A sparrow ( AIM-7 sparrow ) tops out at mach 4, as for hitting a battleship, what era of battleship, first or second world war. Actually give me a specific battleship and I'll try and do the math for you, no guarentee's I'll be able to, but I'll try. From just logical thinking though, one 88 lbs warhead hitting a tens of thousand ton battleship seems to me to be kinda like spitting at a 747, but I'll do the math and let you know!!