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
(a) vertically downward
(b) vertically upward
(c) horizontally
(d) the speed does not depend on the initial direction.

Answer 1

(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
$\mathrm{i}.\mathrm{e}.,(K.E.{)}_i+(P.E.{)}_i=(K.E.{)}_f+(P.E.{)}_f$
$$\begin{gathered} \Rightarrow \frac{1}{2}m{v}^2+mgh=\frac{1}{2}m(v_{max}{)}^2 \\ \Rightarrow v_{max}=\sqrt{v^2+2gh} \end{gathered}$$

From the above expression, we can say that the maximum speed with which stone hits the ground does not depend on the initial direction.