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 $g =10 m / s ^2$.
($1$) The value of $t$ is. . . . . .
($2$) The value of $x$ is. . . . .
Give the answer or qution ($1$) and ($2$)
$50,7.50$
$50,7.60$
$50,7.70$
$50,7.80$
An aeroplane moving horizontally with a speed of $180\, km/hr$. drops a food packet while flying at a height of $490\,m$. The horizontal range is........$m$
Two bullets are fired horizontally and simultaneously towards each other from roof tops of two buldings $100 \;\mathrm{m}$ apart and of same helght of $200 \;\mathrm{m}$ with the same velocity of $25\; \mathrm{m} / \mathrm{s}$. When and where will the two bullets collide. $\left(g=10 \;\mathrm{m} / \mathrm{s}^{2}\right)$
A body of mass $M$ thrown horizontally with velocity $v$ from the top of the tower of height $\mathrm{H}$ touches the ground at a distance of $100 \mathrm{~m}$ from the foot of the tower. A body of mass $2 \mathrm{M}$ thrown at a velocity $\frac{v}{2}$ from the top of the tower of height $4 \mathrm{H}$ will touch the ground at a distance of. . . . ..
A ball of mass $0.2 \ kg$ rests on a vertical post of height $5 m$. A bullet of mass $0.01 \ kg$, traveling with a velocity $V / s$ in a horizontal direction, hits the centre of the ball. After the collision, the ball and bullet travel independently. The ball hits the ground at a distance of $20 \ m$ and the bullet at a distance of $100 \ m$ from the foot of the post. The initial velocity $V$ of the bullet is
Two guns $A$ and $B$ can fire bullets at speed $1\, km/s$ and $2\, km/s$ respectively. From a point on a horizontal ground, they are fired in all possible directions. The ratio of maximum areas covered by the bullets fired by the two guns, on the ground is