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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Linear motion and norms

So I have the following question here... Your friend will lauch a bottle rocket into the air from a launch pad. Upon launch, $0 \leq t \leq 7$ seconds, the rocket will have position $$B(t)=(20t,30t,...
Future Math person's user avatar
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44 views

Modelling Peters Swing from the Becoming Spider-Man Scene - The Amazing Spider-Man (2012)

I am currently working on a project where I model the physics and calculus involved in a successful swing done by spiderman. I have broken down his swing into three segments. The first segment models ...
nicksurz41's user avatar
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1 answer
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Trajectory of a particle in a force vector field

Let's say I have a vector force field as <x, y>, I.e force depends on the position. Now I have a body of mass m, initial position S = <p1, p2> and initial velocity u = <u1, u2>. How ...
DevMayukh's user avatar
0 votes
1 answer
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Using different equations for upwards and downwards travel

I found a mechanics question in the 2022 Mathematics Extension 2 HSC (the final exam in Australia) whose solution didn't quite make sense to me. This is the question: My initial thought was to create ...
Matthew's user avatar
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Dimensional analysis of projectile in nonuniform gravitational field (high altitude projectile)

A well-understood dimensional analysis of the highest point of the projectile in a uniform gravitational field goes like $$ [x_M] = [g^av_0^bm^c]\\ L = (\frac{L}{T^2})^a(\frac{L}{T})^bM^c $$ Equating ...
Il Prete Rosso's user avatar
0 votes
1 answer
108 views

Minimization problem of parametric equations in ballistics (minimum projectile speed)

I am trying to solve a minimization problem for a physics simulation in Unity 3D. In short, a projectile is fired at a certain position with a certain velocity, and experiences a constant acceleration ...
The Innkeeper's user avatar
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90 views

Solution works for 2nd degree polynomial but does not extend to higher degrees.

(I am reposting this from physics stack exchange since they seem to not accept this type of question, and in my case it is also probably more math-focused.) I am trying to solve a 3D ballistics ...
The Innkeeper's user avatar
1 vote
1 answer
109 views

Calculating projectile path between 2 moving objects for given force

For 2 moving objects A and B (mass $m_a$, $m_b$) moving with constant acceleration, given initial accelerations, velocities and positions for both objects, find the velocity required to launch a ...
The Innkeeper's user avatar
19 votes
6 answers
5k views

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'...
Sick Nutmeg's user avatar
0 votes
1 answer
23 views

Unable to determine missing negative in derivation

I am trying to derive an expression for theta (in a projectile motion context). From https://en.wikipedia.org/wiki/Projectile_motion#Angle_required_to_hit_coordinate_.28x.2Cy.29, ; $$\theta=\arctan\...
tophatcollection's user avatar
2 votes
1 answer
175 views

Ball bouncing off a function

Say we have a ball that is dropped from a point $(a,h) $ and falls under acceleration $g$ onto a function $f(x)$, where it hits the function at the point $(a,f(a))$, $h>f(a)$. It will then follow a ...
Sick Nutmeg's user avatar
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Length of a curve given by a function and distance covered by a projectile

Using differentiation, the slope of a curve can be found and using integration, the area under the curve is found. How can calculus be used to determine the length of the curve represented by a given ...
Aurelius's user avatar
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Compute velocity for body with changing mass, constant force

A ball of ice having mass 100 g at time t = 0 s is melting, and therefore losing mass, at a steady rate of 1 g/s. The ball has velocity $\vec{i} + 2 \vec{j}$ at time t = 0 and is subject to a constant ...
userX's user avatar
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1 answer
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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 ...
Belfer4's user avatar
  • 103
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1 answer
219 views

Region of vulnerability of a bullet in projectile motion

I am trying to solve the following question: A gun fires a shot from $O$ with initial speed $V$ at an angle $\theta$ with the horizontal.If the acceleration due to gravity is constant ($g$) prove that ...
Pen and Paper's user avatar
2 votes
1 answer
64 views

Inquiry on Orbital Mechanics

I'm an undergraduate (currently studying precalculus) with an interest in physics. Specifically, I'm interested in the relationship between physics and math which seems to occur often. For example, it ...
muldrowhanif's user avatar
1 vote
1 answer
49 views

Sonic boom of a falling object

Let's say an observer at the bottom of a well of depth $d$ which is situated on an incredibly large planet with gravitational force of $g$. We can assume that the value of $g$ remains constant ...
Sick Nutmeg's user avatar
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0 answers
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Projectile trajectory horizontal travel equation

Working on a system for a game, I'm having a hard time figuring out a reasonable way to predict a trajectory of a projectile. Variables: $a$ - angle in radians $v$ - velocity $t$ - time $y$ - ...
Aras's user avatar
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5 votes
2 answers
422 views

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 ...
Tom's user avatar
  • 301
-1 votes
1 answer
364 views

How to find the angle of a projectile launch knowing only the initial velocity and the coordinates?

I need to find the angle [α] of a projectile launch knowing only the initial velocity and the coordinates of a target that projectile needs to hit [$x_*$, $y_*$]. Coordinates of the start point are ...
Eddy's user avatar
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2 votes
1 answer
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Formulae for projectile motion with resistance proportional to velocity

What are the formulae for resisted projectile motion in which the resistance is proportional to the velocity? I have a problem where my answers don't match up with the textbook answers and I need to ...
Waleed Dahshan's user avatar
0 votes
1 answer
63 views

Find at what initial velocity can the projectile reach $8534m?$ Find velocity and $x$ value when projectile reach $8543m$, without using Graph Method. [closed]

How can I solve this problem not graphically? If it is not possible, what more information do I need? At what initial velocity can the projectile reach $8534m?$ Find velocity and $x$ value when the ...
Cho's user avatar
  • 23
-1 votes
1 answer
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Find a series of expression to describe an objects motion on a non-earth planet

Note: This question is in the context of a Calculus III course. Question: A person throws an arbitrary object on a planet that's not earth. The object is: thrown from height $h_{0}$ thrown at an ...
John's user avatar
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1 vote
0 answers
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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 ...
MacLCM's user avatar
  • 11
0 votes
2 answers
464 views

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 ...
nexo sharp's user avatar
2 votes
2 answers
857 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 ...
Ahmed mk's user avatar
0 votes
1 answer
145 views

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 ...
R3FL3CT's user avatar
  • 113
1 vote
0 answers
43 views

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 ...
Styles's user avatar
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-2 votes
1 answer
46 views

Horizontal SUVAT problem (AS Level)

Could someone please explain how you get the answer for the following question: ...
Habibullah Ahmadi's user avatar
0 votes
1 answer
98 views

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 ...
dekuShrub's user avatar
  • 399
0 votes
0 answers
208 views

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 ...
TTFH's user avatar
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1 vote
1 answer
306 views

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 \...
Daniel D's user avatar
1 vote
1 answer
42 views

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 ...
HARVEER RAWAT's user avatar
0 votes
1 answer
32 views

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 ...
Supreme Poudel's user avatar
0 votes
2 answers
152 views

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 ...
יהודה's user avatar
0 votes
1 answer
155 views

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 ...
op ol's user avatar
  • 465
0 votes
1 answer
97 views

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 ...
Pen and Paper's user avatar
0 votes
1 answer
30 views

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-...
user71207's user avatar
  • 1,543
0 votes
1 answer
37 views

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 ...
nn4l's user avatar
  • 195
0 votes
1 answer
117 views

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 ...
NiFel's user avatar
  • 1
0 votes
0 answers
26 views

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 $...
finlay morrison's user avatar
0 votes
1 answer
169 views

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 ...
Sai Juttu's user avatar
0 votes
1 answer
833 views

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 ...
harpomiel's user avatar
  • 643
0 votes
1 answer
244 views

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 $10 ms^{-2}$ ...
mathshelpmeeee's user avatar
0 votes
1 answer
108 views

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'
Chongzzy's user avatar
1 vote
1 answer
72 views

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 ...
NOTERIC OK's user avatar
0 votes
1 answer
153 views

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 ...
NOTERIC OK's user avatar
2 votes
1 answer
86 views

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 ...
Stephan's user avatar
  • 469
0 votes
3 answers
209 views

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 ...
Large Merge's user avatar
0 votes
0 answers
30 views

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 ...
user1865775's user avatar

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