check the picture below.
so the ball hits the ground when y = 0, namely h(t) = 0.
[tex] \bf \stackrel{h(t)}{0}=-5t^2+14t+3\implies 5t^2-14t-3=0\implies (5t+1)(t-3)=0
\\\\[-0.35em]
~\dotfill\\\\
5t+1=0\implies 5t=-1\implies t=-\cfrac{1}{5}
\\\\[-0.35em]
~\dotfill\\\\
t-3=0\implies \boxed{t=3} [/tex]
we can't use the -1/5 because, the seconds after 0, can't be negative.
