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, $0.5s$ 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 $g=10m/s^2$.
The value of $x$ is ______.

Answer 1

Answer: 7.50

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