Calculate the velocity of the body when it hits the floor.
V = sqrt (2gH) = 2.8 m/s
The time required needed to stop the fall in a distance d is given by
(V/2)*T = d since V/2 is the average velocity during deceleration.
T = 2d/V
acceleration rate = V/T = V^2/(2d)
= 392 m/s^2 for a carpeted floor
Compare the result for a hardwood floor.
Traumatic brain injury such as concussionn results when the head undergoes a very large acceleration. Generally, an acceleration less than 800 m/s^2 lasting for any length of time will not cause injury, whereas an acceleration greater than 1000 m/s^2 lasting for at least 1 ms will cause injury. Suppose a small child rolls off a bed that is .40 m above the floor. If the floor is hardwood, the child's head is brought to rest in approxeimately 2.0 mm. If the floor is carpeted, this stopping distance is increased to about 1.0 cm. Calculate the magnitude and duration of the deceleration in both cases, to determine the risk of injury. Assume that the child remains horizontal during the fall to the floor. Note that a more complicated fall could result in a head velocity greater or less than the speed you calculate.
1 answer