Not trying to scaremonger, but just a reminder, make your way to the next gate straight away. We have had a recent story of someone being made to pay for a new flight as EK deemed they were late for boarding therefore were offloaded and claimed that they should have made the next flight despite the incoming one being late.
Once at the gate, you can determine after speaking to gate staff if you have any time to do anything in the terminal before you have to board.
S