Question

A stone thrown vertically upward, takes $3s$ to attain the maximum height. Calculate the initial velocity of the stone. [Take $g=9.8m{s}^{-2}$]

Answer 1

Step 1: Given data

Initial velocity, $u=?$ (To be calculated)

Final velocity of the stone, $v=0$

Acceleration due to gravity, $g=9.8m{s}^{-2}$

Time taken, $t=3s$

Step 2: Calculating the initial velocity of the stone

Applying equation of motion for the freely falling object,

$$\begin{gathered} v=u+gt \\ \Rightarrow 0=u+(-9.8m{s}^{-2})\times 3s \\ ⟹u=29.4m{s}^{-1} \end{gathered}$$[ '$g$' is taken negative when body is projected upwards]

Hence, the initial velocity of the stone is $29.4m{s}^{-1}$