A stone is thrown vertically up from the top end of a window of height 1.8 m with a velocity of $8 \mathrm{~ms}^{-1}$. The time taken by the stone to cross the window during its downward journey is (Acceleration due to gravity $=10 \mathrm{~ms}^{-2}$ )

• A

  0.8 s
• B

  1.6 s
• C

  1.0 s
• Correct answer
  D

  0.2 s

Solution

Time to reach maximum height (A) from the top end of the window using $\begin{aligned} & v=u+g t \text { or, } 0=8+-10 \times t \\ & \therefore \quad t=0.8 s \end{aligned}$ Height from top end of window to A using $\mathrm{h}=\mathrm{ut}+\frac{1}{2} \mathrm{gt}^2$ $\mathrm{h}=0 \times \mathrm{t}+\frac{1}{2} \times 10 \times(0.8)^2=3.2 \mathrm{~m}$ $\therefore$ Total height $\mathrm{h}+1.8=3.2+1.8=5 \mathrm{~m}$ Time to reach the ground from height $\mathrm{A} 5=\mathrm{ut}^{\prime}+\frac{1}{2} \mathrm{gt}^{t^2}$ $\begin{aligned} & \Rightarrow 5=0+\frac{1}{2} \times 10 \times\left(\mathrm{t}^{\prime}\right)^2 \\ & \therefore \quad \mathrm{t}^{\prime}=1 \end{aligned}$ Hence time to cross the window during its down and journey $=\mathrm{t}^{\prime}-\mathrm{t}=1-0.8=0.2 \mathrm{~s}$

Hence, the correct answer is option: 'D'.