I am accelerating a 20kg projectile downwards using a linear servo motor. The motor can accelerate at 21m/sec^2 for 720mm and attains a peak velocity of 3.9m/sec. At this time the projectile is left to continue falling under its own weight till a final velocity of 20m/sec is attained. Once at its final velocity the projectile hits a target for destructive testing of a sample. Distance travelled after impact is nominally 50mm and is inconsequential as the failure mode dictates the stopping distance. Thus, I need to calculate the required free fall distance for the projectile to attain 20m/sec?

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