Real-World Applicationshard
0:00.0

The flow-density relationship for traffic is q(rho)=umaxrho(1fracrhorhomax)q(\\rho) = u_{max} \\rho (1 - \\frac{\\rho}{\\rho_{max}}), where umax=100u_{max} = 100 km/h (free-flow speed) and rhomax=120\\rho_{max} = 120 vehicles/km (jam density). A traffic jam has density rho2=100\\rho_2 = 100 vehicles/km, while upstream traffic has density rho1=40\\rho_1 = 40 vehicles/km. What is the propagation speed of the shock wave at the boundary between these two states?