The height equation for projectile motion (assuming a constant gravitational field and ignoring air resistance is derived from assuming that g is constant). So acceleration is:
a=g upon integrating with respect to t, time in seconds you get the velocity
da/dt=v=gt+C where C is the initial velocity or
v(t)=gt+v0 integrating again you get h(t)
dv/dt=h(t)=gt^2/2+v0t+C where C is the initial height leaving you with:
h(t)=gt^2/2+v0t+h0 given that g≈-9.8m/s^2, v0=20m/s, h0=10 you have:
h(t)=-4.9t^2+29t+10
...
They want you to use the quadratic formula to solve for when h(t)=0.
t=(-29±√1037)/(-9.8), since t>0
t=6.25 seconds (to nearest hundredth)