The object of the pinball-type game is to project the particle so that it enters the hol...

The object of the pinball-type game is to project the particle so that it enters the hole at E. When the spring is compressed and suddenly released, the particle is projected along the track, which is smooth except for the rough portion between points B and C, where the coefficient of kinetic friction is μ_k. The particle becomes a projectile at point D. Determine the correct spring compression δ so that the particle enters the hole at E. State any necessary conditions relating the lengths d and ρ.