Is 47 mph fast for a 7 year old?

My son was clocked at 47 mph this summer! He just turned 8 on Dec. 19th! I was wondering how that stacks up to other kids his age, who have a gun for an arm. He has great form and is only allowed to throw 30-35 pitches at a time, maybe 3 days a week! We do rubber band work daily and I am careful not to over work his arm. After this Winter, I’m slowly building his arm back up. He knows that he’s not allowed to throw as hard as he can for at least another month or two. That’ll give him a full three months to strengthen his arm back up before he lets it go again! So, in no way am I over working him or abusing his arm. Also, he’s the one who always wants to practice and gets mad when I want to stop. He’s basically obsessive compulsive when it comes to baseball and knows more about the MLB and it’s history than most adults! Also, he gets private lessons, weekly, from a Major Leaguer and the top prospect in the State of Washington. So he is doing everything properly.

Yeah, that’s fast!

How does he do pitching in games? Is he overpowering the batters?