That's called a Standing Liberty quarter. They were minted 1916-1930.
No, 1924 is a Standing Liberty quarter, Washington quarters started in 1932.
On the front of the quarter is George Washington's face. On the back is an eagle (there is no person depicted for the reverse side).
Front: George Washington Back: Eagle
It's not a man carrying a sack. It's Miss Liberty wearing a gown. The coin is called a Standing Liberty Quarter. The Standing Liberty Quarter was minted from 1916-1930. These quarters are composed of 90% Silver and 10% copper.
Not enough information. Is the date missing due to wear? If so, is the coin a Washington quarter or does it have an older design - Liberty standing on the front and a flying eagle on the back, or the head of Liberty on the front and a spread-eagle on the back? If it's a Washington quarter, look at the edge. If it shows copper then it's a modern quarter and is worth only 25 cents. If the edge is silver colored or it's one of the earlier designs you have a 90% silver coin that might sell for $2.50 or $3 for its metal content.
The "person" is Miss Liberty. You have what's called a Liberty Standing quarter. It's considered to be one of the most beautiful U.S. coins of the 20th century. The design was struck from 1916 to 1930. Unfortunately a defect in the original design caused the dates to wear off quickly, and the problem was not corrected until about 1925. As a result many SL quarters are dateless.
Two types of quarters were made in 1916. The most common type is called a "Barber" quarter after its designer Charles Barber. This design has Miss Liberty's head on the front and a spread-winged eagle on the back. The other design is called a Standing Liberty quarter and is much scarcer. Its design features a full-length image of Miss Liberty on the front and a flying eagle on the back. Any such coins should be inspected by an expert to ensure they're genuine. There's more information at the Related Questions.
if their shadow is in front of him
Not enough information. It's possible you have a Standing Liberty quarter, in which case it's not a statue on the front, it's a picture of Miss Liberty. If the coin's date is visible please post a new question with that information. If it's worn off (a common problem with SL quarters) it's at least worth about $2.50 for its silver content.
This type of quarter was designed by Hermon A. MacNeil. The left arm of Liberty is upraised uncovering a shield in the attitude of protection. Her right hand bears the olive branch of peace. There was a modification in 1917 because of public resentment to Liberty's exposed breast. The reverse is an arrangement of the stars and eagle.
The mint mark on a 1929 Standing Liberty Quarter can be found next to Liberty's right foot, just above and to the left of the date on the coin's obverse (front) side.
You can't flee from them.