I do not think yous are getting the right answer. The answer at the back of the book is 393.3 m/s.

I think I was supposed to take gravity into account. we re supposed to assume gravity is constant.so using F=ma it should of read 398500-v^2 -20000g=20000a

so a=(398500-v^2 -20000g)20000

rearrange this and yous will get [1/(202500-v^2) ]dv =1/20000^-1t

http://calculusworld.weebly.com/uplo...gif?1348107889 using the third one from the top ...

integrate this and put in the limits and solve for v and I get v=393.3

so it was quite easy.

I am not sure how to do the last part though. what is the max speed the rocket tends to? the answer at the back of the book is 450.