Projectile

Two people are playing catch. The ball is thrown and caught at the same height. The horizontal distance between them is $s$, and the total time of flight for the pass is $t$.

An object is launched horizontally from an unknown height. It hits the ground with a final speed of $v_f$ at an angle of $\theta$ with the horizontal.

An object is launched at an angle above the horizontal. It reaches its maximum height after $t$. At this highest point, its speed is $v_h$..

An airplane flies horizontally at a height $h$. Directly ahead on the ground, a target moves away from the plane in the same direction with a constant speed $v_t$. The pilot releases a bomb when the horizontal distance to the target is $d$. The bomb successfully hits the target.

An object is launched from level ground with a fixed initial speed $v_0$ at an angle $\theta$ above the horizontal. Air resistance is negligible.

An airplane flies horizontally at a speed $v_1$ at an altitude $h$ above the ground. When the airplane is directly above an anti-aircraft gun, the gun fires a shell with an initial velocity $v_0$ at an angle $\alpha$ with the horizontal. Air resistance is negligible.

A small ball is projected from the base of a hill with a slope of $30^{\circ}$. The initial speed of the ball is $v_0 = 10$ m/s. Let $g = 9.8$ m/s$^2$.

From the same point, many small balls are thrown simultaneously in all different directions, each with the same initial speed $v$. After a time $t$, none of these balls have hit any other objects.

As shown in the figure, a water gun located on the ground is at a perpendicular distance of $d=3.0$ m from a vertical wall of height $h=4.0$ m. A stream of water is ejected from the gun with an initial velocity $v_0$ at an angle $\alpha$ with respect to the horizontal. The water stream must just clear the top of the wall. Air resistance is negligible, and the acceleration due to gravity is $g=10$ m/s$^2$.

An object is projected horizontally from a height $h$. It strikes the ground with a final speed of $v$.