Finding relative speed of space shuttle

[huybinhs]

Homework Statement

The space shuttle, with an initial mass M = 2.81E+6 kg, is launched from the surface of the Earth with an initial net acceleration a = 17.5 m/s2. The rate of fuel consumption is R = 8.20E+3 kg/s. The mass of the shuttle when it reaches orbit is Mo = 6.74E+5 kg. What is the relative speed of the exhaust gas?

The Attempt at a Solution

I got exhaust v = ma dt /dm = 6 km/s

then I got relative speed = exhaust v * (M/Mfuel)

which Mfuel = (2.81* 10^6) - (6.74*10^5) = 2.136 * 10^6 kg

=> I got the relative speed = 1.65 kg/s which is NOT CORRECT!

Please help!

 

[Mindscrape]

Your equation for the speed isn't right.

Vshuttle_final=Vshuttle_initial+v_exhaust*ln(Mf/Mi)+a*t

Where I assume that the initial and final velocities of the shuttle are zero, starts from rest, and ends at orbit (rest).

Also, the fuel consumption will looks like this
dm/dt=R
mf=mi+Rt
which allows you to solve for t

I don't know what level of physics this is, so if you don't know differential equations (I assume you don't as this is "Introductory Physics") then I guess you have some formulas that you never listed. If you have done differential equations, work it out for yourself to see if what I say is true.

 

[huybinhs]

Ok, thanks for your help! ;)

 

[Mindscrape]

Actually, I don't really know what I was saying earlier (it was the morning), you ought to know how high the shuttle orbits because you need that velocity as your final velocity, but the problem doesn't give it, huh...