Edward had to escape from prison to work in the grading room today. He stopped to rest at a place $1,875$ feet from the prison and was spotted by a guard with a crossbow. 

The guard fired an arrow with an initial velocity of $100 \frac{\text{ft}}{\text{s}}$. At the same time, Edward started running away with an acceleration of $1 \frac{\text{ft}}{\text{s}^2}$. Assuming that air resistance causes the arrow to decelerate at $1 \frac{\text{ft}}{\text{s}^2}$, and that it does hit Edward, how fast was the arrow moving at the moment of impact (in $\frac{\text{ft}}{\text{s}}$)?

Let's think step by step and output the final answer within \boxed{}.
user