Apple Safari Mac OS X 10.10.2 will not open
Make sure no parts of Safari are still running

Open Activity Monitor and use the search box in the top right corner to search for "safari". If there are any Safari processes running, select them and quit them using the left most toolbar icon. Once they are gone, try launching Safari again. If that doesn't work...

Delete Safari's Saved Application State folder

You'll find it at /Users/YOURUSERNAME/Library/Saved Application State/com.apple.Safari.savedState and try launching Safari again. If that doesn't work...

Delete Safari's Cache folder

/Users/YOURUSERNAME/Library/Caches/com.apple.Safari and try Safari again. If that doesn't work...

UP TO THIS POINT YOU DON'T REALLY LOSE ANYTHING. FROM HERE ON, YOU COULD SO...

Rename Safari's library folder

/Users/YOURUSERNAME/Library/Safari and try Safari again. If that doesn't work delete the new folder that Safari will likely have created and rename the original back and...

Rename Safari's preference file

/Users/YOURUSERNAME/Library/Preferences/com.apple.Safari.plist and try Safari again. If that doesn't work delete the new preference file that Safari will likely have created and rename the original back.

Let us know how you get on.