Mathematics Stack Exchange
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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/

229 questions
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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 $R$.…
Hypergeometricx
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Firing a projectile over a circular obstacle.

I want to fire a projectile in gravity over an obstacle. The obstacle is bounded by a circle of known radius $r$, resting on the ground (so that its center is $r$ above the $y=0$ plane). I will be firing from zero height; I am free to choose my…
JavadocMD
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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?
SpecialBomb
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Projectile Motion with Gun Fire

A gun at O fires shells with an initial speed of 200m/s but with a variable angle of inclination α. Take g=10 m/s^2. (i) If a fortress F is situated 2km away on top of a mountain 1000 metres high show that if the gun is set at an angle of 45 degrees…
user694587
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finding initial vertical velocity and final vertical velocity - projectile motion

find initial vertical velocity and final vertical velocity when a ball has a mass of 280g, flight time of 0.69s and has a length of 0.76m. height of strike is 0.8m. this is a projectile motion question. i'm a little bit stuck since it doesn't give…
Kemal Celik
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Equation of motion on a rotating disk?

When an object moves across a rotating disk it traces out a loop: What is the equation of this loop? The following image portrays a very similar image of a limacon I am not really sure what approach to take on this problem: Could parametric…
User3910
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A rock is thrown into the air from a 40 foot deck with an initial velocity of 112 ft/s. What is the maximum height the rock will reach?

I wasn’t very sure where to start with this one, so I tried looking online to find an example problem. From the ones I looked through, it seems you need at least one of the following variables - maximum height or time in the air. I was not given any…
Vivi O2
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Year 12 Maths - Projectile Motion - My answer is different from the solution - Please help me find out what went wrong! High School Math

I am racking my brain trying to figure out why my answer for part ii) of this question is so different from the solution. Attached are the question (both parts i and ii), my working out for both parts and the answer of part ii). Could someone please…
BooScout
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A projectile is launched at an angle $\alpha$. At its greatest height the angle of elevation is $\beta$. Show that $\tan \beta=0.5\tan \alpha$

Diagram of the question: https://i.stack.imgur.com/f0NfR.jpg The question I have is part (ii) and (iii) A particle is projected from a point $O$ with speed $Vms^{−1}$ at an acute angle $\alpha$ above the horizontal. Acceleration due to gravity is…
Just_A_User
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Calculate a graph of motion for a projectile

I would like to produce a program that can take in a 2D velocity vector, a projectile's mass (projectile should be modelled as a particle in that all of the mass is concentrated at a single point, although ideally I would like to take into account…
F J
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Projectile Motion Clarification: Ball Passing Through Inclined Hole

I want to write a projectile motion question where a spherical ball is launched from the ground with, say, initial velocity $ v $ (applied to the center of the ball) and angle of projection $ \theta $, which then passes through a hole in a ramp…
A.Abbas
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Arrow fired from height h metres projectiles

I have the question "An arrow is fired from a height h meters at a speed of 55 m/s and at an angle of 5 degrees above the horizontal. The arrow hits a target at a horizontal distance of 60 m from where it was fired and at a vertical height of 1.2 m.…
Dan
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If a ball is thrown vertically with air resistance = kv^2, how long till max height?

The question tells me that I throw a ball directly upwards with a mass = m, initial velocity = U, the velocity at any point = V, air resistance = kv^2 and W = terminal velocity. I have to find the time at max height in terms of V, the max height it…
greenie
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Projectile Motion Question About Angle

An object which is projected from the ground with an angle of $\theta$ passes two walls(without touching) within its motion.The wall which has a height of 'a' is situated in a distance of 'v' from the projected place and the other wall which has a…
Nimantha
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How do I solve the angle of a projectile given a desired max height of the arc?

I'm writing a game where I want the player to shoot projectiles that will hit a target point in 3D, the game designers should be able to tweak arc height and gravity only, speed and angle should be derived from this. So far I've worked out the math…
Belfer4
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