**P. 4629.** An object is left to move along a horizontal surface, on which friction is not negligible. At one moment its kinetic energy is 900 J, and 2 s later it is only 400 J, while the object covers a distance of \(\displaystyle \ell\).

\(\displaystyle a)\) By what factor will the further distance until the object stops be greater than the distance \(\displaystyle \ell\)?

\(\displaystyle b)\) How long does it take to cover this distance?

(4 points)

**P. 4631.** A step ladder is placed to the smooth horizontal surface of ice. The cross section of the ladder is the same everywhere and the angle between its legs is \(\displaystyle \alpha=60^\circ\). The hinge which connects the two legs of mass 5 kg and of length of 2 m is frictionless. The thin, initially tight safety rope breaks.

\(\displaystyle a)\) What is the angle between the legs of the ladder, when the hinge does not exert any force?

\(\displaystyle b)\) What is the force exerted on the ice by the ladder at this moment?

\(\displaystyle c)\) At what speed does the hinge hit the ice?

(5 points)