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 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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63 views

what is the math for gravity causing different kinds of orbit ( ellipse, parabola ,straight line ) for an object in different cases?

case-1: the motion or you can say the orbit of a projectile is parabolic because gravity acts on it. case-2: the motion or the orbit of an object ...
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42 views

Angle of Inclination if Range is at Maximum

If the horizontal range of a projectile launched, without air resistance is given by: $$R = \frac{v_0\cos\theta}{g}\left(v_0\sin\theta +\sqrt{v_{0}^{2}\sin^{2}\theta + 2S_0g}\right)$$ where $S_0$ is ...
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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 ...
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1answer
52 views

Year 12 Maths Mechanics - Projectile motion = range of angle - I got the full working out but I don't know how to conclude the final answer

I did the full working out for the following question (images attached below) but I don't know how to explain that the final answer is angles between the two angles 79.3 and 43.7 I've found. (The ...
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Advanced Dynamics - radius planets can orbit the sun in a circular motion

I need help with this question I dont know where to start: A planet (or comet) of mass m with angular momentum L moves around the sun. The equations of motion are given by: $mr¨ = F_eff_(r)$, and $...
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1answer
211 views

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 ...
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30 views

How Do I Calculate Position from Displacement, pitch, yaw, and roll?

I have an array of time, pitch, yaw, roll, and displacement which was calculated from linear acceleration from an IMU. The sensor has a fusion algorithm, so I want to get the x, y, and z components of ...
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142 views

Two projectiles at an initial height with a missing angle of projection

David and Goliath are testing what they learned in school, that the distance travelled by launching a projectile is dependent on a range of variables; the launch angle, height and velocity of ...
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1answer
50 views

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 $\alpha$ ...
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83 views

Is there any way to rearrange the following equation for x?

Is there any way to rearrange the following equation to get $x$ in terms of $\theta$? $g$, $k$ and $u$ are known constants, and $\theta$ and $x$ are unknowns. $$\frac g{k^2}\ln(\frac {u \cos(\theta)-...
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Need help with this calc 3 question! It deals with projectile motion with 3 different objects being thrown and vectors.

How high would the object be thrown if three objects are to be juggled at 120 beats per minute( each object is thrown in turn one at a time and one per beat) with a horizontal displacement of ...
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1answer
32 views

Ball is thrown downwards with the initial velocity of 20m/s. How hight the ball bounces?

I am having some problems with my physics calculations. The problem goes: Ball is thrown downwards with the initial velocity of $20m/s$. The ball touches the floor and bounces, staying in the air ...
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1answer
58 views

General equation for a parabola given 2 points and the maximum

This is driving me a little nuts. I have a programming need that requires a parabolic trajectory. I must technically do this in 3 dimensions but I think the problem reduces to resolving equations in ...
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2answers
306 views

How do you calculate the trajectory of an arrow?

The problem: I want to calculate at which angle I have to shoot an arrow in order to hit a target which is x meters away. What I know: Force of the bow Weight of the arrow Distance to the target ...
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1answer
38 views

What's wrong with this quest for initial velocity?

If I could borrow your time for a beginner question -- what is the problem with the computation ? The problem is looking for the initial velocity of the projectile launched at an elevation of 1 meter ...
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2answers
33 views

How to Solve for Initial Velocity and Angle?

I hope you're having a pleasant day. Wondering if I could ask for your assistance on some projectile problem in 2d plane. How do I get the initial velocity and angle if maximum height, flight ...
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1answer
32 views

Projectile Motion with Gun Fire [closed]

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 ...
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148 views

How to calculate drag force vector

I am trying to calculate drag in 3D, and I came across the formula $$F_d = \dfrac{1}{2}\cdot C_d \cdot \rho \cdot v(t)^2 \cdot A$$ I understand how this formula is reached, as a proof is given ...
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15 views

How to see if list of coordinates pass through “goalposts”

I am graphing projectile motion and I would like to see if the projectile goes through predefined "goalposts", i.e. does the graph of its motion pass through an area bounded by 2 vertical lines and 2 ...
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24 views

Graphing the movement of a projectile under drag in 3D

I would like to graph the movement of a sphere with mass $m$ and radius $r$ under air resistance, in 3 dimensions. I have already achieved this by ignoring the $y$ component by only projecting along $...
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27 views

How to obtain the distance covered by a projectile if an additional acceleration is taken into account?

The problem is as follows: A projectile is fired from a horizontal ground with a speed of $\vec{v}=10\hat{i}+40\hat{j}\,\frac{m}{s}$. Due the gravity and the wind the shell experiences a constant ...
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29 views

How can I find the distance covered by a stuntman jumping over an incline?

The problem is as follows: A stuntmant in a circus act rides on a motorbike as it is shown in the figure from below. The bike which accelerates $10 \frac{m}{s^{2}}$ goes over an incline forming a $53^...
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4answers
51 views

How can I find the flying time for a projectile fired from some elevation and hitting an incline at a given angle?

The problem is as follows: In the figure from below a projectile is launched from point labeled $A$ with an initial speed of $30\frac{m}{s}$ making an angle of $37^{\circ}$ (with the horizontal)...
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2answers
90 views

Graphing the movement of a projectile under drag

I am trying to write a program to plot the movement of a projectile under the influence of air resistance. The inputs into the program are the initial velocities of the projectile [$i_x, i_z$] in $x$ ...
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1answer
26 views

Why projectile motion equations can be reduced in certain intervals

I am trying to understand projectile motion, but I have gotten stuck at the point at which they state in the limit $t >> v_t/g$ the equation is reduced, and when $t << v_t/g$ we also ...
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1answer
37 views

Integrating projectile motion

I am trying to understand projectile motion, but I am stuck. I'm trying to follow http://farside.ph.utexas.edu/teaching/336k/Newtonhtml/node29.html#e5.23u. However, I don't understand how they reach ...
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39 views

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, ...
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1answer
27 views

How do I find the total flying time of an object given a percentage in its vertical route?

The problem is as follows: At a laboratory a sphere is launched from the ground vertically upwards. The technician in charge measures the time it takes for the ball to reach the launching site again ...
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1answer
226 views

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 ...
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186 views

Projectile Motion-Throwing a Stone

A stone is thrown with a velocity of 20 ms^(-1) and at an angle of 60°. A second stone is thrown at the same time and place,with the same velocity but an angle of 30°. (a) Find which stone ...
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1answer
22 views

Deceleration to stopping point, with snapshot times/speeds

Simple question but I've confused myself over-complicating it. Say initial speed is 72ms distance is 0 (increasing) deceleration rate fixed at -2.2mss How far and what time will it take to stop? ...
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4answers
724 views

A car is moving horizontally along a straight line with a uniform velocity of 25m/s.

A projectile is to be fired in a such a way that it will return to the car after it has travelled 100m. The speed of the projectile must be (ignore air drag) MY SOLUTION u means initial velocity ...
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82 views

Is there an equation for an ellipse as a function of a velocity vector, radius and vector towards the foci.

Trying to model the orbit of electrons around an atom I have used the Rodrigues Rotation formula to rotate the electrons. Now I am dealing with ellipses and I am wondering if there is a rotation ...
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1answer
53 views

Condition for minimum projectile velocity

So I was solving the following problem https://physics.stackexchange.com/questions/237497/somewhat-unusual-projectile-motion-question and the minimum velocity involves the projectile intersecting ...
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97 views

Differentiating the $W$ lambert function to find optimum angle for maximum horizontal range of a projectile with air resistance

Here is the equation I obtained, representing the horizontal range of a projectile in air resistance as a function of its initial release angle- $$x=\frac{V_0\cos(\theta)}{B}-\frac{V_0\cos(\theta)}{...
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35 views

Ambiguous angle for projectile

A projectile is launched with at an angle $\theta$ to the horizontal with speed $v_o$ along an incline of $\alpha$ to the horizontal. Find the angle of projection that maximizes the distance traveled ...
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136 views

Find projectile speed given maximum height and range.

I want to simulate a catapult throwing a rock in my computer game, but by design, I want all my units to shoot from a certain height, reach a maximum height and also hit a target that can be meters or ...
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1answer
22 views

Projectile motion with Cauchy problem

I have the following problem: An airplane P, flying at a height of $h$ needs to hit the target on the ground $T$. The airplane is flying horizontaly at a constant speed $V_0$.Find the Cauchy problem ...
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1answer
129 views

Solving $d = \frac{v^2}{2g} \left( 1+ \sqrt{ 1+ \frac{2g y_0}{v^2 \sin^2{\theta}} } \right)\sin{2\theta}$ for $\theta$ [closed]

$$d = \frac{v^2}{2g} \left( 1+ \sqrt{ 1+ \frac{2g y_0}{v^2 \sin^2{\theta}} } \right)\sin{2\theta}$$ Need to find an equation for the angle. This is the equation for the range of a projectile ...
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1answer
54 views

Equation of Motion of a particle

I've tried this question over and over, and I'm getting nowhere. I've even tried looking for a solution to help make sense of how to get there, but I've had no luck. Can anyone help me please? A ...
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43 views

Projectile motion model

In my studies regarding projectile motion, I recently completed a simple level question surrounding a multileveled golf range. I had to determine the trajectories of these balls after they were shot ...
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212 views

Calculating Launch Angle Given Distance with Added Height (which itself depends on launch angle)

In my physics class we have learned to calculate a desired launch angle to allow a projectile to hit a target given the target’s distance away and the initial velocity. Now in this case the initial ...
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27 views

Baseball Projectile Motion

A baseball batter can hit the ball at an angle between $45°$ and $60°$. At all angles, the initial speed is $30$m/s. There are two catchers, catcher $A$ can run at $5$m/s and catcher $B$ can run at $2....
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103 views

How do you integrate this equation dvx/dt = -kv (Cd vx + CL vy) in order to find distance?

Equation CD is coefficient of drag CL is coefficient of lift Integrating should give v=dx/dt Integrating again should give x But i dont know the steps to do it
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37 views

Complex SUVAT help?

Two objects are dropped from the top of a cliff height $H.$ The second is dropped when the first has travelled a distance $D.$ Prove that the instant when the first object has reached bottom, the ...
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553 views

How to solve Linear motion problem

At point K a particle which is at rest starts motion when $t=0$ it moves with a uniform acceleration $f_1$ for a period of $t_1$. Then it decelerates by $f_2$ for a period of $t_2$. Then it ...
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1answer
66 views

A Projectile Motion Problem

I need more help, but this time it if for a problem involving projectile motion. The question is " A shot leaves the thrower’s hand 6.5 ft above the ground at a 45° angle at 44 ft / sec. Where is it ...
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1answer
41 views

Physics with Kinematics and Projectile motion

A $0.1$ kg nut is thrown by a squirrel off of the top of a $10$ m tall tree. It is thrown with an initial upward velocity of $4$ m/s and an initial horizontal velocity of $3$ m/s. a) How long till ...
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78 views

Projectile motion, initial angle and velocity

Question: A projectile motion passes $(16i+7.1j)$, $(0i+0j)$ and $(32i+4.4j)$. Determine the initial speed and velocity. (At the origin) My attempt: I converted the $i$ and $j$ in $x$ and $y$ to ...