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 

विकल्प

• vertically downward

• vertically upward

• horizontally

• the speed does not depend on the initial direction.

Answer 1

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.