Question about centripetal motion problem

[frostyman202]

Hey I am confused about how to find theta in this problem:

A biker going 20 m/s on a frictionless, circular track of radius 12m banked at an angle of theta degrees

I started by just finding the accel... v^2/r = 400/12 = 33.333

the mass does not matter because it cancels out so...

then I just don't know what to do

any info helps
thanks

 

[frostyman202]

i think it has to do with seperating the Vx and Vy and get tan(theta)= Vy/Vx

the Vx and Vy are maybe the centip accel and grav?

idk

thanks

 

[OlderDan]

i think it has to do with seperating the Vx and Vy and get tan(theta)= Vy/Vx

the Vx and Vy are maybe the centip accel and grav?

idk

thanks

You have the right idea. The only forces acting are gravity and the normal force. Their vector sum has to be horizontal and equal to the centripetal force. Resolve these two forces into horizontal and vertical components as you suggest, and demand that the components lead to the correct sum.