Question

A heavy stone is thrown in from a cliff of height h in a given direction. The speed with which it hits the ground
(a) must depend on the speed of projection
(b) must be larger than the speed of projection
(c) must be independent of the speed of projection
(d) may be smaller than the speed of projection.

Answer 1

(a) must depend on the speed of projection
(b) must be larger than the speed of projection

Consider that the stone is projected with initial speed v.
 
As the stone is 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

\[\text{ i . e} . , (K . E . )_i + (P . E . )_i = (K . E . )_f + (P . E . )_f\]

\[\Rightarrow \frac{1}{2}m v^2 + mgh = \frac{1}{2}m( v_{\text{ max } } )^2 \]
\[ \Rightarrow v_{\text{ max } } = \sqrt{v^2 + 2gh}\]

From the above expression, we can say that the maximum speed with which the stone hits the ground depends on the speed of projection and greater than it.