Automobiles Automobiles are designed with crumple zones that help protect their

Chapter 3, Problem 117

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Automobiles Automobiles are designed with crumple zones that help protect their occupants in crashes. The crumple zones allow the occupants to move short distances when the automobiles come to abrupt stops. The greater the distance moved, the fewer gs the crash victims experience. (One g is equal to the acceleration due to gravity. For very short periods of time, humans have withstood as much as 40 gs.) In crash tests with vehicles moving at 90 kilometers per hour, analysts measured the numbers of gs experienced during deceleration by crash dummies that were permitted to move meters during impact. The data are shown in the table. A model for the data is given by where is the number of gs. (a) Complete the table using the model. (b) Use a graphing utility to graph the data points and the model in the same viewing window. How do they compare? (c) Use the model to estimate the distance traveled during impact if the passenger deceleration must not exceed 30 gs. (d) Do you think it is practical to lower the number of gs experienced during impact to fewer than 23? Explain your reasoning.