the friction coefficient between a road and the tyre of vehicle is 3​​​/4. Find maximum incline the road may have so that once hard brakes are applied and a wheel start skidding,the vehicle going down at a speed of 36km/hr is stopped within 5 minutes

Given: μ = 4/3; initial velocity, u = 36 km/hr = 10 m/s; final velocity, v = 0; distance travelled, s = 5 m.We know, 2as = v2 – u2Or, 2 * a * 5 = 02 – 102Or, a = – 10 m/s2 Let, θ be the maximum angle and the forces acting on the block are shown in the figure.From F.B.D. of block:There is no acceleration perpendicular to the plane of motion.Hence, R = Mg cos θFrictional force, Ff = μR = 4/3 Mg cos θTaking forces along the plane of motion and writing Newton’s second law,We get, Ma = μR – Mg sin θOr, M * 10 = 4/3 M*10* cos θ – M*10* sin θOr, 3 = 4 cos θ – 3 sin θOr, 4√ (1 – sin2 θ) = 3 sin θ + 3Squaring on both sidesWe get, 16 (1 – sin2 θ) = 9 sin2 θ + 18 sin θ + 9Or, 25 sin2 θ + 18 sin θ – 7 = 0Solving the equation we get,Sin θ = (– 18 ± 32)/50 = 14/50 = 0.28 [Taking +ve sign only]Or, θ = sin-1 0.28 = 16Therefore, the maximum incline of the road is 16