Questions tagged [projectile-motion]

This tag is for questions regarding to "projectile motion", the motion of an object thrown or projected into the air, subject to only the acceleration of gravity.

When a particle is thrown obliquely near the earth’s surface, it moves along a curved path under constant acceleration that is directed towards the center of the earth (we assume that the particle remains close to the surface of the earth).The object is called a projectile, its path is called its trajectory and the motion is called projectile motion.

Example: The motion of falling objects, as covered in Problem-Solving Basics for One-Dimensional Kinematics, is a simple one-dimensional type of projectile motion in which there is no horizontal movement.

  • In a projectile motion, the only acceleration acting is in the vertical direction which is acceleration due to gravity $(g)$.
  • Air resistance to the motion of the body is to be assumed absent in projectile motion.
  • Projectile motion only occurs when there is one force applied at the beginning on the trajectory, after which the only interference is from gravity.
  • Equations of motion can be applied separately in $X$-axis and $Y$-axis to find the unknown parameters.

For more details follow the references.

References:

https://en.wikipedia.org/wiki/Projectile_motion

https://byjus.com/physics/projectile-motion/

https://courses.lumenlearning.com/physics/chapter/3-4-projectile-motion/

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What is minimum speed needed to jump over sphere object that has radius $R$ and at distance $d$?

(I am not expert in English. I will write as well as I can.) To understand this question easier, lets see this picture. From this picture, what is minimum initial speed that this grasshopper need to jump over this log? The grasshopper movement path…
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What is the time derivative of speed?

For a particle in projectile motion with a constant upward acceleration of $-9.8\,\mathrm{m/s},$ the time derivative of its speed looks like this: The time derivative of velocity is acceleration, but what is the time derivative of speed,…
Jiamu Yue
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Velocity needed for bullet to circumnavigate earth and land at our feet

Lets say we fire a bullet from a very powerful gun at a height of 1 metre parallel to the surface of the Earth. Assume there is no air resistance and the only force acting on the bullet is from Earth's gravity. Also assume that the Earth is…
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Envelope of Projectile Trajectories

For a given launch velocity $v$ and launch angle $\theta$, the trajectory of a projectile may be described by the standard formula $$y=x\tan\theta-\frac {gx^2}{2v^2}\sec^2\theta$$ For different values of $\theta$ what is the envelope of the…
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Ideal angle to launch from a swing to maximize distance

When I was little (and even now if I can get the chance) I liked to play on swings, and my favorite method of dismounting was to let go mid-swing and fly thru the air. That got me wondering what the best point is to let go of a swing to maximize the…
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Analytical solution of the equation for the launch angle of a projectile travelling the maximum trajectory length

I would like to find an analytical solution to the equation by which the launch angle is found for a projectile to travel the maximum trajectory length. Let $\theta$ be the angle at which the ball is thrown. Then the coordinates are given by $$ x =…
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What is the optimal angle to kick a ball in rugby game?

What is the best angle to kick a ball toward the other team such that when two teams run at each other the teams will meet (when the kicking team tackles the team with the ball) at the distance furthest back from the ball kicker as possible? The way…
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Do these balls collide?

Assume that two balls $B_1,B_2$ of radius $r$ continuously move around inside of a square of size $d$. They bounce off the walls, i.e. the $x$-component of the velocity is multiplied with $-1$ when they hit the left/right wall, and similarly for the…
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Projectile: $v^*w^*=gk$ for minimum launch velocity

A projectile launched from $O(0,0)$ at velocity $v$ and launch angle $\theta$, passes through $P(k,h)$. The velocity of the projectile at $P$ is $w$. The slope of $OP$ is $\alpha$, i.e. $\tan\alpha=\frac hk$, and the length of $OP$ is $R$.…
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Are Position and Velocity (or Velocity and Acceleration) Vectors Always Parallel?

While reading Chapter 1 of an astrodynamics textbook, I came across the statement: $$\mathbf{v}\cdot \mathbf{{\dot{v}}}=v{\dot{v}}$$ In other words, the dot product of velocity and the time-rate-of-change of velocity is simply equal to the product…
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Projectile Motion with Differential Equations

I've been trying to write code that will calculate the required intercept angles of a projectile launch to hit a moving target, a person running around a game world. I have no issues programming things, but I need a bit of help with the…
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High School Projectile Motion and Quadratics

High school students are learning about the basics of solving quadratics and trigonometric ratios, including trigonometric inverses. The eventual goal of their project is to be able to show a reasonable firing solution, given in initial angle…
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Do springs and projectiles under gravity exist in the same family?

Background A 1D vertical spring subject to gravity satisfies Hooke's Law: $$m x''(t) = -kx(t) + g$$ where $m$ is the mass at the end of the spring, $x(t)$ is the position of the mass at time $t$, $x''(t)$ is its acceleration, $k$ is the stiffness…
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Why do so many projectile motion equation examples use $-16$ as the $a$ coefficient?

I see many examples of projectile motion equations using $-16$ as the $a$ coefficent. For example: $$-16t^2+36t+50$$ Why is this?
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How to calculate optimal angle for maximum range of a projectile - on a hill

Basically, the following problem was tasked to the first-time physics students: Calculate the angle needed for the maximum range of a projectile, except in this case the projectile is on a hilltop and there is a steady angle going downwards at 8…
hellowwwww
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