Corrected versions: (a) He accidentally kicked the ball too hard until it rolled into the drain. He ran quickly to pick it up. [Its understood that the ball is the subject and repeating the word "ball" is unnecessary] (b) Anyways acceptable [He kicked the ball very hard.
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Vincent TeoCan I say,
(a) He accidentally kicked the ball too hard until it rolled into the drain. He ran quickly to pick it up / to pick up the ball. The second sentence is fine in both versions. The first won't do, unless you really want to suggest that he repeatedly kicked the ball too hard accidently - This would be so odd that I think you should say He a