Projectile motion (math mechanics)?

Say init speed particle=v..then vert vel=v/2.. (sin30=0.5)..time to reach max height =t=v/(2*g)..now vert dist =10m= ave vert vel*t=v/4(v/2g)=v^2/(8g)..>v=init speed=rt(80g)=28m/s..minspeed is at apex obv when vert vel=0 and horiz speed =const=v(cos30)=28*rt(3)/2=14rt(3)m/s