Ok I\'m having trouble with this problem. Can you provide stepby step solutions

Question

Ok I'm having trouble with this problem. Can you provide stepby step solutions and explain the reasoning behind using theequations.

Thank you


Traumatic brain injury such as concussion results when the headundergoes a very large acceleration. Generally, an accelerationless than 800 m/s2 lasting for any length of time willnot cause injury, whereas an acceleration greater than 1000m/s2 lasting for at least 1 ms will cause injury.Suppose a small child rolls off a bed that is 0.40 m above the floor. If the floor is hardwood,the child's head is brought to rest in approximately 2.1 mm. If the floor is carpeted, this stoppingdistance is increased to about 1.0 cm.Calculate the magnitude and duration of the deceleration in bothcases, to determine the risk of injury. Assume that the childremains horizontal during the fall to the floor. Note that a morecomplicated fall could result in a head velocity greater or lessthan the speed you calculate.
Hardwood floor magnitude 1 m/s2 duration 2 ms Carpeted floor magnitude 3 m/s2 duration 4 ms Hardwood floor magnitude 1 m/s2 duration 2 ms Carpeted floor magnitude 3 m/s2 duration 4 ms

Explanation / Answer

2 a s = vf2 - vi2= vf2 since vi = 0 vf2 = 2 g h = 7.84m2/s2 Using the same equation again to get the deceleration a = vf2 / (2 s) = 7.84 / .0021 = 3730m/s2   for the hardwood a = 7.84 / .01 = 784 m/s2 for the carpetedfloor Use s = 1/2 a t2 to calculate the time for thedeceleration to occur

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