Question

A projectile is thrown from a point $O$ on the ground at an angle $45^{\circ}$ from the vertical and with a speed $5 \sqrt{2} \,m / s$. The projectile at the highest point of its trajectory splits into two equal parts. One part falls vertically down to the ground, $0.5\, s$ after the splitting. The other part, $t$ seconds after the splitting, falls to the ground at a distance $x$ meters from the point $O$. The acceleration due to gravity $g =10 \,m / s ^{2}$.
The value of $x$ is ______.

Answer 1

Velocity of projectile at highest point $5\, m / s \hat{ i }$
Since, there is no external force in horizontal direction so by conservation of momentum
$m (5)=\frac{ m }{2}(0)+\frac{ m }{2}( v )$
$\vec{ v }=10 \,m / s \hat{ i }$
Distance covered by second mass before landing = $\frac{\text { Range }}{2}+10(t)=7.5\, m$