Question

A ball thrown vertically upward rises to a height of $20m$. If the acceleration due to gravity is $10m{s}^{-2}$, calculate the time taken to gain the maximum height?

Answer 1

Step 1: Given data

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

Final velocity of the ball, $v=0$

Acceleration due to gravity, $g=10m{s}^{-2}$

Height attained by the ball, $h=20m$

Step 2: Calculating the initial velocity of the ball

Applying equation of motion for the freely falling object,

$$\begin{gathered} v^2=u^2+2gh \\ \Rightarrow 0=u^2+2\times (-10m{s}^{-2})\times 20m \\ \Rightarrow u=20m{s}^{-1} \end{gathered}$$ [ '$g$' is negative when a body is projected upwards]

Step 3: Calculating the time taken to gain the maximum height

$$\begin{gathered} v=u+gt \\ \Rightarrow 0=20m{s}^{-1}+(-10m{s}^{-2})\times t \\ \Rightarrow t=\frac{20m{s}^{-1}}{10m{s}^{-2}} \\ \Rightarrow t=2s \end{gathered}$$ [ '$g$' is negative when a body is projected upwards]

Hence, the time taken to gain the maximum height is $2s$.