Probably the textbook author was thinking of velocities, but kinetic energy is 1/2 mv^2, going as the square of the velocity. If we imagine superballs with per

Probably the textbook author was thinking of velocities, but kinetic energy is 1/2 mv^2, going as the square of the velocity. If we imagine superballs with perfectly elastic collisions, then yes, the two balls would have the same relative velocity to each other after the collision (100 mph for perfect head-on) as the single 100 mph ball after hitting the wall. If we consider the force experienced by a passenger in any car, then you also have to take into account the crumple zone (larger in modern cars). Here we imagine the cars have perfectly inelastic collisions coming to a complete rest as they crumple, first calculating the KE in each scenario: 100 mph (44 m/s) into a brick wall -> KE = 1/2 m (44)^2 = m(968) 2 50 mph (22 m/s) into each other -> KE = 2 * 1/2 m (22)^2 = m(484) Thus the car in the brick wall scenario has to absorb twice the energy of the overall collision in the two-car scenario, in which each car only has to absorb 1/4 of the brick wall total KE (assuming the brick wall absorbs nothing, maybe a giant granite boulder is a better model). Thus in modern cars it's not just the KE but the crumple zone that reduces the force felt by the two-car passengers. (Incidentally I used Chat GPT4 to help sort this out and it tried to claim that (x/2)^2 == (x^2)/2 so use with care - it did catch the error but only when I said double check that calculation in a step-by-step manner. User beware!)