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.

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How can you make the position vector eqx independent so that it just describes a path instead of path linked to a velocity via its derivative?

So I was attempting to learn how to model trajectories and I cannot connect the dots on how to change the velocity of a trajectory following a path described by a function of time, since the velocity ...
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Calculate Projectile flight time based on Gravity

Hey I want to calculate the flight time of a Projectile in 3D Space based on Bullet's speed, Velocity, Acceleration and Gravity or a custom downward force. I already have a formula that calculates the ...
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2 answers
178 views

maximum range of projectile launched from elevation

I am trying to find the maximum range of projectile from an elevation. I found the answer in this question, but I have two questions: Why does $y$ need to be $0?$ Why do they differentiate with ...
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Initial speed required to reach a certain distance

I have a game where I am trying to calculate the initial speed required of a ball to reach a certain distance. The game is simulated in steps every step the ball is advanced by dx pixels. After every ...
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How to solve equation for drag force?

I've been working on graphing the movements of a sphere when thrown. I'm trying to simulate air resistance. I've found the equation $$F_d=\frac12 C_d\rho V^2A$$ I've separated the velocity into x and ...
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Where will the projectile strike the plane??

A particle is projected with velocity $V $,at an angle of $75^0$ to the horizon,from the foot of a plane whose inclination is $30^0.$I have to find where it will strike the plane. In the given ...
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Horizontal SUVAT problem (AS Level)

Could someone please explain how you get the answer for the following question: ...
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1 answer
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Projectile motion - Initial $y$-velocity to hit $(x,y)$ with given $x$ velocity.

I want a function $f(v_{0x}, x_{end}, y_{end})$ that computes the starting velocity component $v_{0y}$ required to make the projectile land at the specified position $(x,y)$. $v_{0y}$ is thus the ...
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Projectile motion for negative height and angle

I'm trying to implement a turret in a game that compensate for bullet drop, I'm using the equations 1) and 2) from the next image to obtain the angle of the turret and time of flight. But it doesn't ...
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Rearranging with theta on both sides and SEC!

I need to get an equation for theta in terms of x. This is how far I've got but my skill has fully run out. Idek if it is possible tbh. Any help would be super appreciated. theta = arcsin(0.156tan(0....
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Can anyone help me solve this hard physics vector problem? Thanks

River vector problem John is on the west bank of a river that flows from north to south at a speed of $5 \text{m/s}$. She is easily able to swim at a constant speed of $1\text{m/s}$. The river is $30 \...
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How to prove that $v_3t_1=t_2v_1$ for projectile motion

I have the following equation before me: Let $\alpha$, $\alpha-\beta$ and $\alpha-2\beta$ be the angles made with the horizontal by a projectile at three points $A$, $B$ and $C$ respectively where ...
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Projectile motion question when the object releasing body is also in motion. [closed]

So when dealing with this type of questions we separate the motion into horizontal and vertical components and treat them independently. When dealing with the horizontal component for this projectile ...
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What does $\Delta y_{max} = \frac{v_0^2\sin^2(\theta)}{2y}$ mean, and how does one calculate it?

I am learning about projectiles in my physics course and was recently introduced to this equation: $$\Delta y_{max} = \frac{v_0^2\sin^2(\theta)}{2y}$$ I am having a hard time making sense of it. How ...
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Projectile motion in a vacuum

I got stuck on exercise 26, 566p in calculus by morris kline. A projectile is fired at an initial velocity of 160 ft/sec. Find the angle of fire $A$ so that the projectile will strike a wall 480 feet ...
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Determining resistive force components with the quadratic drag model in projectile motion

I'm trying to determine the resistive force components for projectile motion with a resistive force, R that is proportional to the square of the velocity i.e. $R=kv^2$, where $v=\sqrt{v_x^2+v_y^2}$. ...
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Motion question on escape velocity

Assume that the magnitude and direction due to gravity at a point outside Earth at distance $x$ from the Earth's centre is equal to $-\frac{k}{x^2}$, where $k$ is a constant. i) Neglecting atmospheric ...
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Finding the desired angle of projection under conditions

A firework is projected from the origin, whose path is governed by the equations $x = 70t\cos{a}$, $y = 70t\sin{a} - 4.9t^2$. Find $a$ such that the equalities $y>150$ (meters) and $130<x<150$...
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What do the conditions mean in projection motion?

Two people are throwing a ball from shoulder height $S$ in a hallway with ceiling $H$ meters high. The ball is thrown with velocity $v$. Show that the maximum separation is $d=4\sqrt{(H-S)v^2/2g - (H-...
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Motion equations for rocket visiting several checkpoints on its path

For a computer game, I would like to study the motion of a rocket flying from a point A to point B on a two-dimensional plane. It is required that the speed of the rocket is zero both at the start and ...
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Projectile Motion - Trajectories From Points

For a little background, this problem came up due to something I'm trying to code, however the problem itself is disparate from that. I know the basics of projectile motion and kinematics from a pair ...
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Modelling an object travelling through an atmosphere

I am trying to model an object travelling through an atmosphere of uniform density with a uniform gravitational acceleration. I have the two equations that will describe the forces, $F_g = mg$ and $...
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Is this the correct way to calculate the proper shoot angle to compensate for bullet drop?

This is my first post on this website and my friends in robotics recommended it to me for math help, so my apologies if I have any of the formatting wrong or any other issues. So my I have a barrel ...
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Projectiles question involving parallel motion

I'm trying to understand the mark scheme for the following question: A small stone is projected from a point O at the top of a vertical cliff OA. The point O is 52.5 m above the sea. The stone rises ...
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Trajectory of a ball thrown over a wall, from a height, using cartesian equations and differentiation

A person attempts to throw a ball over a wall of height $5m$ that is $12m$ away. It is thrown at a speed of $u ms^{-1}$ from a height of $2m$ at an angle $θ$ to the horizontal. Gravity is $10 ms^{-2}$ ...
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To find the angle a particle makes with the horizontal at any time 't'

Should you vector sum the position vectors at this time 't' or vector sum the velocity vector at this time 't' to find the angle a particle makes with the horizontal at any time 't'
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1 answer
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What is the initial velocity when dealing with projectile motion? [closed]

my question is with the image below what would the initial velocity be? My teacher says the initial velocity is 40 m/s however my textbook says the initial velocity is 20$ \sqrt{3} $ i + 20 j m/s. So ...
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Stuck On A Projectile Motion Question, Is My Answer Correct Or The Textbook Answer?

A stone is thrown to hit a small target, which is at a distance of $14$ m horizontally and $5.5$ m vertically upwards from the point of projection. The stone is thrown from a height of $2$ m above the ...
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2 votes
1 answer
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Projectile motion up a plane.

I'm stuck on the following simple projectile motion problem up a plane. Below is the question: A plane is inclined at an angle $\alpha$ to the horizontal. A particle is projected up the plane with ...
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Finding the initial launch angle of a projectile so that it reaches a certain point when a 2D acceleration is applied.

I'm trying to write an AI that can predict at which angle to throw a projectile so that it reaches a certain target position. It is on a 2D plane where the only acceleration applied to the object is ...
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Can anyone expound this Projectile Motion computation please?

I have this formula for projectile motion that I'm using in Unity for getting the low or high direction of a shot, and it works. However, I'd love to understand the equation. And notably, Why ...
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172 views

How to find the maximum height of a launched projectile

Given the probability density of launching a projectile at an angle $\theta$ directed above the horizontal such that $ f(\theta) = \begin{cases} K, & \text{$\frac{\pi}{6}<\theta<\...
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Is this projectile motion equation correct for a weapon firing a bullet? It appears gravity isn't that strong.

I used this website to help me generate displacement parametric equations for projectile motion. I have these equations: $x= ut\cos(θ)$ and $y=ut\sin(θ)-\frac{1}{2}gt^{2}$ Where $x$ is the distance ...
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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 - ...
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1 answer
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'Simple' Projectile motion question passing through 2 points on the same level

I have, what I think, is a relatively simple projectile motion problem. Yet I'm struggling to come up with a solution. A particle is projected with a speed $u$ at and angle $\alpha$ to the horizontal....
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1 vote
2 answers
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How to extract Parametric Equations from a Problem

How can I extract parametric equations from a scenario which is given in a problem like this: A hitter's bat meets a ball about 3 ft above home plate. Suppose the horizontal component of the ball's ...
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OCR A Level Projectile motion question: Solution verification

Question taken from the book is in the image above. $$$$ The solution in the back of the book is Solution $2$. However, I believe that the partcile is on the way down when $\theta = 37^\circ.$ $\tan \...
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Calculating Launch Angles for a Projectile With a Constant Wind Force

I'm trying to find a way to calculate the azimuth (a) and elevation angle (e) to have a projectile with a velocity of magnitude <...
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Solving a system of (projectile motion) second order differential equations

I have a system of two second order differential equations, and some initial conditions. I know how to solve it using MATLAB but my problem is with the 4 initial conditions, two of them have an ...
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1 vote
2 answers
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Given two points in three dimensions, how can one find the direction of motion and angle of descent of a projectile?

Say you shoot a basketball and you have the data for the ball's x, y, and z coordinates (where z is height and peaks at around z=16) through its time in the air. That's the data that I have. I want to ...
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0 votes
1 answer
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Trouble finding the velocity of a projectile launched from a height

The following question has been giving me trouble for a while now, it states A particle is thrown with speed $10 \space \text{ms}^{-1}$ from a point $2\space \text{m}$ from the ground, at an angle ...
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2 answers
45 views

Formula for range of a projectile landing at some distance above the ground

What will be the formula for range of the projectile if it is launched from the ground level but lands at some height about the ground? I have searched everywhere for the answer, but everyone has ...
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-1 votes
1 answer
132 views

Arc length meaning

I am currently studying about Parametric integration and very confuse about the arc length meaning. In my understanding, the arc length is the total length that an object traveled along a curve in a ...
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2 answers
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Maximal area under projectile trajectory

Problem: A projectile is fired with an initial velocity of $v$ at an angle of $\theta$ from the ground. Then its trajectory can modeled by the parametric equations \begin{align*} x &= vt \cos \...
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Calculating Time of flight of flight from Horizontal velocity component

A question asks to calculate "How long the ball was in the air" and provides following data points: $$ initial\ velocity\ \ v_0=10ms^{-1}\\ Angle\ of\ Launch\ = 45^\text{o}\\ Horizontal\ ...
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2 votes
1 answer
54 views

Mathematics of Skidding When Cornering

I want to do a top down computer model with rectangles representing cars and then the wheels drawn separately. I want this for a road safety class. I want to represent the movement of that car when it ...
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Is the speed of sound modelled by a linear equation?

A cannonball is launched from a point 100 m above ground, at a speed of 20 m/s. This is modelled by the equation $h(t)=-4.9t^2 +20t +100$ The speed of sound (of the cannonball is) 380m/s If a person ...
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1 vote
1 answer
2k views

How can I solve initial velocity for a projectile given the max height and distance

I'm trying to find the initial velocity of a tennis ball (magnitude and angle) given the initial height, max height and max range. I believe this is possible with the equations below but I'm ...
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1 vote
1 answer
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Maximize the distance of projectile motion

In a projectile motion, consider the projectile to be launched from $(0,0)$ as traced to be on cartesian axes. Then the trajectory is given by $$y=x \tan \theta \big(1-x/R)$$ where $\theta$ is ...
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How can I achieve S curve profile

I want to plan robot's motion according to S curve profile.I am following the bellow mention article,which contain basics related to S curve motion profiles in robotic platforms. https://www.pmdcorp....
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