Since h {\displaystyle h} represents the height (in metres) of the rock above the ground level, when the rock hits the surface, h ( t ) = 0 {\displaystyle h(t)=0} .
Solving h ( t ) = 0 {\displaystyle h(t)=0} , we get
h ( t ) = 10 t − 2 t 2 = 2 t ( 5 − t ) = 0 ⟺ t = 0 , 5 {\displaystyle h(t)=10t-2t^{2}=2t(5-t)=0\iff t=0,5} .
Therefore, the answer is t h = 5 {\displaystyle \color {blue}t_{h}=5} .
