# 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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### 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 ...
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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 ...
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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 ...
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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 ...
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### 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 ...
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### 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 ...
1 vote
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### 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 ...
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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 $y$ - ...
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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 ...
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### 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 ...
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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 ...
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### 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 ...
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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 ...
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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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### 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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### 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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### 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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1 vote
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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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