The slightly creepy husband, searching blindly all over the country for his wife

Question

The slightly creepy husband, searching blindly all over the country for his wife, visits an amusement park in California. Also a physicist, he is stunned by the roller coaster ride Superman: The Escape due to its beautiful mathematical quiescence. Forgetting about his run-away wife, he immediately notices that the coaster travels along the track whose arclength is given by s(t)=ct3 with c= 1.0 ft/s3 and t in seconds. He also notices that at t= 2.0 s the magnitude of the coaster's acceleration is 13.3 ft/s2. 1) Find the track's radius of curvature at this instant, i.e. ?(2.0)=? ft.

Explanation / Answer

s(t) = t^3 v(t)= 3t^2 so at t= 2 v= 12 ft/s radius of curvature = v^2/a= 144/13.3= 10.83ft

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