Brain injuries can be caused by strong linear acceleration of the head. Imaging measurements of a human head upon impact show that the magnitude of displacement of the brain relative to the skull is, at most, approximately 1 mm, independent of the magnitude of the acceleration. Studies indicate that the probability of mild traumatic brain injury (MTBI) is approximately 25% for linear accelerations of the head of 50g, where g is the acceleration due to gravity (g = 9.8 m s 2 ). The probability of MTBI is ≈100% for linear accelerations of 150g. For this problem, model the case of a bicycle accident as a human head falling straight down from rest at a height of 2 meters. Assume the ground is very hard and does not compress upon impact. Also assume constant deceleration of the brain upon impact.(a) For the case when the cyclist is not wearing a helmet, what is the deceleration that the cyclist’s head undergoes upon contact with the ground? Express your answer in g’s. What is the probability of suffering a MTBI?(b) Suppose you want to design a helmet that reduces the probability of MTBI to less than 25%. By how much must the helmet compress after impact to achieve this goal for our model assumptions? Express your answer in cm. Do typical bicycle helmets provide this amount of compression?(c) Discuss ways in which our model (a human head falling straight down from rest at a height of approximately two meters onto an incompressible surface) could overor under-estimate the probability of MTBI in a bicycle accident.