Motion Under Gravity

Free fall is a special case of uniformly accelerated motion in which the only acceleration is that due to gravity, directed downward with magnitude $g$. The relevant equation of motion is $h=ut+\frac{1}{2}g{t}^2$, where $h$ is the vertical distance fallen. Since the stone is dropped, its initial velocity $u=0$, so the relation reduces to $h=\frac{1}{2}g{t}^2$. Substituting $g=10{\text{ m/s}}^2$ and $t=3\text{ s}$ gives $h=\frac{1}{2}(10)(3^2)=\frac{1}{2}(10)(9)=45\text{ m}$. The option 30 m is wrong because it mistakenly uses $gt$ rather than the quadratic term. The option 90 m omits the factor of one-half. The option 15 m incorrectly takes $\frac{1}{2}gt$ without squaring the time. This is the classic NCERT free-fall result for a body released from rest. As a sanity check, the distance grows with the square of time, so doubling the fall time would quadruple the height, confirming the strong time dependence characteristic of constant-acceleration descent.