Release from certain height

Question

A stone is dropped from the top of a tower of height h. After 1 s another stone is dropped from the balcony 20 m below the top. Both reach the bottom simultaneously. What is the value of h ? Take g = 10 ms^{-2}.

Moderate

Solution

$h=\frac{1}{2}g{t}^{2}\text{and}h-20=\frac{1}{2}g(t-1{)}^{2}\phantom{\rule{0ex}{0ex}}$

Solving them, we get t = 2.5 s and h = 31.25 m.

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