Browse Problems
33 problems tagged with projectile in Kinematics
P0256
Beginner Mechanics › KinematicsAirplane Bombing a Fleeing Ground Target
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.
P0303
Intermediate Mechanics › KinematicsSymbolic Projectile Motion from Speed Graph
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.
- What is the total horizontal distance $R$ the projectile travels before returning to ground level?
- What is the maximum height $H$ attained by the projectile?
P0290
Intermediate Mechanics › KinematicsProjectile Motion Landing on a Slope
A projectile is launched from the origin with an initial speed $v_0$ at an angle $\theta_0$ above the horizontal. It travels under the influence of gravity $g$. The ground below consists of a flat section followed by a downward slope at an angle $\alpha$ to the horizontal. The angle between the projectile's velocity vector and the slope upon landing is $\phi$.
- In a first case, the projectile lands on the slope at the same vertical level as its launch ($y=0$). Find the angle $\phi$.
- In a second case, the projectile is launched from the edge of the slope and lands on it at a point below the launch level. Find the magnitude of the vertical displacement, $|y|$, for this landing.
- For the landing described in Q2, find the angle $\phi$.
P0294
Intermediate Mechanics › KinematicsProjectile Motion Analysis Over a Wall
A projectile is launched from an initial height $h_0$ and is later caught at the same height. It passes over a wall, first on its way up at time $t_1$ after launch, and again on its way down after an additional time interval $\Delta t$. The horizontal distance between the points where the projectile clears the wall is $D$.
- What is the total horizontal distance $R$ traveled by the projectile?
- What is the magnitude of the projectile's initial velocity, $v_0$?
- What is the angle $\theta_0$ (relative to the horizontal) of the projectile's initial velocity?
- What is the height $H$ of the wall, measured from the ground?
P0255
Beginner Mechanics › KinematicsAngled Projectile Motion Velocity and Height
An object is launched at an angle above the horizontal. It reaches its maximum height after $t$. At this highest point, its speed is $v_h$..
- Find the magnitude of the object's initial velocity.
- Find the maximum height the object reaches relative to its launch point.
- Find the range the object reaches on the horizontal plane at the same height as the launch point.
P0257
Beginner Mechanics › KinematicsTheorems on Projectile Motion Range
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.
- Prove that the horizontal range is maximum when the launch angle is $45^\circ$.
- Prove that the horizontal ranges are equal if two launch angles are complementary.
P0258
Beginner Mechanics › KinematicsCondition for Anti-Aircraft Gun Hitting Plane
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.
P0259
Beginner Mechanics › KinematicsProjectile Motion on an Inclined Plane
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$^2$.
- When the projection angle (the angle between the initial velocity and the horizontal) is $45^{\circ}$, what is the range of the ball on the hill?
- At what projection angle is the range of the ball on the hill maximized, and what is this maximum range?
P0260
Intermediate Mechanics › KinematicsSurface Formed by Projectiles Launched Simultaneously
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.
P0211
Beginner Mechanics › KinematicsInitial Velocity of a Horizontal Projectile
An object is projected horizontally from a height $h$. It strikes the ground with a final speed of $v$.
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