1. You are trapped on the 2 nd floor of a burning building. The only escaping path is to jump through a window and land into a firefighter's net. What can the firefighters do to cushion your fall even more?

1. First, note that your injury risk is directly related to the falling distance. 2. The firefighters can reduce this distance by moving the net closer to your starting point. 3. In other words, if the firefighters lower the net so that it is directly outside the window, you fall almost no distance before landing. 4. Mathematically, if the height of the window from the ground is \( h \) and the net is lowered such that the remaining fall distance is \( d \), then minimizing \( d \) minimizes the impact speed \( v \), where \[ v = \sqrt{2gd} \] with \( g \) being the acceleration due to gravity. By setting \( d \) as near zero as possible, \( v \) becomes very small. Thus, the firefighters can cushion your fall even more simply by lowering the net close to the window so that your falling distance is minimized.