A fire cracker is fired and it rises to a height of 1000 m. Find the velocity by which it was released and the time taken by it to reach the highest point (take a = 10 m/s?).

Dear student,

(1) h=1000m =S
      v= 0 m/s (at highest point)
       g= 10 m/s² ( taken to be negative according to sign convention)
      

Using the 3^rd equation  of motion,
$$\begin{gathered} v^2 - u^2 = 2aS \\ \Rightarrow 0 - u^2 =- 2 \times 10 \times 1000 \\ \Rightarrow u^2 = 20000 \\ \Rightarrow u = 141.42 m/s \end{gathered}$$

(2) u=141.42 m/s (as calculated above)
1^st equation of motion,
$$\begin{gathered} V=u+at \\ \Rightarrow 0=141.42-10t \\ \Rightarrow 10t=141.42 \\ \Rightarrow t=14.142 sec \\ \Rightarrow t=14.1 sec \left(approx\right) \end{gathered}$$

velocity by which it is released is 141.42m/s
and time taken to reach the highest point =14.1 sec
Regards,