With what acceleration does a boy slide down a slippery icy slope if the slope is 13m long and 5m high?

Data: L (length of the icy slope) = 13 m; h (slope height) = 5 m; μ (coefficient of friction on a sprinkled hill) = 0.3.

Constants: g (acceleration due to gravity) = 9.81 m / s2.

1) Slippery icy slope (projection of forces on the slope length): m * a = m * g * sinα = m * g * h / L, whence a = g * h / L = 10 * 5/13 = 3.85 m / s2.

2) A slope covered with sand:): m * a = m * g * sinα – Ftr = m * g * h / L – μ * m * g * cosα = m * g * h / L – μ * m * g * √ (1 – (5/13) ^ 2), whence a = g * h / L – μ * g = 10 * 5/13 – 0.3 * 9.81 * √ (1 – (5/13) ^ 2) = 1.13 m / s2.

Answer: Acceleration on a slippery slope is 3.85 m / s2; on sprinkled with sand – 1.13 m / s2.