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Dropping Objects

A stone is dr...

Question

A stone is dropped from the top of a tall building. A second stone is thrown down from same point 2 seconds later, with an initial speed of 30 m/s. If both stones hit the ground at same instant, find the height of building. ( g = 10 $m / s^{2}$ )

80 m

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60 m

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120 m

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160 m

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Solution

The correct option is A 80 m
$- h = - \frac{1}{2} g t^{2}$ (for 1st stone)
$h = 5 t^{2}$ ---(1)
$- h = - u (t - 2) - \frac{1}{2} g (t - 2)^{2}$ (for 2nd stone)
$h = 30 (t - 2) + 5 (t - 2)^{2}$ ---- (2)
Equating (1) and (2),
$5 t^{2} = 30 t - 60 + 5 t^{2} - 20 t + 20$
$\Rightarrow 10 t - 40 = 0 t = 4$
$h = 5 t^{2} = 5 \times 16 = 80 m$

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