The falling object has a speed v0 when it strikes and subsequently deforms the foam arresting material until it comes to rest. The resistance of the foam material to deformation is a function of penetration depth y and object speed v so that the acceleration of the object is a = g − k1v − k2y, where v is the particle speed in inches per second, y is the penetration depth in inches, and k1 and k2 are positive constants. Plot the penetration depth y and velocity v of the object as functions of time over the first fi ve seconds for k1 = 12 sec−1, k2 = 24 sec−2, and v0 = 25 in./sec. Determine the time when the penetration depth reaches 95% of its final value.
