Less than two percent of motor vehicle crash deaths are bicyclists. The most serious injuries among a majority of those killed are to the head, highlighting the importance of wearing a bicycle helmet. Eighty-nine percent of bicycle deaths are persons 16 and older, so helmet laws should include adults. Helmet use has been estimated to reduce head injury risk. For this prompt, you will investigate and answer what happens if you fall without a helmet.
a. When a person of average height sits on a bicycle, the person’s head is about 5.3ft above the ground. suppose such person falls from a bicycle at rest. Use the function d(t) = 16t2 to estimate the time it takes for the person’s head to hit the ground.
b. The function v(t)=32t gives the speed v(t) in feet per second of an object that falls t seconds. Estimate the speed at which the head of the person in part (a) hits the ground.
c. A cyclist not wearing a helmet will generally have lasting brain damage if the cyclist’s head hits the ground at more than 18ft/s. Based on your answer to part (b), explain why wearing a helmet is a good idea.