Answer: Option A
:
A
Let mass of cannon be$m_1$ = $400kg$
Let mass of cannon ball be $m_2$ =$2kg$
Let initial velocities of the cannon and cannon ball be $u_1$ and $u_2$ respectively.
Let final velocity of cannon and cannon ball be $v_1$ and $v_2$ respectively.
From thelaw of conservation of momentum,
total momentum before firing = total momentum after firing.
$\therefore$ $m_1{u}_1+m_2{u}_2=m_1{v}_1+m_2{v}_2$
As the cannon and cannon ball is at rest initially, the initial velocity will be zero, i.e
$0=m_1{v}_1+m_2{v}_2$
Substituting the values:
$0=400\times (-2)+2\times v$
$\Rightarrow v=\frac{400\times 2}{2}=400m{s}^{-1}$
Hence, the velocity of the cannonball will be $400m{s}^{-1}$​
Since we know,
$time=\frac{displacement}{velocity}$
Thus, time taken to hit the target= $\frac{500}{400}$ = $1.25s$