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# A child on a horizontal merry-go-round gives an initial velocity Vrel to a ball. Find the initial direction and velocity Vrel of the ball relative to the merry-go-round so that, relative to the child, the ball goes around in a perfect circle as he’s sitting on the merry-go-round. Assume there is no friction between merry-go-round and ball. The merry-go-round is rotating at a constant angular velocity of w radians/second, and the ball is released at a radius r from the center of the merry-go-round.

Arun Kumar IIT Delhi
7 years ago
$\vec v_{boy}=wrcos(\theta)\vec i+wrsin(\theta)\vec j \\\vec v_{ball}=\vec v_{boy}+\vec v_{ball,rel\ to \ boy} \\where \\\vec v_{ball,rel\ to \ boy}=vcos(\phi)\vec i+vsin(\phi)\vec j$

Arun Kumar
IIT Delhi