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Work, Energy, and Power — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysicsWork, Energy, and Power1 Mark
MCQ
A heavy stone is thrown from a cliff of height $h$ with a speed $\nu.$ The stone will hit the ground with maximum speed if it is thrown:
  • A
    Vertically downward.
  • B
    Vertically upward.
  • C
    Horizontally.
  • ✓
    The speed does not depend on the initial direction.
✓

Answer

Correct option: D.
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., $(\text { K.E. })_i+(\text { P.E. })_{\mathrm{i}}=(\text { K.E. })_{\mathrm{f}}+(\text { P.E. })_{\mathrm{f}}$
$=\frac{1}{2}\text{mv}^2+\text{mgh}=\frac{1}{2}\text{m}(\text{v}_\text{max})^2$
$\Rightarrow\text{v}_\text{max}=\sqrt{\text{v}^2+2\text{gh}}$
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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