# Day 78: Once Again, Kids Come Up with Good Ideas

The more I teach, the more I find I get stuck in a particular method of problem solving or diagraming I think works best. Over the course of the last two years with Modeling Instruction, I have found that as I steer kids to particular methods less and less, they come up with creative and elegant solutions more and more. Today was no exception.

We were solving a problem where a projectile is launched from a cliff and lands below the launch height, find the time of flight. My typical solution would be to find the time of flight via the quadratic formula from

$\Delta y=v_{0y} t + \frac{1}{2} a t^2$

A student brought up: Why don’t you just solve for $v_y$ in $v_y^2=v_{0y}^2+2a\Delta y$ and plug the solution into $v_y=v_{0y}+at$? So we tried it, result below. Despite that it is using two equations, it’s actually easier than using the quadratic formula symbolically. I love my job.