Safe landings 225 Assumptions e Layers of boxes are comprised of identical boxes laid side-by-side over the entire area of the box catcher The box catcher is large enough compared to the stunt person that edge effects are negligible The boxes are held together so that there is no relative horizontal velocity between them Loose cardboard is placed between layers of cardboard boxes, so that any force transmitted through the top layer of boxes is well distributed to lower boxes, ensuring that only one layer is crushed at a time. In other words, we treat each layer of boxes independently and the box catcher as a sequence of Equations of Motion Since each layer is independent, the equations of motion for the box catcher look similar to the equation of motion for a single box(7). The equations depend on the dimensions of the boxes in each level, so we solve numerically for the motion of the stunt person. At each level of the box catcher, the performer impacts several boxes(approximately)at once. The number of boxes that act to area to the surface area of the top face of a cardboard box. Thus, we altera p decelerate the stunt person is the ratio As /A of the performers cross-sectiona equations of motion by this ratio, getting 1T2,A 2m△ByD <|△H (8) ≥|H where z is the vertical distance measured from the top of the stack, ztop is the value of z at the top of the current box, and As is the cross sectional area of the stunt person Now, given a suggested stack of boxes we can integrate the equations to see whether or not the stack successfully stops the falling stunt person, and if so, where in the stackSafe Landings 225 Assumptions • Layers of boxes are comprised of identical boxes laid side-by-side over the entire area of the box catcher. • The box catcher is large enough compared to the stunt person that edge effects are negligible. • The boxes are held together so that there is no relative horizontal velocity between them. • Loose cardboard is placed between layers of cardboard boxes, so that any force transmitted through the top layer of boxes is well distributed to lower boxes, ensuring that only one layer is crushed at a time. In other words, we treat each layer of boxes independently and the box catcher as a sequence of layers. Equations of Motion Since each layer is independent, the equations of motion for the box catcher look similar to the equation of motion for a single box (7). The equations depend on the dimensions of the boxes in each level, so we solve numerically for the motion of the stunt person. At each level of the box catcher, the performer impacts several boxes (approximately) at once. The number of boxes that act to decelerate the stunt person is the ratio As/A of the performer’s cross-sectional area to the surface area of the top face of a cardboard box. Thus, we alter the equations of motion by this ratio, getting dus dt =    1 2ms∆H T2 S Y V As A |z − ztop| < |∆H|; 1 2 ρAs ms u2 s α2 − g, |z − ztop|≥|∆H|, (8) where z is the vertical distance measured from the top of the stack, ztop is the value of z at the top of the current box, and As is the cross sectional area of the stunt person. Now, given a suggested stack of boxes, we can integrate the equations of motion to see whether or not the stack successfully stops the falling stunt person, and if so, where in the stack