The coefficient of friction between a road and the tyre of a vehicle is 4/3 . Determine the maximum incline the road can have such that when hard brakes are applied and the wheels begin skidding, the vehicle travelling downwards at a speed of 36 km/hr is stopped within 5 m .

Step-by-step solution

Initial speed of the vehicle, u = 36 km/hr = 36 5 18 = 10 m/s Final speed, v = 0 Stopping distance, s = 5 m Using the equation of motion v^2 = u^2 - 2as , we can find the required deceleration a : 0 = (10)^2 - 2a(5) 10a = 100 a = 10 m/s ^2 When the vehicle is moving downwards on the incline, the component of gravity acts downwards and the kinetic friction acts upwards. The net retardation is given by: a = mg - mg m = g( - ) Substituting a = 10 m/s ^2 , g = 10 m/s ^2 , and = 4 3 : 10 = 10 ( 4 3 - ) 1 = 4 3 - 3 = 4 -