# The friction coef

Let the maximum angle of incline be θ.
Initial velocity of the vehicle, u = 36 km/h = 10 m/s
Final velocity of the vehicle, v = 0
distance travel s = 5 m,

μ=4/3, g = 10 m/s2

Using the equation of motion

a = -10 m/s2

From the free body diagram

R = mg cosθ (1)
Again,
ma + mg sinθ = μR
ma + mg sinθ = μmg cosθ
a + g sinθ = μg cosθ

10 +10 sinθ = 4/3×10 cosθ

30 + 30 sinθ = 40 cos θ
3 + 3 sinθ - 4 cos θ = 0
4 cosθ − 3 sin θ = 3

4(1-sin2 θ)1/2=3+3 sinθ

On squaring both sides, we get
16 (1 − sin2 θ) = 9 + 9 sin2 θ + 18 sinθ
25 sin2 θ + 18 sinθ − 7 = 0

sinθ=0.28

θ = 16°

Therefore, the maximum incline of the road, θ = 16°

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