25 g remaining from a 250 g beginning sample size?
The half-life of the given isotope will be 10 days, if after 30 days only 31.25 grams are remaining from a sample of 250 grams of the sample size taken in the beginning.
What is Half-life of an element?
The Half-life is the time which is required for a quantity to reduce the content to half of the amount present as its initial value. The term is used in nuclear physics to describe how quickly an unstable atom undergo radioactive decay or how long does stable atoms survive. The term is also used generally to characterize any type of exponential decay.
The half-life of the isotope can be calculated by the formula:
FR = 0.5n
FR = Fraction Remaining = 31.25 g / 250.0 g = 0.1250
n = number of half lives elapsed = ?
0.125 = 0.5n
log 0.125 = n log 0.5
-0.9031 = -0.3010 n
n = 3.000 half lives have elapsed
3 half lives = 30 days
1 half live = 10 days
Therefore, the half-life of the isotope will be 10 days.
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A hair dryer transforms 10,000J of energy in 4s. What is its power?
Answer:
2500 WExplanation:
Power is the rate at which work is done and can be found by using the formula
[tex]p = \frac{w}{t} \\ [/tex]
p is power in Watts ( W)
w is the workdone in J
t is time in s
From the question
w = 10,000 J
t = 4 s
We have
[tex]p = \frac{10000}{4} = 2500 \\ [/tex]
We have the final answer as
2500 WHope this helps you
Which metals can be extracted from following ores (i) Argentite (ii) Haematite (iii) Chalcopyrite (iv) Bauxite
I hope it's helpful for you ☺️
1) iron
2) aluminium
3) silver
4) copper
Help plz I don’t know it
Answer:
2. thermal insulator. 3. convection current. 4. conduction. 5. thermal conductor. 6. radiation.
Explanation:hope this helps you.
7. a heater heating up the inside of the car
Convection conduction and radiation
when an individual charge flies through a *blank* field, a force is exerted on the charge and the path of the charge bends.
Answer:
"electric or magnetic"
F = q E force on charge q due to electric field E
F = q v x B force on charge q due to magnetic field B
a car dealer sells 4 makes of cars in 5 colors with either standard or automatic transmissions. how many variations does the dealership offer?
The number of variations the dealership have is 40 cars.
Data given;
The number of different product = 4The number of transmission = 2 (standard or automatic)The numbers of colors available = 5Dealership variationThis is the total numbers of cars available in the dealer shop at the moment.
To get that, we simply multiply the numbers of colors available, the number of transmission and the makes of car available.
This is equal to
[tex]4*2*5=40[/tex]
From the above calculation, we can say that the variations the dealership offers is 40
Learn more on combination here
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what are the main component of network
Answer:
A network has 5 basic components viz. clients, servers, channels, interface devices and operating systems.
why is water soaked cloth used on forehead during fever?please can you tell me answer
This is because the cloth soaked in water can absorb and evaporate the heat from your forehead.
Explanation:This technique is used to cool down your fever, and to help you feel better.