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Question
A heavy stone is thrown from a cliff of height h with a speed v. The stoen will hit the ground with maximum speed if it is thrown
Options
vertically downward
vertically upward
horizontally
the speed does not depend on the initial direction.
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Solution
the speed does not depend on the initial direction.
As the stone falls under the gravitational force, which is a conservative force, the total energy of the stone remains the same at every point during its motion.
From the conservation of energy, we have:
Initial energy of the stone = final energy of the stone
\[i . e . , (K . E . )_i + (P . E . )_i = (K . E . )_f + (P . E . )_f\]
\[\Rightarrow \frac{1}{2}m v^2 + mgh = \frac{1}{2}m( v_{\text{max}} )^2 \]
\[ \Rightarrow v_{\text{max}} = \sqrt{v^2 + 2\text{gh}}\]
From the above expression, we can say that the maximum speed with which stone hits the ground does not depend on the initial direction.
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