Projectile

A projectile is launched from the ground with an initial speed $v_0$. To be successful, it must pass over a barrier of height $y$ located at a horizontal distance $x$ from the launch point.

A ball is thrown, landing on a roof a time $t$ later. The landing spot is at a height $h$ above the launch point. Just before landing, the ball's path makes an angle $\theta$ with the horizontal roof. Assume the acceleration due to gravity is $g$ and that the ball is descending when it lands.

A projectile is launched from ground level. At a time $t_1$, its horizontal displacement is $x_1$ and its vertical displacement is $y_1$.

A projectile is launched from ground level. A graph of its speed $v$ versus time $t$ shows an initial speed $v_0$ at $t=0$. The speed decreases to a minimum value $v_{min}$ at time $t_h$ and then increases.

An object is launched from the same point with a constant initial speed $v_0$ but at various different projection angles. The motion occurs within a single vertical plane.

As shown in the figure, an object P is located at the top of a flagpole of height $h$. A boy at point O, a horizontal distance $s$ from the base of the flagpole A, shoots a small stone with a slingshot to hit the object P. The initial speed of the stone is $v_0$.

A person throws a stone from the ground level. The stone is considered a projectile moving under the influence of gravity, and air resistance is neglected. The stone must continuously move farther away from the person who threw it throughout its entire flight.

A soccer player kicks a ball from a penalty spot, which is located at a horizontal distance $s = 11$ m from the goal. The ball is kicked such that it passes just under the center of the crossbar, scoring a goal. The height of the crossbar from the ground is $h = 2.5$ m. The mass of the soccer ball is $m = 0.5$ kg. Air resistance is considered negligible.

Two particles are launched from the same point on level ground with the same initial speed $v_0$ but at different launch angles, $\alpha_1$ and $\alpha_2$. They move in the same vertical plane and land at the same distance R from the launch point, as shown in Figure (a). Air resistance is negligible.

An object is launched from the base of a triangular prism resting on a horizontal surface. The left face of the prism has an inclination angle of $\theta$ with the horizontal, and the right face has an inclination angle of $\varphi$. The object is launched with an angle $\alpha$ relative to the horizontal from the bottom corner of the $\theta$-inclined face. The trajectory is such that the object just grazes the peak of the prism and lands at the bottom corner of the $\varphi$-inclined face.