a particle is projected from a point a with a velocity of 21m/s at an angle of 53.1 degees to the horizontal. one second later another particle is projected at a point 0.3m below a with initial velocity of 31.5m/s at an angle of 36.9 degrees to the horizontal.
(i) prove that the particles collide
(ii) find the time of collision
(iii) find the distance of collision from point of projection
Answers
Answer:
(i) Please see graph of the motion of the particles created with MS Excel and the calculations in the following sections
(ii) The time of collision is approximately 1.0 seconds
(iii) The common horizontal distance of point collision from the point of projection is approximately 25.2 meters
Explanation:
The velocity with which the first projectile was fired, v₁ = 21 m/s
The angle to the horizontal the particle is launched = 53.1°
The time at which the other particle was launched = 1 second later
The location from which the other particle was projected = 0.3 m below the first particle
The initial velocity of the second particle = 31.5 m/s
The angle to the horizontal at which the second particle was projected, θ = 36.9°
(i) The height reached, by each of the particle is given as follows;
y = u·t - 1/2·g·t²
For the first projectile, we have;
y = 21·(t₁+1)×sin(53.1°) - 9.81·(t₁+1)²/2 + 0.3
For the second projectile, we have;
y= 31.5·(t₁)×sin(36.9°) - 4.905·(t₁)²
If the two projectiles collide, we get;
21·(t₁+1)×sin(53.1°) - 9.81·(t₁+1)²/2 + 0.3 = 31.5·(t₁)×sin(36.9°) - 4.905·(t₁)²
Using a graphing calculator for simplifying, we get;
-11.93·t₁ + 12.2 = 0
t₁ = 12.2/11.93 ≈ 1.02
Therefore, at time t₁ = 1.02 seconds, after the launch of the second particle, the two particle will be at the same vertical height
However, whereby at the time, t₂, the particles collide, the horizontal distance travelled, 'x', will be equal;
We have;
x = u·cos(θ)·t₁
For the first particle, we have;
x₁₁ = 21 × cos (53.1°) × (t₂ + 1)
For the second particle, we have;
x₂₂ = 31.5 × cos (36.9°) × t₂
At the point of collision, we have;
x₁ = x₂
∴ 21 × cos (53.1°) × (t₂ + 1) = 31.5 × cos (36.9°) × t₂
31.5 × cos (36.9°) × t₂ - 21 × cos (53.1°) × t₂ = 21 × cos (53.1°)
t₂ = 21 × cos (53.1°)/(31.5 × cos (36.9°) - 21 × cos (53.1°) ) = 1.00219236871
t₂ ≈ 1.0 seconds
Given that t₁ ≈ t₂, the particles reach the same height and the same horizontal distance at the same time, t₂ ≈ 1.0 and therefore, they collide.
(ii) The time of collision is found above as t₁ ≈ t₂ ≈ 1.0 seconds
(iii) The horizontal distance of the point of collision from the starting point, 'x', is given as follows;
x = 21 × cos (53.1°) × (1.0 + 1) ≈ 25.2
The horizontal distance of the point of collision from the starting point, x ≈ 25.2 meters
The vertical distance of the point of collision from the starting point of the second particle, 'y', is given as follows;
y = 21 × (1+1)×sin(53.1°) - 9.81 × (1+1)²/2 + 0.3 ≈ 14
The vertical distance of the point of collision from the starting point of the second particle, y ≈ 14 meters
The magnitude of the distance from the starting point of the second particle, r = √(25.2² + 14²) ≈ 28.8
The magnitude of the distance from the starting point of the second particle, r ≈ 28.4 meters.
Related Questions
A 42.2 N force acts at 40* to the ground, causing the object to move a horizontal distance of 8.15 m. How much work was done on the object?
Answers
Answer:
W=F.dcos angle
w=42.2 x8.15 x cos40
w=343.93× cos 40
W=343.93 x 0.76
W=261.38 J
Work done on the object will be 264.83 J
What is work done ?Work done is the product of the component of the force in the direction of the displacement and the magnitude of this displacement.
given :
F = 42.2 N
let , x = 40°
horizontal distance (s) = 8.15 m
Work done = F s cos (x)
= F * s * cos (x)
= 42.2 * 8.15 * cos 40° = .766
= 343.93 * 0.77
= 264.83 J
Work done on the object will be 264.83 J
learn more about Work done :
https://brainly.com/question/13662169?referrer=searchResults
#SPJ3
In a clear cup there are three substances. Their densities are 3, 1, and 2. From top of the cup to the bottom, what would the order of substances be sitting inside the cup?
Answers
Answer:
1, 2 and 3
Explanation:
The most dense substance will settle at the bottom of the cup
how does electricity work?
Answers
Answer:Electricity works by getting a bunch of conductor elements together and creating a flow of electron-stealing patterns through them. This flow is called a current. ... Once you can control the direction the electrons are going, you can use them to power or charge anything from a light bulb to your TV to your electric car.
Explanation:trust
When you are aware that you are having a dream and can control what you do
in that dream, it's called: ??
A. night terrors.
B. sleepwalking.
C. Stage 4 sleep.
D. lucid dreaming.
Answers
Answer:
D. lucid dreaming
Explanation:
(=^w^=)
(a) If a force of 6 N is applied on a body of mass 4 kg, moving at a uniform
velocity, in the direction of its motion, find the resulting acceleration.
(b) If the above force is applied in the direction opposite to the direction
of motion of the body, find its deceleration.
Answers
Answer:
1.5 m/s ; - 1.5 m/s²
Explanation:
F = ma
F = Force ; m = mass of body ; a = Acceleration
Hence,
a = F/m
F = 6N applied in the direction of motion of the. Body
a = 6N / 4 kg
a = 1.5 m/s² in the direction of motion.
If the force is applied in the opposite direction of motion :
F = ma
a = F/m
a = 6 / 4
a = 1.5 m/s²
Simc efoece is applied in the opposite direction of motion :
We have a negative acceleration (deceleration) = - 1.5 m/s²
the distance between a boy and a hill is 250 meters. if the boy shouts after how long will the echo be heard numerical problem
Answers
Answer:
1.47 s
Explanation:
From the question,
s = 2d/t................... Equation 1
s = speed of sound in air, d = distance between the boy and the hill, t = time to hear the echo.
make t the subject of the equation
t = 2d/s............... Equation 2
Given: d = 250 meters
Constant: s = 340 m/s
Substitute these values into equation 2
t = (2×250)/340
t = 500/340
t = 1.47 s
What are the prevailing winds from the west toward the east called?
Prevailing Westerlies
Jet Stream
Gulf Stream
La Nina
Answers
Answer:
The Coriolis Effect, in combination with an area of high pressure, causes the prevailing winds—the trade winds—to move from east to west on both sides of the equator across this 60-degree "belt."
Explanation:
if its wrong welp sorry that what i know,
How would the motion of the book change if there was LESS friction as it moved across the table?
Answers
Answer:
The motion of the book would change if there was less friction if it moved across the table is that it would spin and have more kenetic energy.
Explanation:
friction slows stuff down so if it had less friction it would speed up and spin when sliding.
What force is caused by tiny collisions, called microwelds, on surfaces that
are stuck together?
A. heat
B. energy
C. air resistance
D. friction
Answers
Answer:
D. Friction
Explanation:
"Friction is caused by microwelds that form between two surfaces. Microwelds are stronger when the two surfaces are pushed together with a greater force." - ( Module 3 • Forces and Newton’s Laws) quoted
hope this helps and is right. p.s. i really need brainliest :)
Answer:
Friction
Explanation:
Took The Test
4. Un móvil viaja en línea recta con una velocidad media de 1200 cm/s durante 9 s, y luego con velocidad media de 480 cm/s durante 7 s, siendo ambas velocidades del mismo sentido: a) ¿cuál es el desplazamiento total en el viaje de 16 s? B) ¿cuál es la velocidad media del viaje completo?
Answers
Answer:
A) El desplazamiento total del viaje es 14160 centímetros.
B) La velocidad media del viaje completo es 885 centímetros por segundo.
Explanation:
A) El desplazamiento es el producto de la velocidad media por el tiempo. El desplazamiento total es la suma de desplazamientos asociados a cada velocidad media, entonces:
[tex]x = \left(1200\,\frac{cm}{s}\right)\cdot (9\,s)+ \left(480\,\frac{cm}{s} \right)\cdot (7\,s)[/tex]
[tex]x = 14160\,cm[/tex]
El desplazamiento total del viaje es 14160 centímetros.
B) La velocidad media del viaje es el desplazamiento total dividido por el tiempo total, es decir:
[tex]\bar v = \frac{14160\,cm }{16\,s}[/tex]
[tex]\bar v = 885\,\frac{cm}{s}[/tex]
La velocidad media del viaje completo es 885 centímetros por segundo.
PLEASE HELP!!
ESSAY: WESTERN POLITICAL THOUGHT
Here is your goal for this assignment:
Write an essay relating the political thoughts in the Declaration of Independence to the Bible
From an encyclopedia, the Internet, or another reference, read the second paragraph of the Declaration of Independence.
Copy each phrase that you think is part of the tradition of Western political thought (for example "all men are created equal").
In an essay of 300 words explain how each of these ideas is related to Biblical teaching.
Hint: Refer to the lesson "Theory, Practice, and Models" for a list of the Declaration's main thoughts that are a part of the tradition of Western political thought (bottom of page 1). Type your findings using proper grammar, punctuation, and spelling.
Proper documentation includes both parenthetical citations within the body of your report anytime you summarize or quote a source, as well as works cited page.
Answers
The question wants to analyze your writing and research skills. For that reason, I cannot write your essay, but I will show you how to write it.
This is the type of essay that requires a lot of research and interpretation, so you should start by searching for articles that analyze the Declaration of Independence, interpret it in detail and show relevant information about it and the concepts it presents.
After that, you should research how these concepts and ideas are treated in the bible. For that, you will need to search for more articles that show how the bible approaches these subjects.
After that, you can start your essay.
Essay StructureIntroduction: Introduce the subject of your essay in a short, succinct paragraph.Body: Write at least two paragraphs. In the first paragraph, you will present the concepts covered in the Declaration of Independence and how they are associated with biblical concepts. In the second paragraph, you will show how this affected society and what impact it has on America today. You will show evidence to support the information provided. This evidence will be taken from the articles you searched for.Conclusion: Summarize all the information provided and reinforce the importance of this topic.You can get more information on how to write essays at the link below:
https://brainly.com/question/683722
Answer:
“We hold these truths to be self-evident, that all men are created equal, that they are endowed by their Creator with certain unalienable Rights, that among these are Life, Liberty and the pursuit of Happiness." So, This is connected to the biblical worldview and teaching in the sense that everyone is created with an equal opportunity or chance to live. No one is created literally equal or we would all look the same, talk the same, and think the same. Instead, we all have an opportunity at life and to live. Also, we all have the right to pursue happiness. Sin provides a certain happiness in our lives. It provides short-term happiness that corrupts us. In the “Declaration of Indepence”, sin is a pursuit of happiness, but also doing good is too. They meant that we should pursue what God says is good happiness. For instance, doing nice things to people and serving them. This makes me happy and every other human being that is not narcissistic or a robot. That happiness is joy and it does not come from our circumstances, but from the happiness in our hearts that shows a relationship with God.
The horizontal distance between two nodes is 1.5 meters what is the wavelength of then standing wave
Answers
Answer:
[tex]\lambda=3\ m[/tex]
Explanation:
Given that,
The horizontal distance between the two nodes is 1.5 meters.
We need to find the wavelength of the standing wave.
If we know the distance between nodes and antinodes, then the equation is :
[tex]\dfrac{\lambda}{2}=D[/tex]
Where
[tex]\lambda[/tex] is the wavelength
So,
[tex]\lambda=2D\\\\=2\times 1.5\\\\=3\ m[/tex]
So, the wavelength of the standing wave is equal to 3 m.
How many degrees equal π in radians? How many revolutions (turns) equal π radians?
Answers
Answer:
It follows that the magnitude in radians of one complete revolution (360 degrees) is the length of the entire circumference divided by the radius, or 2πr / r, or 2π. Thus 2π radians is equal to 360 degrees, meaning that one radian is equal to 180/π ≈ 57.295779513082320876 degrees.
Explanation:
A system releases 150 kJ of heat while 10 kJ of work is done on the system by
the surroundings. Calculate the change in internal energy (in kJ).
Answers
Answer:
160J OR 140J
Explanation:
Depends on teacher which formula your teacher uses.
U=Q+W OR U=Q-W
Method 1:
U=150+10J=160
U=150-10=140J
1. interpret data- based on the data, describe what alicia did.
2. draw conclusions- what conclusions can you draw? what does stirring do in terms of heat transfer?
help :(
Answers
As far as the conclusion goes, you can conclude that her hypothesis, date, research, and the scientific method was successful.
eating disorder Symptoms
Answers
Answer:
some symptoms can be lack of energy, and dizziness.
Explanation:
GIVING BRAINLIEST PLEASE HELP!!
-if you answer correctly ill give you brainliest which will give you 25pts-
Answers
What are tectonic plate boundaries?
A areas where Earth’s core experiences a high amount of stress
B areas where Earth’s core experiences a low amount of stress
C areas where Earth’s crust experiences a high amount of stress
D areas where Earth’s mantle experiences a high amount of stress
Answers
Answer:
c
Explanation:
Answer:
Areas where earth crust experiences a high amount of stress
Explanation:
FCAT review question
please, pretty please help me!
Answers
Answer:
umm
Explanation:
1223565 578633 =334675
A conductor is a material in which what can move through easily? Electrons Water Condensation Oil
Answers
Answer:
Electrons
Explanation:
:) hope this helps. Have a great day!
Una botella vacía tiene una masa de 24.25g y de 86.55g completamente llena de agua, se vacia el agua y se llena nuevamente con 123.95g de solvente tetracloruro de carbono, ¿cual es la densidad del solvente?
Answers
Answer:
La densidad del tetracloruro de carbono es 1.990 gramos por centímetro cúbico.
Explanation:
La masa de agua contenida dentro de la botella es igual a la diferencia entre la masa pesada totalmente llena y la masa pesada totalmente vacía, es decir:
[tex]m_{w} = 86.55\,g-24.25\,g[/tex]
[tex]m_{w} = 62.3\,g[/tex]
Ahora, de acuerdo con la definición de densidad, la masa es directamente proporcional a la densidad, entonces, podemos calcular la densidad del solvente mediante la siguiente relación:
[tex]\frac{m_{x}}{m_{w}} = \frac{\rho_{x}}{\rho_{w}}[/tex] (1)
Donde:
[tex]m_{x}[/tex] - Masa del tetracloruro de carbono, en gramos.
[tex]m_{w}[/tex] - Masa del agua, en gramos.
[tex]\rho_{x}[/tex] - Densidad del tetracloruro de carbono, en gramos por centímetro cúbico.
[tex]\rho_{w}[/tex] - Densidad del agua, en gramos por centímetro cúbico.
Si sabemos que [tex]m_{x} = 123.95\,g[/tex], [tex]m_{w} = 62.3\,g[/tex] y [tex]\rho_{w} = 1\,\frac{g}{cm^{3}}[/tex], entonces la densidad del tetracloruro de carbono es:
[tex]\rho_{x} = \left(\frac{m_{x}}{m_{w}} \right)\cdot \rho_{w}[/tex]
[tex]\rho_{x} = 1.990\,\frac{g}{cm^{3}}[/tex]
La densidad del tetracloruro de carbono es 1.990 gramos por centímetro cúbico.
Dawn is trying to find out how much weight she can push across the room. She is really trying to find her __________. A. flexibility B. muscular endurance C. cardiovascular fitness D. muscular strength Please select the best answer from the choices provided. A B C D
Answers
Answer:
D. muscular strength
Explanation:
Lifting any weight requires force to lift it. This force is the result of the muscular strength of the body. It is the muscular strength that determines the weight that a body can lift without any exhaustion. Muscular strength depends on the size of the muscular fibers and the nerves' ability. They help in activating the strength of the muscle. Lifting the objects and the ability to lift it are the outcome of the strength muscles have.
In the given situation, Dawn is trying to find her muscular strength.
Answer:
d
Explanation:
d
A piece of brass of mass 20.0g is hung on a sprong balance from a rigid support and completely immersed in kerosene of density 8.0 ×10 kgm-³. Determine the reading on the spring balance(g =10m/s², density of brass =8.0×10kgm-³)
Answers
The latent heat of fusion for Aluminium is 3.97 x 105. How much energy would be required to melt 0.75 kg of it?
Answers
Answer:
[tex]E = 2.9775\times10^5 J[/tex]
Explanation:
Given: The latent heat of fusion for Aluminum is [tex]L = 3.97\times10^5 J/Kg[/tex]
mass to be malted m = 0.75 Kg
Energy require to melt E = mL
[tex]E = 3.97\times10^5\times0.75 = 2.9775\times10^5 J[/tex]
Therefore, energy required to melt 0.75 Kg aluminum
[tex]E = 2.9775\times10^5 J[/tex]
A vertical piston-cylinder device initially contains 0.1 m^3 of air at 400 K and 100 kPa. At this initial condition, the piston is resting on a stop. The piston-cylinder device is connected to a supply line with air at 400 K and a pressure of 500 kPa. The valve between the supply line and the piston-cylinder device is opened and is left open until the pressure in the piston-cylinder device reaches 500 kPa. The piston is observed to start moving when the pressure in the cylinder is 200 kPa and the piston continues to rise until it reaches a second stop. At the second stop, the piston-cylinder volume is 0.2 m^3 . The final temperature and pressure in the piston-cylinder device are 440 K and 500 kPa, respectively. Determine the heat transfer to or from the piston-cylinder device for the filling process Determine heat transfer (kJ) during the entire process.
Answers
Answer:
[tex]Q=-38.15kJ[/tex]
Explanation:
From the question we are told that
Piston-cylinder initial Volume of air [tex]v_1=0.1 m^3[/tex]
Piston-cylinder initial temperature [tex]T_1=400k[/tex]
Piston-cylinder initial pressure [tex]P_1= 100kpa[/tex]
Supply line temperature[tex]T_s=400k[/tex]
Supply line pressure [tex]P_s= 500kpa[/tex]
Valve final pressure [tex]P_v=500kpa[/tex]
Piston movement pressure [tex]P_m=200kpa[/tex]
Piston-cylinder final Volume of air[tex]v_2=0.2 m^3[/tex]
Piston-cylinder final temperature [tex]T_2=440k[/tex]
Piston-cylinder final pressure [tex]P_2= 500kpa[/tex]
Generally the equation for conservation of mass is mathematically given by
[tex]Q=m_2 \mu_2-m_1 \mu_1 +W-(m_2-m_1)h[/tex]
where
Initial moment
[tex]m_1=\frac{p_1 V_1}{RT_1}[/tex]
[tex]m_1=\frac{100*0.1}{0.287*400}[/tex]
[tex]m_1=8.7*10^-^2kg[/tex]
Final moment
[tex]m_2=\frac{p_2 V_2}{RT_2}[/tex]
[tex]m_1=\frac{500*0.3}{0.287*440}[/tex]
[tex]m_1=79*10^{-2}kg[/tex]
Work done by Piston movement pressure
[tex]W=Pd[/tex]
[tex]W=P(v_2-v_1)[/tex]
[tex]W=200(0.2-0.1))[/tex]
[tex]W=20000J[/tex]
Heat function
[tex]h=cT_1[/tex]
[tex]h=1.005(400)[/tex]
[tex]h=402[/tex]
Therefore
[tex]Q=(0.792*0.718(440)-0.0871*0.718(400)+20-(0.792-0.087)*402))[/tex]
[tex]Q=-38.15kJ[/tex]
It is given mathematically that the system lost or dissipated Heat of
[tex]Q=-38.15kJ[/tex]
Which of these provides the best explanation for why the pencil appears broken?
A. The pencil absorbs all the light rays that hit it
B. Water reflects light rays away from the pencil
C. Light rays are bent by the water in the glass
D. The surface of the water reflects lights rays
Answers
C. Light rays are bent by the water in the glass.
Explanation:
The light defracts as is it leaves the medium of air and enters the medium of the water/glass.
The link below is to a short video that explains this concept very well.
https://youtu.be/Iq1a_KJTWJ8
What keeps planets in orbit? (i need help asap please T-T 10 points im low on points sorry)
A. Centrifugal force.
B. light energy
C. Gravity
D. All of the Above
Answers
Answer:
the answer is C gravity
Explanation:
30 kg sits on a table the acceleration due to gravity is 10 m/s^2 what force does the table exert on the television.
0.3N
3N
300N
600N
Answers
Answer:
300N
Explanation:
F=m×a
F=30kg×10m/s^2
F=300N
If 30 kilograms sit on a table the acceleration due to gravity is 10 meters/second², then the force exerted by the table on the television would be 300 Newtons,
Therefore the correct answer is option C.
What is acceleration?The rate of change of the velocity with respect to time is known as the acceleration of the object.
As given in the problem If 30 kilograms sit on a table the acceleration due to gravity is 10 meters/second²,
the force exerted = mass × acceleration due to gravity
= 30 kilograms × 10 meters/second²
= 300 Newtons
Thus, the force exerted by the table on the television would be 300 Newtons,
To learn more about acceleration from here, refer to the link;
brainly.com/question/2303856
#SPJ2
If the current in a wire which is placed perpendicular to a magnetic field increases the force on the wire
Answers
Answer:
The force on the wire increases
Explanation:
Since the force on the wire F = BILsinФ where B = magnetic field strength, I = current in wire, L= length of wire and Ф = angle between the magnetic field and the wire.
Given that the magnetic field and the wire are perpendicular, Ф = 90°
So, F = BILsin90° = BIL
Since B and L are constant, F ∝ I
So, if the current in the wire increases, the force on the wire also increases.
HELPPPP PLSSS I NEED HELP
Answers
Answer:
D. Pearl Harbor
Explanation: