Question

A cricket ball is vertically thrown upward, which rises to the height of $10m$. If $g=10m{s}^{-2}$, the time in which it rises up to the maximum height is:

• A. $1.53s$
• B. $1.63s$
• C. $1.55s$
• D. $1.43s$

Answer 1

The correct option is D

$1.43s$

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, $h=10m$

Time taken to attain maximum height, $t=?$

Step 2: Calculating the initial velocity of the ball

Applying 3rd equation of motion for the freely falling object,

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

Step 3: Calculating the time taken to attain maximum height

Applying 1st equation of motion for the freely falling object,

$$\begin{gathered} v=u+gt \\ \Rightarrow 0=10\sqrt{2}m{s}^{-1}+(-10m{s}^{-2})\times t \\ ⟹t=\sqrt{2}s=1.43s \end{gathered}$$[ '$g$' is negative when a body is projected upwards]

Therefore, time taken to attain maximum height, $t=1.43s$

Hence, the correct answer is option (D) i.e. $1.43s$