Which of the following metals react with cold water vigorously ?

$2N{a}_{\left(s\right)}+2H_2{O}_{\left(l\right)}\to 2NaO{H}_{\left(aq\right)}+H_{2\left(g\right)}\Rightarrow \text{vigorous reaction}$ 

${\text{2Mg}}_{\left(s\right)}+2H_2{O}_{\left(l\right)}\to Mg{\left(OH\right)}_{2\left(aq\right)}+H_{2\left(g\right)}\Rightarrow \text{very slow reaction}$

Silver does not react with (cold and hot water) water at all. 

Sulphur does not react with cold water under normal conditions.

Hence Na reacts with cold water vigorously.