A diving board is at a height of ' $h$ ' from the water surface, A swimmer standing on this board thrown a…

A diving board is at a height of ' $h$ ' from the water surface, A swimmer standing on this board thrown a stone vertically upward with a velocity $16 \mathrm{~ms}^{-1}$. It reaches the water surface in a time of 5 s . In the next 0.2 s , the diver can hear the sound from water surface. The speed of sound is (acceleration due to gravity $\mathrm{g}=10 \mathrm{~ms}^{-2}$ )
  1. $450 \mathrm{~ms}^{-1}$
  2. $225 \mathrm{~ms}^{-1}$
  3. $200 \mathrm{~ms}^{-1}$
  4. $275 \mathrm{~ms}^{-1}$

Solution

$\begin{aligned} & \mathrm{u}=16 \mathrm{~ms}^{-1}, \mathrm{t}_1=5 \mathrm{s} \\ & \therefore \mathrm{~h}=-\mathrm{ut}_1+\frac{1}{2} \mathrm{gt}_1^2=-16 \times 5+\frac{1}{2} \times 10 \times 5 \times 5=45 \mathrm{~m} \end{aligned}$
Now, $\mathrm{d}=\mathrm{v} \times \mathrm{t}_2$ $\Rightarrow 45=\mathrm{v} \times 0.2 \quad \therefore \mathrm{v}=225 \mathrm{~ms}^{-1}$

Asked in: AP EAMCET 2024 (23 May Shift 1)

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