maximum allowed value of the speed in roller coaster is given as
[tex]v = 20 m/s[/tex]
now from kinematics we can say
[tex]v^2 - v_i^2 = 2 a s[/tex]
here initial speed will be
[tex]v_i = 0[/tex]
acceleration is due to gravity
[tex]a = 9.8 m/s^2[/tex]
now we can use this to find the height
[tex]20^2 - 0^2 = 2 * 9.8* h[/tex]
[tex]400 = 19.6 *h[/tex]
[tex]h = 20.4 m[/tex]
so maximum allowed height will be 20.4 m
