- I have an arbitrary object with initial velocity $v_1$ pointing upwards. There's also air resistance proportional to the square of speed. So this object goes up, turns around, goes back down and lands with velocity $v_2$, happens to be smaller than $v_1$. What does that tell us about the time of up-motion? Is it smaller, even or greater than time of falling down?
I could probably solve numerically differential equation and somehow deduce it, but I'd rather see a reasoning which does not require use of computer.
- Bonus question: what happens in simplified case - when air resistance depends linearly on speed, not its square?
I don't necessarily want a full solution, but if someone wants to steal the show be my guest.