Question

why do rockets rise up when a thrust is applied on air ?

Answer 1

It is by conservation of momentum.
when no external force is applied, then we conserve momentum,
so what the rocket basically does is that it blows its fuel at high rate from the back of it which makes itself move forward..

Answer 2

Just imagine it like this
U are standing on ice, and you have a ball in your hands.
if you throw the ball towards east your body will automatically move west.

Answer 3

is the application of the newton laws F=-F.