Question

A stone is thrown vertically upward returns back to the thrower in $6s$.The maximum height attained by the stone is: [$g=10m{s}^{-2}$]

• A. $25m$
• B. $35m$
• C. $40m$
• D. $45m$

Answer 1

The correct option is D

$45m$

Step 1: Given data

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

Final velocity of the stone, $v=0$

Time taken by the stone to get back to the thrower , $T=6s$

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

Height attained by the stone, $h=?$

Step 2: Calculating the initial velocity of the stone

Time of ascent is equal to the time of descent. So, the stone has taken $t=\frac{6s}{2}=3s$ to attain the maximum height.

Applying the equation of motion for the freely falling object,

$$\begin{gathered} v=u+gt \\ \Rightarrow 0=u+(-10m{s}^{-2})\times 3s \\ ⟹u=30m{s}^{-1} \end{gathered}$$[ '$g$' is negative when a body is projected upwards]

Step 3: Calculating the maximum height attained by the stone

Applying equation of motion for the freely falling object,

$$\begin{gathered} v^2=u^2+2gh \\ \Rightarrow 0={(30m{s}^{-1})}^2+2\times (-10m{s}^{-2})\times h \\ ⟹h=45m \end{gathered}$$[ '$g$' is negative when a body is projected upwards]

Therefore, the maximum height attained by the stone is $45m$.

Hence, the correct answer is option (D) i.e. $45m$.