the Prophet said: "Whoever is overcome by vomiting, then he is not required to make up (the fast), and whoever vomits on purpose, then he must make it up."  

أَنَّ النَّبِيَّ ﷺ قَالَ مَنْ ذَرَعَهُ الْقَىْءُ فَلَيْسَ عَلَيْهِ قَضَاءٌ وَمَنِ اسْتَقَاءَ عَمْدًا فَلْيَقْضِ قَالَ وَفِي الْبَابِ عَنْ أَبِي الدَّرْدَاءِ وَثَوْبَانَ وَفَضَالَةَ بْنِ عُبَيْدٍ