How hard would a puck have to be shot to be able to knock the goalie himself backwards into the net?

—Tom

This can’t really happen.

It’s not just a problem of hitting it hard enough. This blog isn’t concerned with that kind of limitation. Humans with sticks can’t make a puck go much faster than about 50 meters per second, so we’ll assume this puck is launched by a hockey robot or an electric sled or a hypersonic light gas gun.

The problem, in a nutshell, is that hockey players are heavy and pucks are not. A goalie in full gear outweighs a puck by a factor of about 600. Even the fastest slap shot has less momentum than a ten-year-old skating along at a mile per hour.

Hockey players also can brace pretty hard against the ice. A player skating at full speed can stop in the space of a few meters, which means the force they’re exerting on the ice is pretty substantial. (It also suggests that if you started to slowly tilt a hockey rink, it could get up to 50 degrees before the players would all slide to one end. Clearly, experiments are needed to confirm this.)

From estimates of collision speeds in hockey videos, and some guidance from a hockey player friend, I estimated that the 165-gram puck would have to be moving somewhere between Mach 2 and Mach 8 to knock the goalie backward into the goal—faster if the goalie is bracing against the hit, and slower if the puck hits at an upward angle.

Firing an object at Mach 8 is not, in itself, very hard. One of the best methods for doing so is the aforementioned hypersonic gas gun, which is—at its core—the same mechanism a BB gun uses to fire BBs.

But a hockey puck moving at Mach 8 will have a lot of problems. It’s not on the same scale as a relativistic baseball, but the air ahead of the puck would be compressed and heated very rapidly. It wouldn’t be going fast enough to ionize the air and leave a glowing trail like a meteor, but the surface of the puck would (given enough time) start to melt or char.

The air resistance, however, will slow the puck down very quickly, so a puck going at Mach 8 when it leaves the launcher might be going a fraction of that when it arrives at the goal. And even at Mach 8, the puck probably wouldn’t pass through the goalie’s body. Instead, it would burst apart on impact with the power of a large firecracker or small stick of dynamite.

If you’re like me, when you first saw this question, you might’ve imagined the puck leaving a cartoon-style hockey-puck-shaped hole. But that’s because our intuitions are shaky about how materials react at very high speeds.  

Instead, a different mental picture might be more accurate: Imagine throwing a ripe tomato—as hard as you can—at a cake.

That’s about what would happen.