Question

A spring gun having a spring of spring constant $k$ is placed at a height $h$. A ball of mass $m$ is placed in its barrel and compressed by a distance $x$. Where shall we place a box on the ground so that the ball lands in the box?

• A. $\frac{kh}{mg} x$
• B. $\sqrt{\frac{2kh}{mg}} x$
• C. $\sqrt{\frac{kh}{2mg}} x$
• D. $\frac{kh}{2mg} $

Answer 1

Answer: (B)

From law of conservation of energy, we have

$\frac{1}{2} m v^2 = \frac{1}{2} kx^2$
$\Rightarrow \:\: v = \sqrt{\frac{k}{m} } x$
Time taken to fall, $t = \sqrt{\frac{2h}{g}}$
So, horizontal distance travelled is
$d = vt = \sqrt{\frac{k}{m}} x \sqrt{\frac{2h}{g}} =\sqrt{\frac{2kh}{mg}} x$