The following equation describes the motion of a rocket that is expelling a total mass M of fuel at a rate α = -dm/dt: dv/dt = uα/(M-αt), where u is the speed the fuel is ejected, v is the velocity of the rocket in the x-direction, and t is time. Assume the velocity at t = 0 is v(0) = v0, and that M, and u are constants. The burn rate is proportional to the mass of the rocket, as follows: α = -βm, where m is the current mass of the rocket (which is therefore time-dependent). This means that as less fuel is available to burn, then the fuel is burned at a lower rate. Write an expression for the mass of the fuel as a function of time. Now, write an expression for the velocity as a function of time for the rocket. A particular rocket burns fuel at a rate proportional to the mass of the fuel with the constant of proportionality being 6.4 1/s. The propellant speed is 5.1 m/s. The total mass of fuel is 136.4 kg. What is the speed, in meters per second, of the rocket at t = 2.7 s?

The following equation describes the motion of a rocket that is expelling a total mass M of fuel at a rate α = -dm/dt: dv/dt = uα/(M-αt), where u is the speed the fuel is ejected, v is the velocity of the rocket in the x-direction, and t is time. Assume the velocity at t = 0 is v(0) = v0, and that M, and u are constants. The burn rate is proportional to the mass of the rocket, as follows: α = -βm, where m is the current mass of the rocket (which is therefore time-dependent). This means that as less fuel is available to burn, then the fuel is burned at a lower rate. Write an expression for the mass of the fuel as a function of time. Now, write an expression for the velocity as a function of time for the rocket. A particular rocket burns fuel at a rate proportional to the mass of the fuel with the constant of proportionality being 6.4 1/s. The propellant speed is 5.1 m/s. The total mass of fuel is 136.4 kg. What is the speed, in meters per second, of the rocket at t = 2.7 s?

Similar questions

Let A⃗ =6î −4ĵ and B⃗ =−3î +7ĵ . What is C⃗ =A⃗ −4B⃗ ? Give your answer as a magnitude and direciton. Magnitude: Direction (specify as an angle measured counterclockwise from the positive x axis):
Consider a non-stationary time series is defined as below Yt = B0 +B1t+et Where et is error term and IID in nature. Prove that 1st difference of this series is stationary.
Given vector A=2i-3j and vector B = 2i -4j. If vector C = A -2*B then C equals ..
Vector A = 53.0 cm is at an angle of 270° from the horizontal, and vector B = 82.0 cm is at angle 0. (a) What is |A + BỊ (in cm) as a function of 0? (Use the following as necessary: 0. Do not include units in your answer.) JA + B| = cm (b) Using the result from part (a), for what value of e (in degrees) does |A + B| take on its maximum value? What is this maximum value (in cm)? cm (c) Using the result from part (a), for what value of e (in degrees) does |A + B| take on its minimum value? What is this minimum value (in cm)? cm (d) What If? How would your answers to parts (a)-(c) change if B was now subtracted from A and the magnitude of A - B| was evaluated as a function of 0? (Enter the magnitude as a function of e in cm. Do not include units in your answer. Enter the maximum and minimum values in cm.) A - B = cm Maximum value cm Minimum value cm
A piece of wood moves at a velocity (measured in millimeters per year) of v(1) = r² – 3t – 4 where 1 = 1 would be the end of the first year. If a is the displacement of the wood in the first 5 years and b is the distance traveled in the first 5 years, what is a- b? None of the listed answers
The instantaneous speed of a particle moving along one straight line isv(t) = ate−5t, where the speed v is measured in meters per second, the time t is measured in seconds, and the magnitude of the constant a is measured in meters per second squared. What is its maximum speed, expressed as a multiple of a? (Do not include units in your answer.)
An experimentalist in a laboratory finds that a particle has a helical path. The position of this particle in the laboratory frme is given by r(t)= R cos(wt)i + R sin(wt)j + vztk R,vz, and w are constants. A moving frame has velocity (Vm)L= vzk relative to the laboratory frame. In vector form: A)What is the path of the partical in the moving frame? B)what is the velocity of the particle as a function of time relative to the moving frame? C)What is the acceleration of the particle in each frame? D)How should the accelerartion in each frame be realted?Does your answer to part c make sense?
The Maton family begins a vacation trip by driving 710 km west. Then the family drives 610 km south, 310 km east, and 410 km north. Where will the Matons end up in relation to their starting point? Give direction only, directly East is 0 degrees and the order goes counter clock wise (North is 90 degrees, West is 180 degrees, South is 270 degrees).
A particle of mass m has a time-dependent position vector r(t) = (Rcos(ωt),Rsin(ωt),αt) in Cartesian coordinates, where R, ω and α are positive constants. What are the physical dimensions of R, ω and α? Show that the speed of the particle is constant. Does it mean that the acceleration is zero? Justify.
If A = 4i + 6j and B = 5i + 3j, what is the magnitude of C = A - B
We track the particle’s trajectory between t = 0 to t = T. During this interval, how much time transpires in the particle’s non-inertial reference frame?
The velocity of a particle as a function of time is given by v(t)=(3t-t )i-4 j all in S.I. units. a) What are the dimensions of the "-1 " in the – ti term? What are the units of the "3 " in the 3t i term? b) Find the position vector of the particle, r(t), if r(0) = -5 i- 2j :) Find the time ti > 0 when the position in the i direction is a maximum. d) Find a 1 -> 3 the average acceleration vector in the time interval 1 to 3 seconds.