It's new because I saw it for the first time today.

There is a huge basket with a capacity of holding "X" balls in it. Initially, there is 1 ball in the basket. In the first second, 1 ball is dropped in, in 2nd second, 2 balls are dropped, in 3rd second, 4 balls are dropped, in 5th second, 8 balls are dropped and so on. At the end of 1 hour, the basket is totally filled.

Questions:
At what time was the basket half full?
What is "X"?
And you'll have explain your answer when you solve it (IF you can solve it). Not just copy-paste