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Finding Average Velocity

From the give...

Question

From the given data, can you find average speed?
A stone is dropped from the top of a tower. When it crosses a point 5 m below the top, another stone is let fall from a point 25 m below the top. Both stones reach the bottom of the tower simultaneously. Find the height of the tower. Take g = 10 $m / s^{2}$ .

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Solution

let the height of the tower =h
time taken by the first stone to travel 5m from the top = $\sqrt{\frac{2 \times 5}{g}}$

time taken by the second stone to reach the ground = $\sqrt{\frac{2 (h - 25)}{g}}$

$⟹$ $\sqrt{\frac{2 h}{g}}$ - $\sqrt{\frac{2 \times 5}{g}}$ = $\sqrt{\frac{2 (h - 25)}{g}}$

$⟹$ $\sqrt{2 h}$ - $\sqrt{10}$ = $\sqrt{2 h - 50}$
$∴$ h = 45m

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