For this discussion, you will work in groups to answer the questions. In a video game, airplanes move from left to right along the path described by LaTeX: y=2+\frac{1}{x} y = 2 + 1 x . They can shoot rockets tangent to the direction of flight at targets on the x-axis. Where will a rocket fired from LaTeX: \left(1,3\right) ( 1 , 3 ) hit the target? Where will a rocket fired from LaTeX: \left(2,2.5\right) ( 2 , 2.5 ) hit the target? Where will a rocket fired from LaTeX: \left(2.5,2.4\right) ( 2.5 , 2.4 ) hit the target? Where will a rocket fired from LaTeX: \left(4,\:2.25\right) ( 4 , 2.25 ) hit the target?
Answers
Answer:
When fired from (1,3) the rocket will hit the target at (4,0)
When fired from (2, 2.5) the rocket will hit the target at (12,0)
When fired from (2.5, 2.4) the rocket will hit the target at [tex](\frac{35}{2},0)[/tex]
When fired from (4,2.25) the rocket will hit the target at (40,0)
Explanation:
All of the parts of the problem are solved in the same way, so let's start with the first point (1,3).
Let's assume that the rocket's trajectory will be a straight line, so what we need to do here is to find the equation of the line tangent to the trajectory of the airplane and then find the x-intercept of such a line.
In order to find the line tangent to the graph of the trajectory of the airplane, we need to start by finding the derivative of such a function:
[tex]y=2+\frac{1}{x}[/tex]
[tex]y=2+x^{-1}[/tex]
[tex]y'=-x^{-2}[/tex]
[tex]y'=-\frac{1}{x^{2}}[/tex]
so, we can substitute the x-value of the given point into the derivative, in this case x=1, so:
[tex]y'=-\frac{1}{x^{2}}[/tex]
[tex]y'=-\frac{1}{(1)^{2}}[/tex]
m=y'=-1
so we can now use this slope and the point-slope form of the line to find the equation of the line tangent to the trajectory of the airplane so we get:
[tex]y-y_{1}=m(x-x_{1})[/tex]
[tex]y-3=-1(x-1})[/tex]
[tex]y-3=-1x+1[/tex]
[tex]y=-x+1+3[/tex]
[tex]y=-x+4[/tex]
So we can now set y=0 so find the x-coordinate where the rocket hits the x-axis.
[tex]-x+4=0[/tex]
and solve for x
x=4
so, when fired from (1,3) the rocket will hit the target at (4,0)
Now, let's calculate the coordinates where the rocket will hit the target if fired from (2, 2.5)
so, we can substitute the x-value of the given point into the derivative, in this case x=2, so:
[tex]y'=-\frac{1}{x^{2}}[/tex]
[tex]y'=-\frac{1}{(2)^{2}}[/tex]
[tex]m=y'=-\frac{1}{4}[/tex]
so we can now use this slope and the point-slope form of the line to find the equation of the line tangent to the trajectory of the airplane so we get:
[tex]y-y_{1}=m(x-x_{1})[/tex]
[tex]y-2.5=-\frac{1}{4}(x-2})[/tex]
[tex]y-2.5=-\frac{1}{4}x+\frac{1}{2}[/tex]
[tex]y=-\frac{1}{4}x+\frac{1}{2}+\frac{5}{2}[/tex]
[tex]y=-\frac{1}{4}x+3[/tex]
So we can now set y=0 so find the x-coordinate where the rocket hits the x-axis.
[tex]-\frac{1}{4}x+3=0[/tex]
and solve for x
x=12
so, when fired from (2, 2.5) the rocket will hit the target at (12,0)
Now, let's calculate the coordinates where the rocket will hit the target if fired from (2.5, 2.4)
so, we can substitute the x-value of the given point into the derivative, in this case x=2.5, so:
[tex]y'=-\frac{1}{x^{2}}[/tex]
[tex]y'=-\frac{1}{(2.5)^{2}}[/tex]
[tex]m=y'=-\frac{4}{25}[/tex]
so we can now use this slope and the point-slope form of the line to find the equation of the line tangent to the trajectory of the airplane so we get:
[tex]y-y_{1}=m(x-x_{1})[/tex]
[tex]y-2.4=-\frac{4}{25}(x-2.5})[/tex]
[tex]y-2.4=-\frac{4}{25}x+\frac{2}{5}[/tex]
[tex]y=-\frac{4}{25}x+\frac{2}{5}+2.4[/tex]
[tex]y=-\frac{4}{25}x+\frac{14}{5}[/tex]
So we can now set y=0 so find the x-coordinate where the rocket hits the x-axis.
[tex]-\frac{4}{25}x+\frac{14}{5}=0[/tex]
and solve for x
[tex]x=\frac{35}{20}[/tex]
so, when fired from (2.5, 2.4) the rocket will hit the target at [tex](\frac{35}{2},0)[/tex]
Now, let's calculate the coordinates where the rocket will hit the target if fired from (4, 2.25)
so, we can substitute the x-value of the given point into the derivative, in this case x=4, so:
[tex]y'=-\frac{1}{x^{2}}[/tex]
[tex]y'=-\frac{1}{(4)^{2}}[/tex]
[tex]m=y'=-\frac{1}{16}[/tex]
so we can now use this slope and the point-slope form of the line to find the equation of the line tangent to the trajectory of the airplane so we get:
[tex]y-y_{1}=m(x-x_{1})[/tex]
[tex]y-2.25=-\frac{1}{16}(x-4})[/tex]
[tex]y-2.25=-\frac{1}{16}x+\frac{1}{4}[/tex]
[tex]y=-\frac{1}{16}x+\frac{1}{4}+2.25[/tex]
[tex]y=-\frac{1}{16}x+\frac{5}{2}[/tex]
So we can now set y=0 so find the x-coordinate where the rocket hits the x-axis.
[tex]-\frac{1}{16}x+\frac{5}{2}=0[/tex]
and solve for x
[tex]x=40[/tex]
so, when fired from (4,2.25) the rocket will hit the target at (40,0)
I uploaded a graph that represents each case.
Related Questions
out of solid and liquid which has more effect on gravitation
Answers
Answer:
The effect of gravitation is more in liquid than on solid because inter molecular force of attraction is less in liquid and it is weak than that of solid. ... Whereas in solid the molecule are densely packed together an the inter molecular forces are constantly acting upon one another, this results in higher forces.
Which type of electromagnetic wave is deliberately used in some
circumstances to cause damage to living cells in the human body?
A. Infra-red
B. Gamma rays
C. Microwaves
D. Radio waves.
Answers
Gamma rays
used in radiotherapy
State one effect of increase in heat for a temperature range of 50°C to 100°C
on Plastic
Answers
Answer:
why is fraction called a necessary evil
The heat for a temperature in plastic increases at the range of 50°C to 100°C then the plastic decreases its stiffness or flexural modulus.
It is given that the temperature is increased from 50°C to 100°C that means temperature is increasing.
It is required to state the effect of increase in heat on plastic.
What will be the effect of increase in heat for a temperature range of 50°C to 100°C on Plastic?The plastic starts to lose its stiffness or we say that it converts into a softened material as long as we increase the temperature of the material.
So if we increase the temperature too much or exceed above the limit of temperature range then it will distort.
Also there are many qualities that can be affected by increasing the temperature like mechanical property, material fatigue or chemical phenomenon.
Therefore, the heat for a temperature range of 50°C to 100°C
Plastic increases then the plastic decreases its stiffness or flexural modulus.
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A motorcycle moving with velocity and 30m/s accelerate with 4m/s2 to gain velocity of 6mls. calculate its time to gain that velocity
Answers
Using first equation of kinematics
[tex]\boxed{\sf v=u+at}[/tex]
[tex]\\ \sf\longmapsto t=\dfrac{v-u}{a}[/tex]
[tex]\\ \sf\longmapsto t=\dfrac{30-6}{4}[/tex]
[tex]\\ \sf\longmapsto t=\dfrac{24}{4}[/tex]
[tex]\\ \sf\longmapsto t=6s[/tex]
A simple machine has efficiency 90%. What does it mean? No machine has 109 efficiency,why?
Answers
Answer:
Efficiency of a machine is 90% this means that the total energy produced to the machine only 90% is useful and given as a output.
Machines are not 100% efficient because some of the work done by a machine is used to overcome friction
Which quantity can be measured directly using a micrometer screw gauge? A the area of a sheet of paper B the mass of a sheet of paper с the thickness of a sheet of paper D the volume of a sheet of paper
Answers
Answer: C) the thickness of a sheet of paper.
Explanation:
A micrometer screw gauge is a tool that measures distances (in order of millimeters), from this, we can see that the correct option is C: the thickness of a sheet of paper.
Now let's expand on this.
Knowing that the micrometer only can measure distances, we need to analyze which of the options is only a distance.
Notice that while area and volume have similar units, are really different things.
So analyzing the options we have:
A) "the area of a sheet of paper"
To find the area we need two measures (length and width) and then multiply this, but with a micrometer, we never measure the length of a sheet of paper (the maximum measure that you can get in a micrometer is of a few centimeters).
B) "the mass of a sheet of paper"
We can't measure mass with a micrometer.
C) " the thickness of a sheet of paper"
The thickness of a sheet of paper is of the order of 1mm, so we can easily measure this with a micrometer screw gauge.
D) " the volume of a sheet of paper"
We have a similar problem as the one seen in A.
Then the correct option is C.
If you want to learn more, you can read:
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The net force determines how and if and object will
Answers
Answer:
Move. It also determines the total amount of force put on an object
Explanation:
The question is incomplete, the complete question is;
The net force determines how and if an object will?
A) make a balanced force
B) change its mass
C) move or accelerate
When unbalanced forces act on an object, the object moves or accelerates. The correct answer is option C: move or accelerate
Force is considered as a push or pull. Unbalanced forces refers to a system of forces acting in opposite direction and are not equal in magnitude.
Unbalanced forces cause an object to move or accelerate in the direction of the larger force.
Hence, The net or resultant force determines how and if an object will move or accelerate when under the action of unbalanced forces.
For more about an unbalanced forces see:
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the force of attraction between the earth and objects on it is called..
Answers
Answer: gravitational pull? gravity
Explanation:
A body having uniform velocity has zero acceleration? give reason
Answers
Answer:
A body having uniform velocity has zero acceleration because
there is not change in velocity.
Phương trình chuyển động thẳng đều của một chất điểm có dạng: x = 2t – 10. (x: km, t: h). Quãng đường đi được của chất điểm sau 2h là bao nhiêu?
Answers
Answer:
Distance cover in 2 hour = 6 kilometer
Explanation:
Given equation:
x = 2t - 10
where
x = kilometer
t = hour
Find:
Distance cover in 2 hour
Computation:
T = 2
So,
x = 2t - 10
x = 2(2) - 10
x = 4 - 10
x = -6
Distance cover in 2 hour = 6 kilometer
Answer:
The distance is 6 km.
Explanation:
The equation of uniform linear motion of a particle has the form: x = 2t – 10. (x: km, t: h). What is the distance traveled by the particle after 2 hours?
x = 2t - 10
distance traveled after t = 2 hours
Substitute t = 2 in the given expression
x = 2 x 2 - 10
x = 4 - 10
x = - 6 km
So, the distance is 6 km.
A 210 Ohm resistor uses 9.28 W of power. How much current flows through the resistor? (unit=A)
Answers
Answer:
.21
Explanation:
i see everyone got it wrong so ill give you the answer, good luck :)
what is the kinetic energy of a 2,000-kg car moving at 20m/s
Answers
Answer:
400k
Explanation:
Formula for KE = [tex]\frac{1}{2} mv^{2}[/tex]
Plug in:
KE = [tex]\frac{1}{2} mv^{2}[/tex]
KE = [tex]\frac{1}{2}[/tex] × 2000 × 20^2
Solve:
1000 × 400 = 400,000 or 400k
Hope this helped.
Answer : 400000J OR 4×10^4J
Kinetic energy= 1/2mv^2
Here, m=2000kg; V=20m/s
1/2×2000×20×20=400,000J
.............................
Answers
The T-chart compares the average temperature and humidity of two different environments. Which of the following correctly labels the environments?
a t-chart with one column labeled A listing: High humidity: 70%, Temperature Range: 2 degrees Celsius (35 degrees Fahrenheit) in the winter to 24 degrees Celsius (75 degrees Fahrenheit); and another column labeled B listing: Low humidity (13-15%), Temperature Range: -18 degrees Celsius (-1 degrees Fahrenheit) to 49 degrees Celsius (120 degrees Fahrenheit)
A is a desert, and B is a tundra.
A is a grassland, and B is a desert.
A is a tundra, and B is a rainforest.
A is a tundra, and B is a swamp.
Answers
Answer:
A turndra B rainforest
Explanation:
(2) Why do spring balance shows wrong reading after they had been uses for a long time?
Answers
This is because of continuous usage, the wire loses its elasticity and dose not regain it original dimension
Answer:
When a spring balance has been used for a long time, the spring in the balance fatigued and there is loss of strength of the spring. In such a case, the extension in the spring is more for a given load and hence the balance gives wrong readings.
What benefits does using this model have over preforming the modeled procedure with physical materials?
Please help!!
Answers
Explanation:
Advantages of physical models include accuracy, safety, visualization, education, and trying things out that would be impossible in the real world due to safety, cost, or practical concerns. You can visualize things that are extremely tiny, happened millions of years ago, or that otherwise can't be viewed directly.
Define derived unit with example
Answers
Answer:
A derived unit is a SI unit of measurement comprised of a combination of the seven base units. Like SI unit of force is the derived unit, newton or N where N=s21×m×kg. There are some commonly used derived units which includes: 1. Pressure = AreaForce=m2N.
Explanation:
How do we aquire knowledge in science?
Answers
Answer:
By studying.
By paying attention to what the teacher is saying.
That's the way to receive knowledge.
HAVE A GREAT DAY
Explanation:
Please give me that little crown...
AND REMEMBER TO SMILE
In a lunar experiment, a 950-g aluminum (920 J/(°Ckg)) sphere is dropped from the space probe while is 75 m above the Lunar ground. If the sphere’s temperature increased by 0.11°C when it hits the ground, what percentage of the initial mechanical energy was absorbed as thermal energy by the aluminum sphere?
Answers
Answer:
13.759 % of the initial mechanical energy is lost as thermal energy.
Explanation:
By the First Law of Thermodynamics we know that increase in internal energy of the object ([tex]U[/tex]), in joules, is equal to the lost amount of the change in gravitational potential energy ([tex]U_{g}[/tex]), in joules:
[tex]\frac{x}{100} \cdot \Delta U_{g} = \Delta U[/tex] (1)
Where [tex]x[/tex] is the percentage of the energy loss, no unit.
By definition of the gravitational potential energy and internal energy, we expand this equation:
[tex]\frac{x\cdot m \cdot g \cdot h}{100} = m\cdot c\cdot \Delta T[/tex] (1b)
Where:
[tex]m[/tex] - Mass of the object, in kilograms.
[tex]g[/tex] - Gravitational acceleration, in meters per square second.
[tex]h[/tex] - Initial height of the object above the lunar ground, in meters.
[tex]c[/tex] - Specific heat of aluminium, in joules per degree Celsius-kilogram.
[tex]\Delta T[/tex] - Temperature increase due to collision, in degree Celsius.
If we know that [tex]m = 0.95\,kg[/tex], [tex]g = 9.807\,\frac{m}{s^{2}}[/tex], [tex]h = 75\,m[/tex], [tex]c = 920\,\frac{J}{kg\cdot ^{\circ}C}[/tex] and [tex]\Delta T = 0.11\,^{\circ}C[/tex], then the percentage of energy loss due to collision is:
[tex]x = \frac{100\cdot c\cdot \Delta T}{g\cdot h}[/tex]
[tex]x = \frac{100\cdot \left(920\,\frac{J}{kg\cdot ^{\circ}C} \right)\cdot (0.11\,^{\circ}C)}{\left(9.807\,\frac{m}{s^{2}} \right)\cdot (75\,m)}[/tex]
[tex]x = 13.759\,\%[/tex]
13.759 % of the initial mechanical energy is lost as thermal energy.
balance the following equations: CUCO3+H2SO4- CUSO4+H2O+CO2
Answers
Answer:
It is already balanced
Explanation:
It is already balanced
What is the centripetal acceleration of a point on the perimeter of a bicycle wheel diameter 70.0 cm when the bike is moving 8.0 m/s? (160 m/s)
Answers
It’s 180 m/s^2 dude. I think I have you in my class lol.
The centripetal acceleration of an object is due to the changing velocity in a circular path and the centripetal acceleration of the bicycle is 182.85 m/s².
What is Centripetal acceleration?Centripetal acceleration of an object can be defined as the property of the motion of an object which is traversing a circular path. Any object which is moving in a circular path and has an acceleration vector pointed towards the center of that circular path is known as Centripetal acceleration.
The centripetal acceleration of an object can be calculated by the formula:
ac = v²/ r
where, ac = centripetal acceleration,
v = velocity of the object,
r = radius of the circular path
The centripetal acceleration of the object will be:
ac = (8)²/ r
radius = diameter/ 2
radius = 70/ 2
radius = 35cm or 0.35 m
ac = 64/ 0.35
ac = 182.85 m/s²
Therefore, the centripetal acceleration of the bicycle will be 182.85 m/s².
Learn more about Centripetal acceleration here:
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Tick (3) the correct statement about electrostatic charges.
(a) Earthing causes positive charges to flow from the object to the ground.
(b) Similar types of electric charges attract one another.
(c) An electroscope is used to determine the presence of electrostatic charges.
Answers
Answer:
similar type of electric charges attract one another
I think this is a coorect staement
Answer:
C ) An electroscope is used to determine the presence of electrostatic charges
(9x10^2) + (1x10^2)
10x10^4
10x10^3
1x10^4
1x10^3
Answers
Answer:
10 x 10⁴
I hope it's helps you
Answer:
Yes
Explanation:
A man sees a deer in the road and slams on his brakes. If he is traveling at 45.2 m/s and comes to a stop in 2.74 s, what is his acceleration? O -6:02 m/s2 -0.0606 m/s2 -47.9 m/s2 0 -16.5 m/s2
Answers
Answer:
16.50 m/s²
Explanation:
initial velocity(u)=45.2 m/s
final velocity(v)= 0 (it stops)
time taken(t)= 2.74 s
now,we have
acceleration(a)= (v-u)/t
= (0-45.2 m/s)/2.74s
= -45.2 m/s / 2.74s
= -16.50 m/s²
Answer:
[tex]\boxed {\boxed {\sf -16.5 \ m/s^2}}[/tex]
Explanation:
We are asked to find the acceleration of a man driving. Acceleration is the change in velocity over the change in time. Acceleration is calculated with the following formula.
[tex]a= \frac{v_f- v_i}{t}[/tex]
The driver's initial velocity is 45.2 meters per second. His final velocity is 0 meters per second because he came to a stop. He stopped in 2.74 seconds.
[tex]\bullet \ v_f= 0 \ m/s \\\bullet \ v_i= 45.2 \ m/s \\\bullet \ t= 2.74 \ s[/tex]
Substitute these values into the formula.
[tex]a= \frac{0 \ m/s - 45.2 \ m/s }{ 2.74 \ s}[/tex]
Solve the numerator by subtracting.
[tex]a= \frac{- 45.2 \ m/s }{ 2.74 \ s}[/tex]
[tex]a= -16.49635036 \ m/s^2[/tex]
The original measurements of velocity and time have 3 significant figures, so our answer must have the same. For the number we calculated, that is the tenths place. The 9 in the hundredth place tells us to round the 4 in the tenths place up to a 5.
[tex]a \approx -16.5 \ m/s^2[/tex]
The acceleration is approximately -16.5 meters per second squared. The acceleration is negative because the man slowed down and came to a stop.
What would be the acceleration in a body moving with uniform velocity and why?
Answers
Explanation:
The derivative of a constant term is always 0. So the acceleration of the body would be zero. Hence, the acceleration of a body moving with uniform velocity will always be zero.
hope it helps you
A ball is dropped from the roof of a 25-m-tall building. What is the velocity of the object when it touches the ground? Suppose the ball is a perfect golf ball and it bounces such that the ve locity as it leaves the ground has the same magnitude but the op posite direction as the velocity with which it reached the ground How high will the ball bounce? Now suppose instead that the ball bounces back to a height of 20 m. What was the velocity with which it left the ground?
Answers
Answer:
a) [tex]h=25m[/tex]
b) [tex]v=19.8m/sec[/tex]
Explanation:
From the question we are told that:
Height [tex]h=25m[/tex]
Bounce Height [tex]h'=20m[/tex]
Generally the Kinematic equation is mathematically given by
[tex]V=\sqrt{2gh}\\\\V=\sqrt{2*9.81*25}[/tex]
[tex]V=22.1m/sec[/tex]
Therefore Height
[tex]h=\frac{V^2}{2g}\\\\h=\frac{22.1^2}{2*9.81}[/tex]
[tex]h=25m[/tex]
b)
Generally the Kinematic equation is mathematically given by
[tex]v^2=2ah[/tex]
[tex]v^2=2*9.8*20[/tex]
[tex]v=\sqrt{2*9.8*20}[/tex]
[tex]v=19.8m/sec[/tex]
Q: Riri wants to bake a cake. She adds flour, sugar, egg, baking soda, and yeast into a bowl and mixed them together. After all the ingredients are mixed, she leaves the dough for 30 minutes and the dough starts to rise. Which changes Occurred in this process? Explain your reason.
Answers
Answer:
I don't know what you mean about which changes occurred in this process but if its why the dough starts rising then its caused by the carbon dioxide in baking soda and yeast which is a fungus
Answer:
When baking,flour is mixed with water,the other ingredients and yeast to form a paste called a dough.what happens is that the zymase enzyme from the yeast acts on the sugars to form carbon dioxide and alcohol.the carbon dioxide begins to form bubbles in the dough causing it to rise..
I hope this helps
can someone help me asap please
Answers
Answer:
Resultant force is 20 N
Explanation:
Resolving vertically:
[tex]{ \sf{F_{y} = (8 \cos 30 \degree) + (12 \cos 30 \degree) }} \\ { \sf{ \sum F_{y} = 17.3 \: newtons }}[/tex]
Resolving horizontally:
[tex]{ \sf{F_{x} = (8 \sin 30 \degree) + (12 \sin 30 \degree) }} \\ { \sf{ \sum F _{x} = 10 \: newtons}}[/tex]
Resultant force:
[tex]{ \boxed{ \bf{F = \sqrt{ {F _{x} }^{2} + {F _{y} }^{2} } }}} \\ { \sf{F = \sqrt{ {17.3}^{2} + {10}^{2} } }} \\ { \sf{F = \sqrt{399.29} }} \\ F = 19.98 \approx20 \: newtons[/tex]
Object A has a mass of 5 kg and a velocity of 6 m/s to the east while Object 1 point B has a mass of 12 kg and velocity 0.6 m/s also to the east. What is the momentum of the system? (Let east be positive)
help plss I got family
Answers
Answer:
Momentum of system = 37.2 Kgm/s.
Explanation:
Given the following data;
Mass A = 5 kgVelocity A = 6 m/sMass B = 12 kgVelocity B = 0.6 m/sTo find the momentum of the system;
Momentum can be defined as the multiplication (product) of the mass possessed by an object and its velocity. Momentum is considered to be a vector quantity because it has both magnitude and direction.
Mathematically, momentum is given by the formula;
Momentum = mass * velocity
For object A;
Momentum A = 5 * 6
Momentum A = 30 Kgm/s
For object B;
Momentum B = 12 * 0.6
Momentum B = 7.2 Kgm/s
Next, we would determine the momentum of this system using the formula;
Momentum of system = Momentum A + Momentum B
Substituting the values into the formula, we have;
Momentum of system = 30 + 7.2
Momentum of system = 37.2 Kgm/s.
Write down the conservation of momentum?
Answers
Let,
m
A
= Mass of ball A
m
B
= Mass of ball B
u
A
= initial velocity of ball A
u
B
= initial velocity of ball B
v
A
= Velocity after the collision of ball A
v
B
= Velocity after the collision of ball B
F
ab
= Force exerted by A on B
F
ba
= Force exerted by B on A
Now,
Change in the momentum of A= momentum of A after the collision - the momentum of A before the collision
= m
A
v
A
−m
A
u
A
Rate of change of momentum A= Change in momentum of A/ time taken
=
t
m
A
v
A
−m
A
u
A
Force exerted by B on A (F
ba
);
F
ba
=
t
m
A
v
A
−m
A
u
A
........ [i]
In the same way,
Rate of change of momentum of B=
t
m
b
v
B
−m
B
u
B
Force exerted by A on B (F
ab
)=
F
ab
=
t
m
B
v
B
−m
B
u
B
.......... [ii]
Newton's third law of motion states that every action has an equal and opposite reaction, then,
F
a
b=−F
b
a [ ' -- ' sign is used to indicate that 1 object is moving in opposite direction after collision]
Using [i] and [ii] , we have
t
m
B
v
B
−m
B
u
B
=−
t
m
A
v
A
−m
A
u
A
m
B
v
B
−m
B
u
B
=−m
A
v
A
+m
A
u
A
Finally we get,
m
B
v
B
+m
A
v
A
=m
B
u
B
+m
A
u
A
This is the derivation of conservation of linear momentum.
