A horizontal disc rotates at 3 revolutions per second around its centre, with the top of the disc at ground level.
At 2 m from the centre of the disc, a ball is held in place at ground level on the top of the disc by a spring-loaded projectile launcher. At position \(X\), the launcher fires the ball vertically upward with a velocity of 5.72 m s\(^{-1}\).
Calculate the ball's position relative to the launcher's new position, at the instant the ball hits the ground. (7 marks)
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