Overall, this is good. I especially like the beginning. However, I do think you should dwell more on why bioengineering, which is, after all, your final choice. You explain why medicine and you explain why engineering. The you explain bioengineering by saying it's ideal because it's a combination of the two. What I think you should do next is give one more reason why you like bioengineering without relating it to your previous choices; give the career its own merit, what about it do you find specifically interesting?
As we watched our little paper aeroplane take its flight we argued on how far it would go before it falls and how we could make the next one fly further.
In this sentence I'd recommend deleting 'its.' Add a comma after flight and change 'falls' for 'fell.'
On your other essay: What motivated me to apply?
It got locked, but I thought the beginning was especially good. The way you introduced you interest for Rice was, well, interesting :)
