When hard brakes are applied (so as to lock the wheels) in a car travelling on a wet road it can “hydro-plane”. A film of water is created between the tires and the road and, theoretically, the car can slide a very long distance. [In practice film is destroyed much before such distances can be achieved]. Consider a car of mass M moving on a wet road with speed `v_(0)`. Hard brakes are applied. Let the area of film under all four tires be A and thickness of the film be h. Coefficient of viscosity is `eta`.
(a) Calculate the distance (x) to which the car will slide before coming to rest.
Calculate the value of x for `M=10^(3)`kg, `A=0.2 m^(2), h=0.1` mm, `v_(0)=20ms^(-1)`, and `eta=10^(-3)`kg `m^(-1)`

Answer

(a) `x=(Mhv_(0))/(eteA)` (b) 10km