A stone is thrown horizontally from a tower with a certain velocity and at the same time, another stone is dropped freely from the same height which stone reaches earlier? Explain.

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Solution

Case:1 $u_{x} = u, u_{y} = 0$
Case:1 $u_{x} = o, u_{y} = 0$ where
$u_{x}$ =initial velocity in x-direction
$u_{y}$ =initial velocity in y-direction
In case-1, $u_{y} = 0$
$H = u_{y} t + \frac{1}{2} g t^{2}$
$t = \sqrt{\frac{2 H}{g}}$ [t-time of flight]
In case2, $u_{y} = 0$
$H = \frac{1}{2} g t^{2}$
$t = \sqrt{\frac{2 H}{g}}$
Therefore,both reach at same time.

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A stone is thrown horizontally from a tower with a certain velocity and at the same time, another stone is dropped freely from the same height which stone reaches earlier? Explain.

Case:1 ux=u,uy=0Case:1 ux=o,uy=0 where ux=initial velocity in x-directionuy=initial velocity in y-directionIn case-1, uy=0H=uyt+12gt2t=√2Hg [t-time of flight]In case2,uy=0H=12gt2t=√2HgTherefore,both reach at same time.