A rocket accelerates by burning its onboard fuel, so its mass decreases with time. Suppose the initial mass of the rocket at liftoff (including its fuel) is m, the fuel is consumed at rate r, and the exhaust gases are ejected with constant velocity ve (relative to the rocket). A model for the velocity of the rocket at time t is given by the equation

v(t)=−gt−velnm−rt/m

where g is the acceleration due to gravity and t is not too large. If g=9.8 m/s^2, m = 30000 kg, r = 160 kg/s, and ve = 3000 m/s, find the height of the rocket one minute after liftoff.

Answers

Answer 1

This question is incomplete, the complete question is;

A rocket accelerates by burning its onboard fuel, so its mass decreases with time. Suppose the initial mass of the rocket at liftoff (including its fuel) is m, the fuel consumed at rate r, and the exhaust gases are ejected with constant velocity v(sub e) [relative to the rocket]. A model for the velocity of the rocket at time t is given by the equation:

v(t) = -gt - v(sub e) ln [(m-rt)/m]

where g is the acceleration due to gravity, and t is not too large. If g = 9.8 m/s^2, m = 30,000 kg, r = 160 kg/s, and v(sub e)= 3000 m/s, find the height of the rocket one minute after liftoff.

Answer:

the height of the rocket one minute after liftoff is 14.8441 km

Step-by-step explanation:

Given the data in the question;

Velocity of the rocket at time t is;

v(t) = -gt - [tex]V_{e\\}[/tex] ln( [tex]\frac{m-rt}{m}[/tex])

[tex]\int\limits^t_0 {v(t)} \, dt[/tex] = ₀∫⁶⁰(  -gt - [tex]V_{e\\}[/tex] ln( [tex]\frac{m-rt}{m}[/tex]) )dt

= -g([tex][\frac{t^{2} }{2}]^{60}_0[/tex]  - [tex]V_{e\\}[/tex] ₀∫⁶⁰In( [tex]\frac{m-rt}{m}[/tex]) dt

= -g([tex][\frac{t^{2} }{2}]^{60}_0[/tex]  - [tex]V_{e\\}[/tex] [ t In( [tex]\frac{m-rt}{m}[/tex]) + [tex]\frac{m}{r}[/tex] - t - mr[tex]\frac{1}{r^{2} }[/tex] In |m-rt| [tex]]^{60}_0[/tex]

= -g([tex][\frac{60^{2} }{2}][/tex]  - [tex]V_{e\\}[/tex] [ 60 (In(1 -  [tex]\frac{60r}{m}[/tex])-1) + [tex]\frac{m(In(m^{2})-In((m-60r)^2))) }{2r}[/tex] ]

we input our given values; g=9.8 m/s², m=30000 kg, Ve = 3000 m/s, r = 160 kg)

= -9.8([tex][\frac{60^{2} }{2}][/tex]  - 3000 [ 60 (In(1 - [tex]\frac{60(160)}{m}[/tex])-1) + [tex]\frac{30,000(In(30,000^{2})-In((30,000-60(160))^2))) }{2(160)}[/tex] ]

[tex]\int\limits^t_0 {v(t)} \, dt[/tex] =  14844.10 m

we convert to kilometer

[tex]\int\limits^t_0 {v(t)} \, dt[/tex] =  14844.10 ÷ 1000

[tex]\int\limits^t_0 {v(t)} \, dt[/tex] =  14.8441 km

Therefore, the height of the rocket one minute after liftoff is 14.8441 km

   


Related Questions

In a group of 38 pupils, 13 play the flute only.
7 play the piano only.
5 play neither instrument.
How many pupils play both instruments?

Answers

13 pupils play both instruments I believe is the correct answer

lol please help me !

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Answer:  (a + 2)(a - 2)  which is the first answer choice

=========================================================

Explanation:

Use the difference of squares factoring rule which is x^2 - y^2 = (x+y)(x-y)

In this case, x = a and y = 2

x^2 - y^2 = (x+y)(x-y)

a^2 - 2^2 = (a+2)(a-2)

a^2 - 4 = (a+2)(a-2)

Aiden is eating from the box of cereal

shown. Find the total surface area of the box.

cereal

13.5 in.

2.5 in.

8 in.

Total surface area?

Answers

Answer:

323.5 square inches

Step-by-step explanation:

The cereal box is not shown. However, the given details are enough to arrive at a solution

[tex]Length = 13.5in[/tex]

[tex]Width = 2.5in[/tex]

[tex]Height = 8in[/tex]

Required

The total surface area (TSA)

This is calculated as:

[tex]TSA = 2 * (Length * Width + Length * Height + Width * Height)[/tex]

[tex]TSA = 2 * (13.5 * 2.5 + 13.5 * 8 + 2.5 * 8)[/tex]

[tex]TSA = 2 * (161.75)[/tex]

[tex]TSA = 323.5[/tex]

Hence, the total surface area is 323.5 square inches

- Functions F and A are defined by these equations below. Which function has a greater value when x is 2.5?

A. F(x) = 80-15x
B. A(x) = 25 + 10x

Answers

Answer:

The answer is D- A(x)=25+10x

Step-by-step explanation:

I cant really explain how i got the answer but i got it right

The function A(x) has greater value then F(x) for x = 2.5.

What is a function?

A function is a relation between a independent variable and a dependent variable such that the value of dependent variable depends upon the independent one.

Given are two functions of [x] as follows -

F(x) = 80 - 15x

A(x) = 25 + 10x

We have the following functions -

F(x) = 80 - 15x

A(x) = 25 + 10x

Now, we will evaluate each function at x = 2.5.

F(2.5) = 80 - 15 x 2.5 = 42.5

and

A(2.5) = 25 + 10 x 2.5 = 50

It can be seen that A(2.5) > F(2.5)

So, the function A(x) has greater value then F(x) at x = 2.5

Therefore, the function A(x) has greater value then F(x) for x = 2.5.

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It takes 2 workers 6 days to paint a mansion. How many days would it take 4
workers to do the same job?

Answers

Answer:

2 workers = 6 days

4 workers = 3 days

Step-by-step explanation:

If it takes 2 workers 6 days, if you seep up the process with 4 workers, you would divide the days by 2 because you multilpied the workers by 2. So, it would take 3 days with 4 workers. I hope that makes sence.

solve the system of equations 5x+3y=5 5x+7y=25

Answers

Answer:

(-2,5)

Step-by-step explanation:

-3x =21
1/3x =6
-1/2x =-7

Answers

-3x = 21
Divide -3 from both sides and you get x = -7

1/3x = 6
Divide 1/3 from both sides and you get x = 18

-1/2x = -7
Divide -1/2 from both sides and you get x = 14 (you get a positive answer from 2 negatives)

Dividing 1/3 is just multiplying by 3, and dividing -1/2 is just multiplying by -2

5 km
5 km
7 km
Find the surface area

Answers

Answer:

190km

Step-by-step explanation:

2(wl + hl + hw)

2 · (5 · 7 + 5 · 7 + 5 · 5) = 190

good luck, i hope this helps :)

Complete the table to show an equivalent ratio where the total amount is 100 grams.

Answers

Answer:32

Step-by-step explanation:

i did it, just multiply by 4

The percent of 32% of her daily amount of fiber, she has at breakfast.

What is ratio?

The numerical relationship between two values that demonstrates how frequently one value contains or is contained within another.

Given:

Keesha keeps track of the fiber she eats to make sure she gets enough each day.

Her breakfast contains 8 grams of fiber, and her recommended daily amount is 25 grams per day.

Keesha wants to know what percent of her daily amount of fiber she has at breakfast.

The table to show an equivalent ratio where the total amount is 100 grams.

Let n be the required value.

That means,

8/25 = n/100

n = 800/25

n = 32

Therefore, her daily amount of fiber is 32%.

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What is the relationship between CE and AD?
I’ll give brainly

Answers

It’s the second one because it can’t be half but it can be 1/4 and if you do the measurements you can tell it is the second one

The diameter of a round rug is 42 inches. What is the approximate area of the rug?
A. 5,539 square inches
B. 10 square inches
C. 38 square inches
D. 1,385 square inches

Answers

Answer:

D, It would be 1,385 Square Inches

Step-by-step explanation:

If the Pixie Sticks cost 4.50 per pound and Nicholas spends 8.10, How many pounds did he purchase?

Answers

Answer:

Step-by-step explanation:

Nicholas has purchased 1.8 pounds of pixie sticks.

Jane has purchased 3.0 pounds of Jolly ranchers.

Step-by-step explanation:

Cost of 1 pounds of pixie sticks = $4.50

Let the number of pixie sticks = x

Total  money spend on x pounds of pixie sticks = $8.10

Nicholas has purchased 1.8 pounds of pixie sticks.

Cost of 1 pounds of Jolly ranchers = $3.25

Let the number of Jolly ranchers = y

Total  money spend on y pounds of Jolly ranchers = $9.75

Jane has purchased 3.0 pounds of Jolly ranchers.

In AMNO, the measure of Z0=90°, OM = 1.7 feet, and NO = 6.7 feet. Find the measure of ZN to the nearest degree.​

Answers

Answer:

14°

Step-by-step explanation:

deltamath

Classify each real number. List all the subsets in which the number belongs.

Answers

Answer:

Step-by-step explanation:

1-integer

2-rational

3-whole

4- irrational

what is j+m, j times m and j divided by m

Answers

Answer:

j + m

jm

[tex]\frac{j}{m}[/tex]

Step-by-step explanation:

We have j and m and are asked to add, multiply and divide them both.

When it comes to adding, its all about like terms, if the terms are not alike meaning ending in the same variable they cannot be added.

Therefore j + m is equal to just j + m.

Now for multiplying, this is free rule, you can freely multiply any variable you want without reprecussion.

Therefore, j * m is equal to jm.

Now for dividing, this works like adding, where you can divide only if the terms are the same, since j and m are not the same. J divided by M is equal to [tex]\frac{j}{m}[/tex]

Please help me please ! Also the answer is not a

Answers

Answer:

The answer is c

Step-by-step explanation: Since both terms are perfect squares, factor using the difference of squares formula to get the answer i hope this helps

Hey there!

The answer is C.

To factor an expression, you take the root (same as exponent variable has) of the terms and put them into parantheses. We can also check the choices to see if they're correct by solving them.

A is incorrect, because if you solve it, you would have [tex]x^2-121[/tex]

B is incorrect, because if you solve it, you would have [tex]121x-x^2[/tex]

C is correct, because if you solve it, you would have [tex]121-x^2[/tex]

D is incorrect, because it CAN be factored.

Have a super awesome day! :)

2.8.9 An e-mail filter is planned to separate valid e-mails from spam. The word free occurs in 60% of the spam messages and only 4% of the valid messages. Also, 20% of the messages are spam. Determine the following probabilities: a. The message contains free. b. The message is spam given that it contains free. c. The message is valid given that it does not contain free.

Answers

Answer:

.

Step-by-step explanation:

Answer:

ਜੇ ਤੁਹਾਡਾ ਆਪਸ ਵਿੱਚ ਭੜਕਣਾ ਵੀ ਬਹੁਤ ਚੰਗਾ ਹੁੰਦਾ ਹੈ,

Step-by-step explanation:

Edie is trying to decide which printing service to use to publish her neighborhood newsletter . The first printer charges a $5.00 fee plus $ 0.25 per full color page, while the second charges a $10 fee plus $0.20 per full color page . Over what range of pages will Edie pay less by using the first printer ? A. Less than 100 pages B. More than 100 pages C. Less than 50 pages D. More than 50 pages E. More than 100 pages but less than 200 pages

Answers

Answer:

A) less than 100 pages

Step-by-step explanation:

p = # pages

Printer 1:

y = .25p + 5

Printer 2:

y = .20p + 10

.25p + 5 < .20p + 10

.05p + 5 < 10

.05p < 5

p < 5/.05

p < 100

I need HELPPPPPP some one please help me :(

Answers

Answer:

well i just know its 9 out of 27

Step-by-step explanation:

Answer:

33.33% of the pizzas DO NOT have pepperoni.

Step-by-step explanation:

27 - 18 = 9

9/27 = ?%

33.33% = ?%

2x + 3 – 4 = 5x - 7



2

-2

- 9

9

Answers

2x + 3 - 4 = 5x - 7

=> 2x + 3 - 4 + 7 = 5x

=> 3 - 4 + 7 = 5x - 2x

=> 3 - 4 + 7 = 3x

=> -1 + 7 = 3x

=> 6 = 3x

=> 6/3 = x

=> 2 = x

x = 2

Step-by-step explanation:

2x + 3 - 4 = 5x - 7 2x - 1 = 5x - 7 (-1 + 7 )= 5x - 2x6 = 3x 6 ÷ 3 = x2 = x

MARK ME AS BRAINLIST

Solve the system of equations using elimination

Answers

Answer:

(1, 3).

Step-by-step explanation:

x + 2y = 7

3x - 2y = -3

Adding the 2 equations will eliminate y:

4x  = 4

x = 4/4

x = 1

Plug x = 1 into the first equation:

1 + 2y = 7

2y = 6

y = 3.

In a lab experiment, 5400 bacteria are placed in a petri dish. The conditions are such that the number of bacteria is able to double every 4 hours. How many bacteria would there be after 17 hours, to the nearest whole number?

Answers

It will become 45900 bacteria in 17 hours
Step-by-step explanation:
In 4 hours 5400 bacteria becomes 5400*2 = 10800
Therefore in 17 hours, it will become
17*10800/4
= 183600/4
= 45900

Answer:

1.62

Step-by-step explanation:

hope it helps god bless

What is the equation of the line that passes through the point (−1,−1) and has a slope of −6?

Answers

Answer: y= -6x -7

Step-by-step explanation:

Point slope formula : y-y1=m(x-x1)

y- (-1)=-6(x- (-1))

y+1= -6(x+1)

y+1= -6x-6

y+1-1=-6x-6-1

y=-6x-7

Standard from 6x+y=7

Please help ASAP if you know how. Thanks so much

Answers

Answer:

The answer is C.

Step-by-step explanation:

You should plug the numbers into the quadratic formula to get the answer.

Answer:

A:  -5 ± √ 17 / 2

Step-by-step explanation:

Consider the following equations:

ax^2 + bx + c - This is an equation you use in understanding quadratic functions.

x= (−b± √b^2−4ac) / 2a - This is the quadratic formula used to solve quadratic functions

So:  ax^2 + bx + c = x^2 + 5x + 2

SOLVE:

-(5) ± √ 5^2−4(1)(2)) / 2(1)

= -5 ± √ 25− 8 / 2

= -5 ± √ 25− 8 / 2

= -5 ± √ 17 / 2

PLEASE HELP ITS URGENT
DONT GUESS
WILL MARK BRAINLIEST

Answers

Answer:

Listed below:

Step-by-step explanation:

P: 192

A:2079

B. Area

C. Perimeter

Hope this helps :)

Find the value needed for the “?” to make the equation true.

1/x^? = x^6

Answer: ? =__

Answers

Answer:

[tex]? =-6[/tex]

Step-by-step explanation:

Given

[tex]\frac{1}{x^?} = x^6[/tex]

Required

Find ?

Apply law of indices

[tex]x^{-?} = x^6[/tex]

Cancel x on both sides

[tex]-? = 6[/tex]

Multiply both sides by -1

[tex]-1*-? = 6*-1[/tex]

[tex]? =-6[/tex]

Solve 17 x 5/8 as a mixed number

Answers

Answer:

it's 10 and 5/8

Step-by-step explanation:

I hope this has helped you

The solution of expression [tex]17 \times \dfrac{5}{8}[/tex] in the form of mixed number would be  [tex]10 \dfrac{5}{8}[/tex].

Used the concept of multiplication that states,

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

Given that the expression to solve,

[tex]17 \times \dfrac{5}{8}[/tex]

Now multiply separately with the numbers given,

[tex]17 \times \dfrac{5}{8}[/tex]

[tex]\dfrac{85}{8}[/tex]

It can be written as,

[tex]10 \dfrac{5}{8}[/tex]

Therefore, the mixed form of solution is [tex]10 \dfrac{5}{8}[/tex].

To learn more about multiplication visit:

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The family size bottle of sunscreen holds 12 fluid ounces (fl oz) of sunscreen. the regular bottle holds 75% less. how many fewer fluid ounces does the regular bottle hold?

Answers

Answer:

9

Step-by-step explanation:

12×0.75=9

Refer to the figure to answer the following.
5
F
m 2 BFG = (0.5)(mCD + mGB)
True False
Please help

Answers

Answer:

True

Step-by-step explanation:

∠BFG is an interior angle, then:

m∠BFG=[m arc(GB) + m arc(CD)] / 2

or in other words

m∠BFG = (0.5)(m arc CD + m arc GB)

Answer:

TRUEEEEEEEEEEEEEEEEEEEEEEE

Step-by-step explanation:

Please help me with this work

Answers

Answer:

1. (5y) = 35

2. (6y) = 1

3. (4y) = 2

4. (11y) = 15

5. 18, 24, 42, 60

The number of miles Henry rides his bike in 10 days is 60miles

Step-by-step explanation:

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