If a ladder leans against a smooth wall and makes a $60^\circ$ angle with the floor, how far up the ladder, X, can a person climb before the ladder begins to slip?

Take the mass of the person to be 10 times the mass of the ladder, and the coefficient of friction $\mu_s =0.5$ between the ladder and the floor. The ladder has a uniform mass density and has length $\ell$.

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