A girl stands on a flat cart that moves along a straight, level track at $4.0\ \text{m/s}$. She throws a ball straight up, as she sees it, at $15\ \text{m/s}$ relative to herself. At the moment of the throw, the cart begins to speed up with a steady acceleration of $2.0\ \text{m/s}^2$ along the track. Her hand stays at the same place on the cart. Ignore air resistance and take $g = 10\ \text{m/s}^2$. When the ball comes back down to the height from which it was thrown, how far behind her hand is it? Give the answer in $\text{m}$.