A roadway speed bump is being installed on a level road to remind motorists of the existing speed limit. If the driver of the car experiences at G a vertical acceleration of as much as g, up or down, he is expected to realize that his speed is bordering on being excessive. For the speed bump with the cosine contour shown, derive an expression for the height h of the bump which will produce a vertical component of acceleration at G of g at a car speed v. Compute h if b = 1 m and v = 20 km/h. Neglect the effects of suspension-spring flexing and finite wheel diameter.

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y h + cos ) 2 9. 9.