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?

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) (kh/mg) x (B) √(2kh/mg) x (C) √(kh/2mg) x (D) (kh/2mg)

Tardigrade Admin · Accepted Answer

From law of conservation of energy, we have

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

\Rightarrow v = \frac{k}{m} x

Time taken to fall,

t = \frac{2 h}{g}

So, horizontal distance travelled is

d = v t = \frac{k}{m} x \frac{2 h}{g} = \frac{2 kh}{m g} x

Q. 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?

$\frac{kh}{m g} x$

$\frac{2 kh}{m g} x$

$\frac{kh}{2 m g} x$

$\frac{kh}{2 m g}$

From law of conservation of energy, we have

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

Q. 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?

mgkh​x

mg2kh​​x

2mgkh​​x

2mgkh​