Browse Problems
33 problems tagged with projectile
P0295
Intermediate Mechanics › KinematicsProjectile Minimum Speed vs Flight Time
A projectile is launched from level ground with a constant initial speed $v_0$. The launch angle $\theta_0$ can be varied. The maximum possible range is $R_{max}$, and the maximum possible flight time is $t_{max}$.
P0296
Intermediate Mechanics › KinematicsBall Rolling Horizontally Off a Staircase
A ball rolls horizontally off the top of a stairway with an initial speed $v_0$. The steps each have height $h$ and width $w$.
P0299
Intermediate Mechanics › KinematicsProjectile Initial Velocity from Position Data
A projectile is launched from ground level. At a time $t_1$, its horizontal displacement is $x_1$ and its vertical displacement is $y_1$.
- What is the horizontal component of the initial velocity, $v_{0x}$?
- What is the vertical component of the initial velocity, $v_{0y}$?
- What is its horizontal displacement, $x_{peak}$, when it reaches its maximum height?
P0312
Advanced Mechanics › KinematicsLocus of Projectile Trajectory Apexes
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.
P0314
Advanced Mechanics › KinematicsMaximum Launch Angle for a Receding Projectile
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.
P0315
Advanced Mechanics › KinematicsMinimum Work to Kick a Soccer Ball
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.
P0278
Expert Mechanics › KinematicsProjectile Motion and Parabolic Safety Envelope
A small ball is thrown with an initial velocity $v_0$ in a uniform gravitational field. The plane of motion of the ball is the xz plane. The x-axis is horizontal, and the positive z-axis is opposite to the direction of gravitational acceleration $g$. Air resistance is ignored.
- Assume the ball is launched from the origin with a constant initial speed $v_0$. By adjusting the launch angle, all targets within the region $z \le z_0 - kx^2$ can be hit. This inequality does not need to be proven. Find the expressions for the parameters $z_0$ and $k$.
- Now, the launch point of the ball can be chosen anywhere on the horizontal plane $z=0$, and the launch angle can also be adjusted. The objective is to hit the highest point of a spherical building of radius $R$ (Figure 1.1), which rests on the ground at the origin. The ball must not bounce on the building before hitting the target. Qualitatively determine the shape of the ball's optimal trajectory (the one requiring minimum initial speed).
- In order to hit the highest point of the spherical building of radius $R$, find the expression for the minimum initial launch speed $v_{min}$.
P0254
Beginner Mechanics › KinematicsAnalyzing a Horizontal Projectile's Trajectory
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.
- Find the initial height from which the object was launched.
- Find the horizontal range of the object.
P0305
Intermediate Mechanics › KinematicsProjectile Range from an Elevated Height
A projectile is launched with an initial speed $v_0$ from a height $h$ above the ground. The launch angle is $\theta$ with respect to the horizontal.
P0342
Intermediate Mechanics › KinematicsProjectile Motion Normal Acceleration and Curvature
A small ball is launched horizontally from the top of a building with an initial speed of $v_0 = 10$ m/s. Air resistance is negligible. At a certain point in its trajectory, the magnitude of the ball's normal acceleration is $a_n = 5$ m/s².
- Find the vertical distance the ball has fallen to reach this point.
- Find the radius of curvature of the trajectory at this point.
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