A skater weighing 50 kg pushed a sled weighing 0.5 kg and traveled 20 m in 2 seconds find the speed of the skater.

mk = 50 kg.

mс = 0.5 kg.

S = 20 m.

t = 2 s.

Vк -?

We will assume that the sled was moving uniformly to a complete stop. At the end of the movement, they stopped, which means their speed became equal to 0: Vc = 0 m / s ..

The path of the sleigh to a complete stop S is expressed by the formula: S = (Vc0 ^ 2 – Vc ^ 2) / 2 * a, where a is the acceleration of the sleigh.

S = Vc0 ^ 2/2 * a.

a = (Vc0 – Vc) / t = Vc0 / t.

S = Vc0 ^ 2 * t / 2 * Vc0 = Vc0 * t / 2.

Vc0 = 2 * S / t.

According to the law of conservation of momentum: mc * Vc = mc * Vc0.

Vk = mc * Vc0 / mk = mc * 2 * S / mk * t.

Vk = 0.5 kg * 2 * 20 m / 50 kg * 2 s = 0.2 m / s.

Answer: after pushing the sled, the skater began to move at a speed of Vk = 0.2 m / s.