An object is thrown horizontally from a point $A$ from a tower and hits the ground $3 \mathrm{s}$ later at $B$. The line from $A$ to $B$ makes an angle of ${30}^o$ with the horizontal. The initial velocity of the object is (Take $\mathrm{g}=10 \mathrm{m} {\mathrm{s}}^{-2}$)

A particle is projected from point $A$ with velocity $u\sqrt{2}$ at an angle of ${45}^o$ with the horizontal as shown in the figure. It strikes the plane $BC$ at a right angle. What is the velocity of the particle at the time of impact?

A projectile projected with speed $u$ takes time $t$ to reach from $A$ to $B$. Distance $AB$ is equal to

$CE$ and $DF$ are two walls of equal height $\left(20 \mathrm{m}\right)$ from which two particles $A$ and $B$ of the same mass are projected as shown in the figure. $A$ is projected horizontally towards left while $B$ is projected at an angle $37°$ (with the horizontal) towards left with velocity $15 \mathrm{m} {\mathrm{s}}^{-1}$. If $A$ always sees $B$ to be moving perpendicular to $EF$, then the range of $A$ on the ground is

As shown in the figure, a body is projected with velocity $u_1$ from the point $O$. At the same time, another body is projected vertically upwards with the velocity $u_2$ from the point $B$. The value of $\frac{u_1}{u_2}$ so that both the bodies collide is

Two particles separated at a horizontal distance $x$ are as shown in the figure. They are projected at the same line as shown in the figure with different initial speeds. The time after which the horizontal distance between them becomes zero is

In the figure shown, the two projectiles are fired simultaneously. Find the minimum distance between them during their flight.