To illustrate the use of a multistage rocket consider the following:
(a) A certain rocket carries 60% of its initial mass as fuel. (That is, the mass of fuel is 0.6mo) What is the rocket's final speed, accelerating from rest in free space, if it burns all its fuel in a single stage? Express your answer as a multiple of v ex .
(b) Suppose instead it burns the fuel in two stages as follows: In the first stage it burns a mass 0.3m o of fuel. It then jettisons the first-stage fuel tank, which has a mass of 0.1m o , and thenburns the remaining 0.3m 0 of fuel. Find the final speed in this case, assuming the same value of vex throughout and compare.
Answer:
a
[tex]v_f = 0.916 v_{ex}[/tex]
b
[tex]v_f = 1.05 v_{ex}[/tex]
Explanation:
Considering question a
From the question we are told that
The mass of the rocket is [tex]m_o[/tex]
The mass of the fuel which is in the rocket is m = 0.6 M
Generally given that the rocket burns all it fuel in a single stage , the final velocity of the rocket is mathematically represented as
[tex]v_f = v_{ex} ln [\frac{m_o}{m_k} ][/tex]
Here [tex]m_k[/tex] is the mass of the rocket without fuel which is mathematically evaluated as
[tex]m_k = m_o- m[/tex]
=> [tex]m_k = m_o -0.6m_o[/tex]
=> [tex]m_k = [1- 0.6] m_o[/tex]
=> [tex]v_f = v_{ex} ln [\frac{m_o}{[1 - 0.6]m_o} ][/tex]
=> [tex]v_f = 0.916 v_{ex}[/tex]
Considering question b
From the question we are told that
The mass of the fuel it burn at the first stage is [tex]m = 0.3 m_o[/tex]
The mass of the first stage fuel tank [tex]m_1 = 0.1 m_o[/tex]
The mass of the fuel at the second stage is [tex]m_f = 0.3m_o[/tex]
Generally the velocity of the rocket at the first stage is mathematically represented as
[tex]v_i = v_{ex} * ln [ \frac{m_o }{[1- m]m_o } ][/tex]
=> [tex]v_i = v_{ex} * ln [ \frac{m_o }{[1- 0.3]m_o } ][/tex]
=> [tex]v_i = v_{ex} * ln [ \frac{1 }{0.7 } ][/tex]
=> [tex]v_i =0.357 v_{ex}[/tex]
Generally the mass of the rocket after first stage is
[tex]m_r = m_o - 0.3m_o -0.1m_o[/tex]
=> [tex]m_r = 0.6m_o[/tex]
Generally the final velocity of the rocket at the second stage is
[tex]v_f = v_i + v_{ex} * ln [\frac{m_r}{ m_f } ][/tex]
=> [tex]v_f = v_i + v_{ex} * ln [\frac{0.6 m_o }{0.3mo } ][/tex]
=> [tex]v_f = 0.357 v_{ex} + 0.693 v_{ex}[/tex]
=> [tex]v_f = 1.05 v_{ex}[/tex]
observe the figure given carefully volume of water in each vessel is shown arrange them in order of decreasing pressure at the base of each vessel explain the reason
Answer:
See the explanation below
Explanation:
The pressure is defined as the product of the density of the liquid by the gravitational acceleration by the height, and can be easily calculated by means of the following equation.
[tex]P=Ro*g*h[/tex]
where:
Ro = density of the fluid [kg/m³]
g = gravity acceleration = 9.81 [m/s²]
h = elevation [m]
In this way we can understand that the greater pressure is achieved by means of the height of the liquid, that is, as long as the fluid has more height, greater pressure will be achieved at the bottom.
Therefore in order of decreasing will be
The largest pressure with the largest height of the liquid, container B. The next is obtained with container D, the next with container A and the lowest pressure with container C.
The pressure decreases as we go from the container B - D - A - C
In a perfectly insulated container of negligible mass, 4.00 × 10−2 kg of steam at 100◦C and atmospheric pressure is added to 0.200 kg of water at 50.0◦C.
A) If no heat is lost to the surroundings, what is the final temperature of the system? B) At the final temperature, how many kilograms are there of steam and how many of liquid water?
Answer:
Following are the solution to this question:
Explanation:
Given value:
[tex]m_s= 4.00 \times 10^{-2} \ kg \\\\L_v=2256 \times 10^{3} \ \frac{J}{kg}\\\\m_w= 0.2 \ kg\\\\\Delta T= 50^{\circ}[/tex]
In point A:
[tex]Q_{Steam}=m_s \ L_v[/tex]
[tex]=0.04 \times 2256 \times 10^{3}\\\\=9.02 \times 10^4 \ J[/tex]
[tex]Q_{water}= m_w \ c_w \ \Delta T\\\\[/tex]
[tex]=0.2 \times 4190 \times 50\\\\=4.19 \times 10^4 \ J[/tex]
[tex]Q_{steam}> Q_{water}[/tex], that's why the final temperature is [tex]= 100^{\circ}[/tex]
In point B:
[tex]\to \Delta m_s L_v=m_w\ c_w \Delta T\\\\\to \Delta m_s \times 2256\times 10^3= 0.2 \times 4190 \times 50\\\\\to \Delta m_s= 1.86 \times 10^{-2} \ kg\\\\\to m_s = 2.14 \times 10^{-2} \ kg\\\\\to liquid \ left = 0.2+ 2.14 \times 10^{-2} = 2.34 \times 10^{-2} \\[/tex]
The lift goes up 14m the total mass of the people is 280kg
Answer:
What is your Question.
Explanation:
Ask it Clearly.
The speed of sound through air is approximately 340 m/sec. What is the wavelength of a sound wave with a frequency of 706 Hz? Round to the nearest hundredth
Answer:
Wavelength = 0.48 m (Approx)
Explanation:
Given:
Speed of sound = 340 m/s
Frequency = 706 hz
Find:
Wavelength
Computation:
Wavelength = Speed of sound / Frequency
Wavelength = 340 / 706
Wavelength = 0.48 m (Approx)
Which of the following statement(s) about electrical charges are correct?
A. Point charges of the same charge only attract.
B. Charged and neutral extended objects can attract.
C. Charged and neutral extended objects do not interact.
D. Point charges of the same charge only repel.
E. Extended objects of opposite charge can only attract.
F. Point charges of opposite charge only attract.
G. Point charges of opposite charge only repel.
H. Extended objects of the same charge can both repel and attract.
I. Extended objects of the same charge can only attract.
J. Extended objects of the same charge can only repel.
K. Extended objects of opposite charge can both repel and attract.
Answer:
The true statements are;
F, D, E, J
Explanation:
F and D are true because they agree with our knowledge of electrostatic interaction. Like charges repel while unlike charges attract. Statements B and C are not in line with the principles of electrostatics because neutral objects do not interact with charged bodies in an electric field.
E and J are true for the same reasons outlined above. Remember that like charges always repel each other and unlike charges always attract each other.
help me pleaseeeee
Answer:
Explanation:
Frequency, in physics, the number of waves that pass a fixed point in unit time; also, the number of cycles or vibrations undergone during one unit of time by a body in periodic motion...............
How do the prefixes micro,
nano and pico relate to each
other?
Answer:
because they are same and their properties
which term describes the image of an object that is placed in front o a convex mirror?
Answer:
The answer of this question is :- Virtual image
Explanation:
Virtual image is the correct answer
A stone is thrown straight up. While the stone is rising:
A. its acceleration is upward and decreasing
B. its acceleration is upward and constant
C. its acceleration is upward and increasing
D. its acceleration is zero
E. None of the above.
Answer:
D. its acceleration is zero
Explanation:
Acceleration can be defined as the rate of change of the velocity of an object with respect to time.
This simply means that, acceleration is given by the subtraction of initial velocity from the final velocity all over time.
Hence, if we subtract the initial velocity from the final velocity and divide that by the time, we can calculate an object’s acceleration.
Mathematically, acceleration is given by the equation;
[tex]Acceleration (a) = \frac{final \; velocity - initial \; velocity}{time}[/tex]
In this scenario, a stone is thrown straight up. While the stone is rising its acceleration is zero because it's initial velocity is zero and it's until the stone reaches its highest point before the acceleration becomes constant and acting downward.
Which quantity is a vector quantity?
А.
acceleration
B.
mass
C.speed
D.
volume
Answer:
acceleration .......
How are speed and velocity alike?
A.) They both require a reference point
B.) They both include total distance traveled
C.) They both describe a rate of motion
D.) They both include the direction of motion
Answer:
im pretty sure B
Explanation:
Answer:
B
Explanation:
They both describe a rate of motion
What is the density of a piece of quartz with a mass of 30g and a volume of 6cm^3
Answer:
[tex]\boxed {\boxed {\sf d= 5 \ g/cm^3}}[/tex]
Explanation:
Density can be found by dividing the mass by the volume.
[tex]d=\frac{m}{v}[/tex]
The mass of the quartz is 30 grams and the volume is 6 cubic centimeters.
[tex]m=30 \ g \\v= 6 \ cm^3[/tex]
Substitute the values into the formula.
[tex]d=\frac{30 \ g}{6 \ cm^3}[/tex]
Divide.
[tex]d= 5 \ g/cm^3[/tex]
The density of this piece of quartz is 5 grams per cubic centimeter.
4. What is the speed of a walking person in m/s if the person travels 1000m in 20 minutes?
Answer:
0.80 m/s
Explanation:
What is the speed of a walking person in m/s if the person travels 1000 m in 20 minutes?
A motorcyclist drives around a bend with a 20 m radius, with a constant velocity of 3 m/s. The motorcyclist and the motorcycle have a combined mass of 50 kg. What is the motorcyclist’s centripetal acceleration?
Answer:
[tex]a=0.45\ m/s^2[/tex]
Explanation:
Given that,
The radius of a bend, r = 20 m
Velocity of motorcyclist, v = 3 m/s
The combined mass of motorcyclist and the motorcycle is 50 kg
We need to find the motorcyclist’s centripetal acceleration. The formula used to find the centripetal acceleration is given by :
[tex]a=\dfrac{v^2}{r}\\\\a=\dfrac{(3)^2}{20}\\\\a=0.45\ m/s^2[/tex]
So, the acceleration of the motorcyclist is [tex]0.45\ m/s^2[/tex].
What is called gravitational potential energy?
Answer:
Potential gravitational energy is the energy that the body has due to the Earth's gravitational attraction. In this way, the potential gravitational energy depends on the position of the body in relation to a reference level.
Explanation:
A machine that operates a ride at the fair requires 2500 J to lift a 294 N child 5.0 m. What is the efficiency of this machine?
Answer:
η = 58.8%
Explanation:
Work is defined as the force applied by the distance traveled by the body.
[tex]W =F*d[/tex]
where:
W = work [J] (units of joules)
F = force = 294 [N]
d = distance = 5 [m]
[tex]W = 294*5\\W = 1470 [J]\\[/tex]
Efficiency is defined as the energy required to perform an activity in relation to the energy actually added to perform some activity. This can be better understood by means of the following equation.
[tex]efficiency = W_{done}/W_{required}\\efficiency = 1470/2500\\efficiency = 0.588 = 58.8%[/tex]
Explain why when a firefighter rescues a dog that has fallen through ice on a
lake, they put their ladder on the ice first and then crawl out to the dog on the
ladder.
Answer:
This can spread their weight.
Explanation:
The ladder has a much larger surface area than the firefighter. Hence, his weight is spread out much more than usual, decreasing the pressure on the ice, preventing the ice from breaking/cracking.
Hope this helped!
10. Scientists created models that show a rocky asteroid crashing into a moon (less mass) a
planet (more mass). In both crashes, the asteroid was the same mass. Scientists want to kno
happened to the asteroid. Use the information in the diagram to answer.
In which crash did the asteroid experience a stronger force? How do you know?
a
Crash 2; the force on the planet was stronger in this crash, so the force on the astero
also stronger.
There was no force on the asteroid. Only the moon and planet experienced a force in
Answer:
The diagram doesn’t tell you anything about the force on the asteroid. It only gives information about the force on the planet and the moon.
Explanation:
We do not use water instead of mercury in a barometer.. why.
Answer:
Required Answer:-We don't use water as Water don't expand when it came in connection of temperature.angela runs and slides across an icy path in her driveway. she comes to a stop because of friction. which free-body diagram shows her while she is sliding?
Answer: C
Explanation: You always have weight pushing down and natural force pushing up to neutralize those forces. The you add in friction and that’s how you find the answer. Plus I got it right in my quiz
The photo shows two yeast cells. Each cell is an individual organism. Which sentence best describes what happened to each cell during cell growth?
A. It will become many different cells.
B. It will produce offspring with a mate.
C. It will divide in half to form two new cells.
D. It will become larger by taking in nutrients.
The answer is option c - It will divide in half to form two new cells..
Explanation:
The sentence that best describes what happened during cell growth is ;
( D ) It will become larger by taking in nutrients
As the yeast cells begin to grow ( i.e. cell growth ), they will require more nutrients and as they take in the necessary nutrients they will gradually increase in size ( becoming larger ) which is a vital sign of cell growth and development, which will be seen in the yeast cells as they undergo cell growth.
The production of offsprings with a mate does not describe an activity that occurs in cell growth.
Hence we can conclude that The sentence that best describes what happened during cell growth is, It will become larger by taking in nutrients.
Learn more : https://brainly.com/question/24893507
Your car is initially at rest when you hit that gas and the car begins to accelerate. The forward force of the car is 5630 N while the resisting force total 330 N. The car has a mass of 1313 kg and the acceleration lasts for 2.6s. What is the final speed of the car and how much ground does it cover during this acceleration?
Please simplify and write the below paragraph.
The field lines due to a current in a
circular coil become straight and
perpendicular to the plane of the coil
at the centre. This is because at every
point of circular loop the concentric
circles representing the magnetic field
become larger and larger as we move
away from the wire.
Field lines become straight and perpendicular because every point of circular loop the concentric circles become larger and larger as we move away from the wire.
A motorbike is traveling to the left with a speed of 27.0 m s 27.0 s m 27, point, 0, start fraction, start text, m, end text, divided by, start text, s, end text, end fraction when the rider slams on the brakes. The bike skids 41.5 m 41.5m41, point, 5, start text, m, end text with constant acceleration before it comes to a stop. What was the acceleration of the motorbike as it came to a stop?
Answer:
Explanation:
Initial velocity , u = 27 m/s
displacement before stop, s = 41.5 m .
final velocity, v = 0
acceleration a = ?
v² = u² + 2 a s
0 = 27² + 2 x a x 41.5
a = - 27² / 2 x 41.5
= - 8.78 m /s
How fast can Usain Bolt run if it takes him 9.9 s to run 100m?
Answer:
27.8 mph
Explanation:
May I have brainliest please? :)
HELP ME! PLEASE! SOMEONE! THIS QUESTION IS VERY HARD! THERE ARE 3 ANSWERS! HELP ME PLEASE! MAKE SURE TO EXPALIN
Question:
The teacher told Fatima that all types of energy are kinetic energy, potential energy, or both. Fatima drew this diagram to help her organize this information. She then sorted each type of energy into its correct category: chemical, electrical, electromagnetic, mechanical, nuclear, and thermal.
Three of the types of energy can be either kinetic or potential energy. Identify these three types. For each type, explain why it can be either kinetic or potential.
Answer:
search up the kinetic energy and potential energy etc. then take them and look at the characteristica are they the same? What makes them similar? Why are they different ? How? Then add the chemical nuclear and electrical changes it creates. Now the rest! There you’ve got this! If you need support I’m here! Hope this helped!
Explanation:
In a lacrosse game a ball is thrown with a force of 2000 N. The throwing force acted for 0.8
seconds. If the ball had a change in velocity, Av, of 50 m/s, what is the mass of the ball?
Answer:
Mass, m = 32 kg
Explanation:
Given that,
Force, F = 2000 N
The change in velocity, (v-u) = 50 m/s
Time, t = 0.8 s
We need to find the mass of the ball. The net force acting on an object is given by :
F = ma
Where a is acceleration
[tex]F=\dfrac{m(v-u)}{t}\\\\m=\dfrac{Ft}{(v-u)}\\\\m=\dfrac{2000\times 0.8}{50}\\\\m=32\ kg[/tex]
So, the mass of the ball is 32 kg.
An automobile travels a displacement of 75 km at 45 degrees north of East. How many kilometers north does it travel?
Answer:
the number of kilometers north it traveled is 53.03 km
Explanation:
The computation of the number of kilometers north it traveled is shown below:
Given that
The Displacement of 75 km
At east north of 45 degrees
Based on the above information, the number of kilometers is
= 75 × cos 45
= 53.03 km
Hence, the number of kilometers north it traveled is 53.03 km
We simply applied the above formula so that the correct value could come
And, the same is to be considered
Snails crawl very slowly. If a garden snail crawls at 0.013 m/s north, how far will it travel in 60 seconds?
Answer:
.78 m/s north
Explanation:
Pls give brainliest if I correct