The problem is a homemade rocket, with an initial speed of 20m/s only in the y axis. Yo want to know the maximun high it can reach and the time it takes to reach that high
The speed diagram is the next one:
Solution
[tex]\begin{gathered} v_0=\frac{20m}{s} \\ v_f=\frac{0m}{s} \end{gathered}[/tex]The final speed is 0 because is when it reach the maximum high
[tex]\begin{gathered} v_f=v_0-gt \\ \frac{\mleft(v_f-v_0\mright)}{-g}=t \\ \frac{-\frac{20m}{s}}{-\frac{9.81m}{s^2}}=2.03s=t \end{gathered}[/tex][tex]\begin{gathered} v^2_f=v^2_0-2gd \\ \frac{-\sqrt[]{20^2}}{-2\cdot9.81}=1.02m=d \end{gathered}[/tex]