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.

Answers

Answer 1

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]

 


Related Questions

help!


Jerome solves a problem using the law of conservation of momentum. What should

Jerome always keep constant for each object after the objects collide and bounce apart?


velocity

mass

momentum

direction

Answers

Answer:

What shouldJerome always keep constant for each object after the objects collide and bounce apart? That would be Mass.

Answer:

B: Mass

Explanation:

A merry go round at the park is spinning. You stand on the outer edge and are traveling at constant speed of 5 m/s. You walk halfway toward the center. What happened to your acceleration?

Answers

Answer:

a' = 2a

Explanation:

The acceleration during this circular motion is the centripetal acceleration. Initially, the acceleration will be given as:

a = v²/r   --------------------- equation (1)

Where,

a = centripetal acceleration at outer edge

v = speed of merry go round = 5 m/s

r = distance from center of round to person (outer edge)

Now, when the person moves half way towards center. Then, the acceleration becomes:

a' = v²/r'

where,

r' = r/2

Therefore,

a' = v²/(r/2)

a' = 2v²/r

using equation (1):

a' = 2a

Which of the following has the greatest mass?
A. star
B. moon
C. planet
D.galaxy

Answers

Answer: I think the answer is d

Explanation: sry if wrong

You fire a paintball from a paintball gun straight up into the air at 25.0 m/s. What is the ball velocity at the higher point that the ball reaches? Pleaseee helppp mee

Answers

Given :

You fire a paintball from a paintball gun straight up into the air at 25.0 m/s.

To Find :

What is the ball velocity at the higher point that the ball reaches.

Solution :

We know, when ball is moving upward acceleration due to gravity is applied downward.

So, the ball will decelerate and when ball reaches maximum height its velocity will become zero.

Therefore, ball velocity is 0 m/s at maximum height.

Hence, this is the required solution.

Question 4 (point)
What is the charge of the nucleus for the atom below?
O a
varies
Positive
Oc
Od
Neutral
Negative

Answers

Answer:

Positive

Explanation:

Tbh I dont have an explanation I just wanted to give the answer but its for sure correct!

PLEASE HELP ASAP I WILL GIVE BRAINLIEST!!

Answers

Answer:

Q1: I'm going to say the fence is a polarizing filter.

Q2: On the second question: (b). BTW, It's not a very well-phrased question (and I'm a particle physicist, so...)

Explanation:

Q1:

So... hard to say for sure the intent here without knowing what you've been learning in class, but a frisbee - being a flat disk - will only go through the fence if it is oriented as shown, much like polarized light will only go through a polarizing filter if the EM waves are polarized in the direction that they will pass through a polarizing filter.

Q2:

It's not a) because ALL waves require a source of energy.  

b) is for sure true and is about energy transfer - mechanical waves need a medium (like water) but EM waves do not. (Early on they thought maybe there was a medium for EM waves... they called it "aether" ... but it was proven via the Michealson-Morley experiment that no the speed of light was an absolute constant - fundamental to special relatively - which meant that light did not travel in any medium!)

(c) - depends on what you mean by "vibration", but yeah... EM waves result in varying electric fields for an observer. However, nothing to do with energy transfer per se (except that those varying fields are what transfer energy to objects that experience them...)

(d) - As above, the speed of light is a constant - cannot change speed ever *in a vacuum*.  However, the speed of light is different in various materials, and can be bent (refracted) or reflected, which means the fields change direction in interacting with matter, although they do not change speed or direction "on their own" (in a vacuum).  Similarly, mechanical waves can change speed or direction when there are changes or discontinuities in the media they travel in.  So, arguably about energy transfer (the direction and speed related to the direction and rate of energy transfer) but not really different between EM and mechanical waves.

Anyway, like I said, it's not a very clear question, so YMMV with my advice here, but (b) is for sure the best single choice.


What important example, shown in the picture, is given regarding a real-life
connection to these elements?

Answers

Answer:

Explanation:

There is no picture!

a race car is travelling at +76m/s when it slows down at -9m/s2 for 4 seconds. whats his new velocity?

Answers

Answer:

40 m/s. 1) Bumble bee jumps straight upwards with a velocity of 14.0 m/s. What is his displacement of after 1.80 s

A :-) for this question we should apply
v = u + at
Given - u = 76 m/s
v = ?
a = - 9 m/s^2
t = 4 sec
Solution -
v = u + at
v = 76 + ( -9 ) x 4
v = 76 - 9 x 4
v = 76 - 36
v = 40 m/s

.:. The new velocity is 40 m/s


can somone pls help me??!! i’m very stuck

Answers

Answer:

R

Explanation:

Her distance from home and Time increase

the stops when she gets to the library

then her distance from home decreases while her time increases

at what angle work done is equal to zero​

Answers

Answer:

work done=0 when angel between 2 objects is 90 degree

1. Which of the following is a unique feature of light waves?

Answers

Answer: they are compression waves

Explanation:

The unique property of light waves is that they do not require a medium for propagation.

Generally; waves are classified into electromagnetic waves and mechanical waves. Mechanical waves require a medium of propagation while electromagnetic waves do not require a medium for propagation.

Also, waves are classified into transverse waves and longitudinal waves. In transverse waves, the disturbance is perpendicular to the wave front while in longitudinal or compressional waves, the disturbance is parallel to the wave front.

Light is both an electromagnetic wave and a transverse wave. This means that it requires no material medium for propagation. This is the unique property of light waves.

Learn more: https://brainly.com/question/2673886

Which of the examples below is an example of convection?
A)
rubbing your hands together.
B)
heating a fish tank.
basking in the sun.
D)
striking a match.

Answers

basking in the sun :)

Un prisma rectangular de cobre, de base igual a 36 centímetros cuadrados y una altura de 10 cm se sumerge hasta la mitad por medio de un alambre en un recipiente que contiene alcohol ¿que volumen de alcohol desaloja?

Answers

La respuesta correcta es 180 centímetros cúbicos o 180 [tex]cm^{3}[/tex]

Explicación:

El primer paso para saber cuanto alcohol desaloja el prisma es calcular el volumen total del prisma. El volumen se puede encontrar usando la formula V (Volumen) = B (base) x h (altura). El proceso se muestra a continuación:

V  = B x h

V = 36 [tex]cm^{2}[/tex] x 10 cm

V= 360 [tex]cm^{3}[/tex]

Finalmente, el volumen total del prisma debe dividirse en 2 considerando que solo la mitad del prisma fue sumergida y esta mitad equivale al volumen del alcohol desplazado.

360 [tex]cm^{3}[/tex] ÷ 2 = 180 [tex]cm^{3}[/tex]  

El volumen de fluido desplazado es de 180 cm^3.

Sabemos que el objeto va a desplazar su propio volumen de fluido. Por lo tanto, necesitamos obtener el volumen del objeto a, este es el volumen del fluido que eventualmente será desplazado por el sólido.

El volumen del sólido es;

V = 36 cm^2 * 10 cm^2 = 360 cm^3

desde que se sumergió a la mitad, volumen de alcohol desplazado = 360 cm^3/2 = 180cm^3

Obtenga más información sobre el volumen: https://brainly.com/question/7932885

An apple and a stone dropped from certain height accelerates:Required to answer. Single choice.Immersive Reader
(1 Point)
equally.
differently.
depending on density.
depending on the position of the sun.

Answers

An apple and a stone dropped together from any height accelerate equally.

If the x and y vector components of Vector A are 11 and 7,
what is the magnitude of Vector A? Round your answer to the
nearest hundredth.

Answers

Answer:

R=13.04

Explanation:

Using pythagoras theorem

Assuming the vector A is the resultant force R

R^2=11^2+7^2

R^2=121+49

R^2=170

R=13.038

R=13.04

Dorji weight 1500n.if the total surface area of soles of his feet is 0.5 m2 what is the pressure exerted by his body on the ground​

Answers

Answer:

P = 3000 Pa

Explanation:

Weight of Dorji, W = F = mg = 1500 N

The total surface area of soles of his feet is 0.5 m²

We need to find the pressure exerted by his body on the ground​. The pressure is equal to the force acting per unit area. So,

[tex]P=\dfrac{1500\ N}{0.5\ m^2}\\\\=3000\ Pa[/tex]

So, the pressure exerted by his body on the ground​ is 3000 Pa.

A hot air balloon is acted on by two forces. One force is its weight, equal to

2448 newtons. The second force is a buoyant force acting straight up,

equal to 2448 newtons. What change in the motion of the balloon will

result from the action of these two forces?

no change

rising

falling

Answers

Answer:

no change

Explanation:

The Newton's Second Law of motion states that when an unbalanced force is applied to an object, it causes an accelerated motion in the object, in the direction of the unbalanced force. So, if there is no unbalanced force, then there is no motion. In this case both the forces have same magnitude and opposite direction. Therefore, the unbalanced force will be zero:

Unbalanced Force = Upthrust - Weight

Unbalanced Force = 2448 N - 2448 N

Unbalanced Force = 0 N

hence, there will be no motion in the vertical direction. Therefore, the correct option is:

no change

high heels shoes are more likely to damage floor than flat shoes . do you agree? explain.​

Answers

yesssss I am agree ......

Answer:

Yes, I agree. The pressure exerted upon the floor is larger for high heel shoes than flat shoes, hence causing more damage to the floor.

Explanation:

Pressure is force/area. High heel shoes have a sharp point at which they touch the floor, while flat shoes have a flatter surface at which they touch the floor. Due to you exerting the same force anyway, the area is smaller for high heel shoes.

As you might know, the smaller a denominator is, the larger the number is. As an example, 3/1 is larger than 3/2. 3/1 is 3, and 3/2 is 1.5. Hence, the force is larger for high heel shoes, and it will cause more damage.

Hope this helped!

Why is the astronomical unit used to measure distances in the solar system?

Answers

Answer:Astronomers often use the astronomical unit to describe distances within solar systems because it is convenient and easier to understand. The astronomical unit (au or AU) is defined as exactly 149,597,870,700 meters (about 93 million mi), which is roughly equal to the average distance between the Sun and Earth.

Explanation: google

A balloon is launched at 2.5 m every second, how far did it travel in 10 seconds?

Answers

Answer:

25 meters

Explanation:

1 sec is 2.5, 1x10 so 2.5x10=25

the weight of a body floating in a liquid is​

Answers

Answer:

The apparent weight is the weight of the body minus the weight of the liquid displaced. The body will float only when both the weights are same. In this case, the given body of weight W is floating and hence the apparent weight is zero.

Answer:

Zero

Explanation:

The apparent weight is the weight of the body minus the weight of the liquid displaced. The body will float only when both the weights are same. In this case, the given body of weight W is floating and hence the apparent weight is zero.

PLEASE HELP ASAP
describe how the equations for gravitational force and electrostatic force are similar

Answers

they are both forces ?

How much net force is needed to accelerate a 200 kg satellite 9.8 m/s2 ?

Answers

Answer:

1960 N

Explanation:

The force acting on an object given it's mass and acceleration can be found by using the formula

force = mass × acceleration

From the question we have

force = 200 × 9.8

We have the final answer as

1960 N

Hope this helps you

A bike is traveling to the left with a speed of 27\,\dfrac{\text m}{\text s}27 s m ​ 27, 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 for 41.5\,\text m41.5m41, point, 5, start text, m, end text with constant acceleration before it comes to a stop.

Answers

Answer:

Explanation:

Given

Speed v =27m/s

Distance covered after skidding = 41.5m

Acceleration a = ?

Using the equation of motion

v² =u²+2aS

27² = 0²+2a(41.5)

729 = 0+83a

a = 729/83

a = 8.78m/s²

Hence it's acceleration is 8.78m/s²

find the distance traveled in km when the average speed is 60 km per hour and the time taken is 3 and 1/2 hours​

Answers

Answer:

210 km

Explanation:

60 x 3  1/2 = 210

An object moves along the grid through the points A, B, C, D, E, and Fas shown below.

Find the distance covered by the moving object.

The object moves 3 km to the East, turns North for 1 km, turns west for 1.5 km, moves

north 0.5 km, and finally turns east for 0.5 km.

Answers

Answer:

Total distance = 6.5 km

Explanation:

Let the distance be denoted by the vectors drawn from A, B, C, D, E, and F.

Then the distance covered can be calculated by adding the vectors in the direction given.

Total distance = 3km + 1km+ 1.5km+ 0.5km+ 0.5km

Total distance = 6.5 km

If we were to find the displacement ( shortest distance) then the head to tail rule would be applied using the vectors.

state three ways of conserving energy​

Answers

energy drinks

sitting

watching TV

Answer:

use natural lights

turn off electrical appliances..if not in use

check your wires every next Month

brainliest please help opposite 8n is 5n it could not come full picture

find the resultant force ​

Answers

Answer:

resultant force=16N→(TOWARDS THE DIRECTION OF 8N)

Explanation:

resultant force=8N+13N-5N

                        =16N→(TOWARDS THE DIRECTION OF 8N)

what was the temperature changes in Celsius degrees if it is
changed from 44°F to -56°F?

Answers

Answer:

so, the answer is 56 whole number if round it, or 55.6(round it to 10th decimal)

Explanation:

(formula, idk it is wrong or right)   °C =°F - 32 then / 1.8000

44°F =  6.6666666667°C

-56°F = -48.888888889°C

So, if u want whole number as the answer

it is something like 6.6666666667°C +  48.888888889°C = 55.5555555557 °C

so, so, the answer is 56 whole number if round it, or 55.6(round it to 10th decimal)

Which situation provides the best evidence that a chemical reaction is taking place?


Help please !!!!

Answers

Answer:

A new product is formed

Explanation:

Physical reactions generally result in a change of state (solid, liquid, gas). Chemical reactions generally result in the production of a new product/ substance (structure/ properties are different than the intial reactants'... example= burning wood)

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