Is there a way to solve for time all in one step?

Projectile motion question:

Knowns:
Θ = 30°
Vo = 10 m/s : Voy = 10 * sin(30°) ;
Yo = 1.15m
a = g


So, to solve this I have been solving for time(t) when projectile reaches max height (Vy = 0). Then use that to find what the max height is (new Yo). and then just calculate the time (t2) it takes for the free fall . Adding the 2 times (t + t2) gives me total time.

This just seems tedious. Is there a way to get time (t) for the whole whole thing all at once? It's easy if Yo = 0 but can't think of way when Yo != 0.

This post was edited by kasey21 on Feb 16 2019 01:17pm

http://www.bergentechstudents.org/2016/fracol/kinematicEquations.gif

Use first equation, replace all x with y. You are solving for when y equals zero. Make sure sign on acceleration is correct.

It will form a quadratic, solve with quadratic equation or some sort of graphing calculator. Hint: time can't be negative.

Let me know if you need more hints.