The myth was originally that he threw a silver dollar across the mile-wide Patomac river.
This was adjusted to throwing a silver dollar across the Rappahannock to make it more possible.
I now point out that silver dollars didn't exist when Washington was young and you want to change the coin (and the wrong coin at that). If you want to substitute a coin, use the Spanish reale.
"Thomas Jefferson was among the proponents for a silver dollar coin as early as 1785. These were difficult economic times for the young country. The Spanish 8-reales coin filled the need in the absence of a U.S. Mint and federally issued currency.
When Secretary of the Treasury Alexander Hamilton presented Congress with a report on a Mint and a monetary system, a dollar coin with the approximate weight and purity of the Spanish 8-reales coin was taken into serious consideration. The very first statute of the Mint Act of April 2, 1792, authorized striking of silver dollar denomination coins. Our federal coinage actually begins in 1792 with what could be argued to be patterns, regular production of some denominations commencing during 1793."
http://www.coinfacts.com/historical_notes/history_of_the_silver_dollar.htm
Give it up it is a myth
Of course there weren't.
But from 1794 to the 1820s silver dollars and British half-crowns were both current in the US and about the same size and weight and considered fungible. In other words, if someone in 1810 Virginia told you that he wanted two dollars for the bridle you were buying in his shop and you handed him a half-crown piece and a silver dollar, he wouldn't be likely to raise a fuss.
The term "silver dollar" is one that was used very loosely in the early 1800s.
I'm not saying to story is not apocryphal - I am merely pointing out that a athletic teenage sixfooter can quite feasibly throw a small object 250 feet.
I now point out that silver dollars didn't exist when Washington was young and you want to change the coin
Just like you said that a major league baseball player couldn't throw a baseball 300 feet and then changed the criteria.