The driver of car moving towards a rocket launching pad with a speed of $6m{s}^{-1}$ observed that the rocket is moving with speed of $10m{s}^{-1}$. The upward speed of the rocket as seen by the stationary observer is 

Velocity of rocket w.r.t driver in car = velocity of rocket w.r.t ground - velocity of car w.r.t ground

$$\begin{gathered} {\overrightarrow{V}}_{RD}={\overrightarrow{V}}_{RG}-{\overrightarrow{V}}_{DG} \\ Let us assume car is moving along x-axis and rocket is moving along y-axis \\ {\overrightarrow{V}}_{DG}=6\hat{i} , {\overrightarrow{V}}_{RG}=v\hat{j} \\ \overrightarrow{V_{RD}}=-6\hat{i}+v\hat{j} ,given \left|{\overrightarrow{V}}_{RD}\right|=10m{s}^{-1} \\ \Rightarrow \sqrt{v^2+6^2}=10 \\ \Rightarrow v=8 \\ So{\overrightarrow{V}}_{RG}=8m{s}^{-1} \end{gathered}$$