I learnt this in college but can't for the life of me remember how to do it. I've searched stack exchange and the internet for answers but it isn't clicking. It doesn't help my teacher has decided to word it oddly. The question is this, Spider-man leaps upwards at a rate of $20$m/s and daredevil drops off the top of a $50$m high building. Assuming gravity is $10$m/s$^2$, at what height do they collide? I've tried using $v^2=u^2+2as$ but I ended up with something like $20s=v^2$ or something weird.
Thanks for your help as always!
Ps: I apologise If the tag is incorrect but I couldn't find an appropriate one. Sorry.
By inspection, they meet after $2.5$ seconds. Then Daredevil has fallen $\frac{1}{2}(10)(2.5)^2$, and they meet at height $50-\frac{1}{2}(10)(2.5)^2$.
If inspection does not make the time of meeting obvious, at (reasonable) times $t$, Spidey is at height $20t-\frac{1}{2}(10)t^2$, and Daredevil is at height $50-\frac{1}{2}(10)t^2$.
Setting these heights equal, we get $20t=50$.