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$m/s^2$.

Answer 1

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

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

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

$\therefore$ h = 45m