Cars around a bend

Cars around a bend#

Two cars travel at constant speeds around a curve as shown below. The front end of both cars crosses line \(C\) at the same time and each driver minimizes their time in the curve. The maximum centripetal acceleration for car A is \({{params.max_acc_A}}g\) with \(R\_{A} = {{params.ra}}\) \(\rm{m}\) and for car B is \({{params.max_acc_B}}g\) with \(R\_{B} = {{params.rb}}\) \(\rm{m}\), where \(g\) is the gravitational constant. The angle \(\theta = {{params.angle}}^{\circ}\).

Two cars are on a curved road. The radius or curvature of the road for car A (R_A) is less than that of car B (R_B). Both cars start at radial line C. Radial line D, which is some distance in front of the cars, makes an angle (theta) with radial line C.

Question Text#

Determine the distance \(S\) that the second car has yet to travel to reach line \(D\) when the first car reaches line \(D\).

Answer Section#

Please enter in a numeric value in \( m{m}\).

Attribution#

Problem is licensed under the CC-BY-NC-SA 4.0 license.
The Creative Commons 4.0 license requiring attribution-BY, non-commercial-NC, and share-alike-SA license.