Not really. Although when you only get a narrow view like the video below of Cleveland Indian's Jose Ramirez it can seem like it.
A wider view (barely) shows the kick that sent the helmet flying up and forward making it a projectile moving horizontally the same way Ramirez was although probably not at the same speed.
WIRED Magazine has a nice write-up, with the physics behind it to boot. The article shares a quick projectile demo that many of us use, illustrated by these videos as well:
Vertical Projectile Launch from a Horizontally Moving Cart:
Walter Lewin's "Horizontal Motion remains constant" from MIT:
So how can you use this in the classroom? I use this demonstration to illustrate the fact that the horizontal motion and vertical motion of a projectile are independent from each other. You can tell students this over and over and over again but for some it is one of those conceptual sticking points and they just don't understand.
When I demonstrate this with a ballistic cart in my classroom I first give the cart that will launch the ball straight up a small push so it moves slowly. The second time (because they will all want to see it again) I give it a big of a bigger push. If you want to have a faster horizontal velocity you'll want to really make sure your track is level and the cart doesn't rattle on the track. If the ball doesn't land back in the cart, usually through a funnel type mechanism as seen above, your students won't believe you. So take care, their comprehension depends on it!
Even after students have seen this demonstration I think the video of Ramirez is something to share. I'm going to start with the narrow point of view and ask them, "What happened?!" with no other information. [Depending on your level of students feel free to add an expletive from dramatic affect.] Just based on their previous knowledge of projectile motion, and hopefully due to careful observation, they should realize the helmet has some initial horizontal motion before it separates from Ramirez. Ideally, a discussion follows when someone realizes, "Wait, he totally kicked it!" and students can then focus on what that kick (ahem, force) did to that helmet.
As Dean Baird says, sometimes we have to pretend to be the dumbest person in our classroom so that we can lead students to their own understanding through critical thinking. I'll keep asking them questions, usually with a bit of "How do you know that? What would that mean? What does that remind you of [that we have learned about]?" Once students have gotten close enough to the "real reason" this happens I plan to show them the wider angle and perhaps printed copies of the WIRED article to solidify the whole experience.
And if you want a funny ending to it all, the Cleveland Indian's mascot, Slider, tried to help Ramirez out: