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Could we use a hot air balloon to carry a rocket and send it into orbit at a higher altitude? That is, do I need to reach a specific speed to be completely free of Earth's gravity, or can I just ascend to some height?

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If I am reading your question correctly, I believe you are asking whether or not you can reach outer space by simply ascending to a certain distance rather than reaching a specific velocity--that is, if by climbing in a hot air balloon you can reach a point where the gravitational potential energy is zero.

If this is what you're asking, then there is a speed (known as the escape velocity) you need to achieve to escape the Earth's pull: it is given as

$$ v_e=\sqrt{\frac{2GM}{r}} $$ where $M$ is the mass of the Earth, $r$ is the radius, and $G$ is the gravitational constant. If you are leaving from the Earth's surface, then it is around $11.2$ kilometers per second. However, if you fly your balloon to a certain altitude and then attempt to fly into space there, you will see a decrease in the escape velocity. You can read more about it on the wikipedia article for escape velocity.

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    $\begingroup$ wow your answer just awesome!, that's exactly what I want, thanks allot :D $\endgroup$ – narzan Jun 23 '15 at 15:25
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What you're describing is called an air launch.See also the Wikipedia article on air launch to orbit. As far as I know balloons are not used because they can't lift heavy enough loads. The launch is generally done using a large airliner.

There is some related discussion in the question Why do spacecrafts take off with rockets instead of just ascending like an aircraft until they reach space?.

At the moment air launches can't handle big payloads, and there are some concerns about safety when launching very powerful rockets. However, as the Wikipedia article mentions, there are studies being done into launching rockets capable of lifting payloads of up to six tonnes. I suspect there is a reluctance to invest lots of money in researching air launches when ground launched rockets are a mature technology and work very well.

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