Problem # p025

Forces - Acceleration, path normal
The car of a roller coaster ride is hitting the bottom of a hill with v=20 m/s. To prevent the passengers from blacking out the absolute value of the acceleration at the bottom of the hill is not to exceed 3*g ( g=9.81 m/s2 ).
As shown in the figure, around the bottom of the hill the track is described by a parabola given by :

y = k * x2      k is a constant

  1. What are the units of "k" in above equation to make the equation dimensionally correct ?

  2. What is the size of the radius of curvature of the track at the bottom for v=20 m/s and a normal acceleration of 3*g ?

  3. Under these conditions, what is the value of the constant "k" in above equation ?