At what distance from the intersection should the driver start to brake with a red light, if the car is moving

At what distance from the intersection should the driver start to brake with a red light, if the car is moving uphill with an angle of 30 degrees at a speed of 60 km / h, the coefficient of friction between the tires and the road is 0.1.

V0 = 60 km / h = 16.7 m / s.

V = 0 m / s.

∠α = 30 °.

μ = 0.1.

g = 9.8 m / s2.

S -?

Let’s find the forces that act on the car when braking downhill.

Let us write Newton’s 2 law in vector form: m * a = Ftr + m * g + N, where m * g is the force of gravity, N is the surface reaction force, Ftr is the friction force.

ОХ: m * a = Ftr + m * g * sinα.

OU: 0 = – m * g * cosα + N.

a = (Ftr + m * g * sinα) / m.

N = m * g * cosα.

Ftr = μ * N = μ * m * g * cosα.

a = (μ * m * g * cosα + m * g * sinα) / m = g * (μ * cosα + sinα).

The acceleration of the car a is expressed by the formula: a = (V0 ^ 2 – V ^ 2) / 2 * S = V0 ^ 2/2 * S.

V0 ^ 2/2 * S = g * (μ * cosα + sinα).

S = V0 ^ 2/2 * g * (μ * cosα + sinα).

S = (16.7 m / s) ^ 2/2 * 9.8 m / s2 * (0.1 * cos30 ° + sin30 °) = 24.3 m.

Answer: the braking distance of the car was S = 24.3 m.