Did You Find Out? Get the Answer to the Riddle of E-News Issue No. 4, September 2016

You may assume the second scenario is worse, because the "relative velocity" of the two colliding men is double (7 km/h + 7km/h = 14 km/h), and thus greater than the woman jogger’s velocity with 12 km/h. However, this is a misconception.

The following thought experiment gives a better understanding:

In a safety test, at the same time, two cars run into both sides of a bridge pier. Since the bridge pier is very thick (high mass), the two cars do not notice each other's impact. Now, visualize the bridge piers getting thinner and consider whether anything changes. If both cars are the same weight and speed, the bridge piers can be as thin as desired. It does not have to withstand the power (more accurately the impulse), because on the other side, exactly the same power (the same impulse) acts.

The events in our riddle behave in a similar way. When the two men collide, in each case, only 7 km/h effects them and not—as initially assumed—the double speed of 14 km/h. Thus, the woman jogger sustains greater injuries from her unfortunate meeting with a tree at 12 km/h, as 12 km/h is greater than 7 km/h.