If we want to know what would happen to a human crashing into a car while wrapped in a bubble, then the direction of the acceleration doesn't matter. When it comes to estimating possible injury to a person’s body, it doesn’t matter which way they bounce. What matters is the magnitude of the bounce’s acceleration. We need to know the total acceleration—we call this the magnitude of a vector.
Since the x and y components of the acceleration are perpendicular to each other, they form a right triangle with the hypotenuse being the magnitude. That means that I can square the components, add them together, and take the square root to find the magnitude of the acceleration.
It's common to put "absolute value" lines around a vector to show that you are using just the magnitude of the vector. But still, there is just one more thing to consider: Guy's acceleration is calculated in units of meters per second per second. (We write that as m/s2.) However, it's very common to talk about the acceleration of humans in terms of g's where 1 g = 9.8 m/s2. With this, Guy has an acceleration on impact with a value of 25 g's.You already have an intuitive feel for the value of 1 g. It's what you experience every day due to your gravitational interaction with the Earth. (Unless you aren't on Earth—in which case, that's cool.) Yes, that force you feel pushing down on you as you are sitting on the couch is 1 g. It’s the same force that you feel as you are walking around town or eating ice cream. As long as you aren’t accelerating, you feel 1 g.
Why is gravity like an acceleration? It's complicated and rooted in Einstein's equivalence principle, but in practical terms it means that having an acceleration of 25 g's would be like sitting down with a force equal to 25 times your weight. Oof.Here we are fortunate that NASA and others have experimentally determined the maximum acceleration a human can withstand—they call it g-force tolerance. It’s not a single number. The maximum tolerance also depends on the duration of the acceleration, the orientation of the person during impact, and even how quickly the acceleration increases.
Well, how about Guy’s acceleration of 25 g's? It seems that if this bouncing impact lasts a little over 0.1 seconds, then Guy might be in trouble. It’s very likely that Guy would be at least partially injured—maybe even critically injured.