Step 1 :Substitute $t=1$ into the function $h(t)=-16 t^{2}+64 t$ to find the height of the rocket 1 second after it was fired.
Step 2 :Calculate the result: $h(1)=-16(1)^{2}+64(1)=48$
Step 3 :\(\boxed{48}\) feet is the height of the rocket 1 second after it was fired.