Question

A stone is projected at an angle ${45}^{\circ }$ to the horizontal with a velocity $12\sqrt{g}$, where $g$ is acceleration due to gravity at the place. It just passes over a wall $27\text{m}$ high, at a horizontal distance of $108\text{m}$ from the point of projection. Take $g=10{\text{ms}}^{-2}$

• A. The stone passes over the wall during ascent.
• B. The stone passes over the wall during descent.
• C. The difference in velocity at the initial and final point on ground is zero.
• D. The difference in speed at the initial and final point on ground is zero.

Answer 1

Answer: (B), (D)

The correct options are
B The stone passes over the wall during descent.
D The difference in speed at the initial and final point on ground is zero.



During projectile motion, x-coordinate of any point is given by
$x=\left(u\cos {45}^{\circ }\right)t$
$=\left(\frac{12\sqrt{g}}{\sqrt{2}}\right)t=\left(6\sqrt{2g}\right)t$
When stone is just at the wall then,
$x=108\text{m}\Rightarrow 6\sqrt{2g}t=108\Rightarrow t=\frac{108}{6\sqrt{2g}}$
And time taken will be
$t=\frac{18}{\sqrt{2g}}=\frac{9\sqrt{2}}{\sqrt{g}}$
$t_a=\frac{u\sin {45}^{\circ }}{g}=\frac{12\sqrt{g}}{g}\times \frac{1}{\sqrt{2}}=\frac{6\sqrt{2}}{\sqrt{g}}$
(where $t_a=$ the time of ascent)
$\therefore$ clearly, $t>t_a$
$\therefore$ Stone passes over the wall during descent.