Question

In a spring gun having spring constant $100\text{N/m}$, a small ball $B$ of mass $100\text{g}$ is put in its barrel (as shown in the figure) by compressing the spring through $0.05\text{m}$. There should be a box placed at a distance $d$ on the ground so that the ball falls in it. If the ball leaves the gun horizontally at a height of $2\text{m}$ above the ground. The value of $d$ in meter is _______.

Take $g=10{\text{m/s}}^2$

Answer 1

From energy conservation,

$\frac{1}{2}k{x}^2=\frac{1}{2}m{v}^2$

$\Rightarrow v=x\sqrt{\frac{k}{m}}=0.05\sqrt{\frac{100}{0.1}}$

$\Rightarrow v=\sqrt{2.5}\text{m/s}$

For vertical motion,

$s_y=u_{y}t+\frac{1}{2}{a}_y{t}^2$

$\Rightarrow -2=0\times t-\frac{1}{2}\times 10\times t^2$

$\Rightarrow t=\sqrt{\frac{2}{5}}\text{s}$

For horizontal motion,

$d=vt=\sqrt{2.5}\times \sqrt{\frac{2}{5}}=1\text{m}$