The description of the movement of bodies by their position, velocity, acceleration (and possibly higher time derivatives, such as, jerk) without concern for the underlying dynamics/forces/causes.

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Calculating angle of projectile motion [closed]

I realize that similar questions have been asked but I'd like to put my problem here and what I have to make sure everything is right. So my problem is: I've got a rock $2.5$ meters above the ground ...
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2answers
172 views

Difference between the two equations for acceleration

I came upon this while studying S.H.M. Well,is there a difference between writing $$a=\frac{dv}{dt}\;$$ and $$a=v\frac{dv}{dx}\;$$ do they differ on the basis of one being a vector and the other ...
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1answer
162 views

Parametric equations in ballistics

while studying some material on ballistic trajectories (the basic gravity-only parabola), I've tried to come up with closed-form expressions for another case, where in addition to gravity we add a ...
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1answer
102 views

Homework: A parachutist jumps from a plane [closed]

I need help with the following problem. I think I almost have it . . . A parachutist bails out and freely falls a distance of $y_1$. Then the parachute opens and thereafter, the parachutist ...
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3answers
454 views

Direction of motion

What does the term direction of motion actually mean? Is it a direction where a particle is moving or the direction of its velocity? For example, what is the direction of motion of a projectile in ...
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0answers
67 views

General motion of a cone on an inclined surface

Suppose that a solid cone is placed horizontally on an inclined surface and is initially at rest. How will the cone move when it starts motion due to its weight? I know that its motion depends on the ...
2
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1answer
374 views

Mandelstam variable equality derivation for $s$-channel process

I am supposed to show that the Mandelstam variable $s=(p_1^2 + p_2^2) = 4(P_{cm}^2 + m^2)$ for an electron/positron interaction, where $p_1$ is the incident 4-momentum of the electron and $p_2$ is ...
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2answers
135 views

Why does a small object stay in one place after being shot from a big gun?

This video shows what I mean. Basically they shoot a bullet from a huge gun at an iPhone. What I don't get is why does the phone move only so little after being shot? As far as I can tell it isn't ...
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2answers
208 views

Projectile motion maximum distance to origin

Is there an elegant or easy way to derive the maximum distance from the origin to a point of the parabola created by projectile motion (assume initial position is the origin)? Other than ...
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1answer
845 views

Distinguish between instantaneous speed and instantaneous velocity

I encountered a line in my text book of physics that: Average speed over a finite interval of time is greater or equal to the magnitude of the average velocity. But instantaneous speed at an ...
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2answers
57 views

how to find last position given a time

I found this formula (I dont know its name) and I'm trying to apply it in order to find the last position given a time and velocity. $ s = s_0 + v_0 \cdot t + \frac{1}{2} \cdot a \cdot t² $ given $ ...
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2answers
617 views

Finding the optimal angle of a projectile motion [closed]

I am trying to solve a task in which I need to calculate the optimal angle($\alpha$) with which the projectile will land the furthest from a height ($h$), so what I basically have is the equations for ...
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1answer
289 views

Applying multiple forces to one object and calculate net movement and rotation?

I'm working on a small game as a hobby project, and I've run into a problem that would seem simple, to me, but that I can't find any information on or solution to. How would one go about figuring ...
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2answers
521 views

Oscillation of a rolling sphere in a bowl [closed]

This is a homework task. I already came to a result but I am very unsure. The task: In a bowl with the shape of a semi-circle ($R$ = 0.5m) a sphere (there is no specification for the size of the ...
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1answer
226 views

Equations of motion of particle mass on parabolic surface

Given a parabolic surface $$ Z = \frac{\Omega^2}{2g}\left(X^2 + Y^2\right)$$ My textbook (Introduction to Geophysical Fluid Dynamics, 2nd ed, p.50) states: "Provided that the paraboloid is ...
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0answers
46 views

prediction of a moving object

OK, this may be a hard question to answer and really all I am looking for is an equation as I don't even know what to call this. This is all for a game so bare with me please. In the game two ...
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3answers
3k views

Force applied to wheel in pure rolling motion at contact point with road

Suppose a wheel with radius $R$ is resting on a non-inclined surface. A torque $\tau$ is applied to the wheel center. In an attempt to prevent wheel from spinning, the ground applies a static friction ...
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2answers
376 views

Increase in velocity by loss of mass? [closed]

A trolley of mass 300kg carrying a sand bag of 25kg is moving uniformly with speed of 27km/h on a frictionless track. After a while, sand starts leaking out of a hole on the floor of the trolley at ...
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3answers
155 views

Why isn't centripetal acceleration considered in this problem

Fairgoers ride a Ferris wheel with a radius of 6.00 m. The wheel completes one revolution every 30.0 s. If a rider accidentally drops a stuffed animal at the top of the wheel, where does it land ...
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1answer
90 views

What is “kinematic inversion” (from geophysics) in mathematical terms?

I am a mathematician working on a seismic imaging problem, and am currently (attempting to) read some geophysics papers (this one (Ruiz, Madariaga 2011) and this one (Di Carli, Francois-Holden, ...
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2answers
86 views

Relative velocity decomposition

In my fluid dynamics course notes is stated a change in relative velocity can be decomposed: $$\delta \mathbf{v} = \left\{ \begin{pmatrix} \Delta & 0 \\ 0 & \Delta \end{pmatrix} + ...
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1answer
137 views

Optimal velocity in rain [closed]

Problem statement: A sphere is rolling in rain from point A to point B. The vertical speed of rain is V and horizontal speed of rain is v, as shown in the picture. Angle between horizontal ...
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2answers
63 views

A block in motion explodes [closed]

A 9.5 kg block (A) is traveling in the positive x-direction with a speed of 3.0 m/s. At some point, it explodes and breaks into two pieces. After the explosion, block C, which is 6.0 kg, moves off ...
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1answer
83 views

Why does a difference in approach to projectile motion yields different results?

A body is projected vertically upwards from the surface of the earth with a velocity equal to half the escape velocity. If $R$ is the radius of the earth, then find the maximum height attained by the ...
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2answers
151 views

How to find time, acceleration under this situation

I am trying to solve the following. An object of mass $m$ slides on a horizontal surface with initial velocity $v_0$. If the kinetic friction between the object and mass is given by $\mu$, find ...
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1answer
597 views

Why there is a $\frac{1}{2}$ in the distance formula $d=\frac{1}{2}at^2$?

I'm preparing for my exam, but I have difficulties in perceiving why there is a $\frac{1}{2}$ in the distance formula $d=\frac{1}{2}at^2$?
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4answers
392 views

Calculate average speed with unknown variable accelaration

I am in the middle of a vehicle tracking project where I have to calculate the distance traveled by the vehicle in a given amount of time. Data I am getting: ...
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2answers
121 views

The velocity of a cloud?

I noticed an unusually fast moving cloud this morning. My questions: What is the average velocity of a cloud on Earth? What is the greatest ever recorded cloud velocity? What factors affect the ...
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2answers
100 views

How many years would it take the Pioneer space probe to travel to Proxima Centauri with its current speed? [closed]

Pioneer space probe moving at a speed of $30km/s$. Assuming its heading for Proxima Centauri, which is situated at $4.2ly$ from earth, calculate how long it would take to get there in years, to the ...
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2answers
125 views

Relative velocities of boats and a stone thrown by the boat [closed]

Question: A police boat is chasing a boat with criminals along a straight river by moving against the stream. The speed of the river stream is 3 miles per hour, the speed of the boat with ...
2
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1answer
194 views

Integration on a general equation for instantaneous angular acceleration

An equation for instantaneous angular acceleration is given as: $$ \alpha \equiv \lim_{\Delta t\to0}\frac{\Delta \omega}{\Delta t} = \frac{d\omega}{dt} $$ The text I am reading says writing this ...
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1answer
72 views

Homework - Mechanics [closed]

Just started mechanics and I'm not sure what I'm doing wrong on a question. Car accelerates uniformly from a speed of $50\: \mathrm{kmh}^{-1}$ to a speed of $80\: \mathrm{kmh}^{-1}$ in $20$ ...
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132 views

Relative velocity of boat

I am trying to understand fully the following question: A boat is traveling west at 100m/s and is partially helped by a strong wind blowing at 20m/s 30 degrees north of west. What speed could the ...
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2answers
198 views

Is two cars colliding at 25 mph the same as one car colliding into a wall at 50 mph in reference to injuries?

This question has been asked using 50 & 100 mph reference, see this Phys.SE post and links therein. However, I am interested in the potential injuries to occupants of the autos. As the one going ...
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1answer
135 views

Missing centrifugal acceleration

I am trying to get correct equations for acceleration of a point in reference frame A, given position, velocity and acceleration in rotating reference frame B. Let $\mathbf{x}_A(t)$, ...
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1answer
191 views

Write a parabolic equation in kinematics

How might I go about writing a parabolic equation in standard form $ax^2 + bx + c$ given all of the following measurements: $X_0, X_f, Y_o, Y_f$: the initial and final x and y positions. ...
2
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1answer
91 views

Relative motion of airplane in the wind [closed]

I have a relative motion problem in which I cannot get my answer to match the book answer. The question is: An airplane has to travel $189\, \mathrm{km}$ due east to point $B$ from point $A$. It ...
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1answer
212 views

Is there a better, faster way to do this projectile motion question? [closed]

The question is In a combat exercise, a mortar at M is required to hit a target at O, which is taking cover 25 m behind a structure of negligible width 10 m tall. This mortar can only fire at an ...
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1answer
226 views

Vector Maths to Simulate Car Physics [closed]

I'm working on a 3D program that involves controlling a Cube on-screen (which represents a car). I use C++, OpenGL and GLM (for vector and matrices etc, if you're familiar with programming; Once the ...
4
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2answers
147 views

Work done on stationary rocket

Suppose I have a rocket thats exerts a force (with negligible loses in mass), which cancels out the downward force of gravity. Clearly my rocket could be moving at a constant velocity (ignore air ...
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1answer
546 views

Distance formula in kinematics?

I've always seen it $d = v_i t + \frac{1}{2} at^2$ However, I also saw it as $d= d_i + v_i t + \frac{1}{2} at^2$ where $d_i$ = initial position. This was applied to 2D kinematics. Can anyone explain ...
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2answers
1k views

If I lift a box vertically, why is the work I do equal to the distance I lift it times the force of gravity on the box? [duplicate]

I have problems fully understanding the concept of work, so please forgive me if this is simple. If I take a box of mass $ m $, and lift it a distance $ d $ vertically, why is the work I have done ...
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1answer
405 views

I am unable to combine two equations in kinematics

Sorry people, very basic kinematic stuff here. (1) Velocity: $$v=\frac{d}{t}$$ (2) Acceleraton: $$a=\frac{v_{f}-v_{i}}{t}$$ (3) Re-arrange acceleration: $$v_{f} = v_{i}+at$$ (4) Ok here is my ...
2
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1answer
83 views

Applying kinematics issue

I've been having an unusually difficult time solving kinematics problems in comparison to all the other students in the classroom. It appears that I'm one of the unfortunate people with an anti-math ...
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1answer
59 views

when to consider linear kinetic energy and when to use angular kinetic energy?

I saw a problem about a pivoting rod online (http://dev.physicslab.org/Document.aspx?doctype=3&filename=RotaryMotion_RotationalDynamicsPivotingRods.xml), I am thinking the problem if we initially ...
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2answers
164 views

Does $y$-motion really have nothing to do with $x$-motion?

I am watching a Physics 1 for physical science majors on coursera.com, and in one of the concept tests there is a question that goes like this; "A bullet is fired horizontally from a rifle on the Moon ...
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3answers
6k views

Kinetic energy and momentum conservation in an explosion?

My physics book says, "A firecracker sliding on ice has the same total momentum before and after it explodes." I understand this part. This is because of Newton's 3rd law, and no external forces. This ...
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820 views

I don't understand the idea of perpendicular vectors being independent of each other?

So problem 71-75 is about vectors. The problem says: A river has a current flowing with a velocity of 2.0 meters per second due east. A boat is 75 meters from the north riverbank. It travels at ...
8
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2answers
270 views

What is the physical meaning of $|f''(\xi )|\leq\frac{4(f(b)-f(a))}{(b-a)^{2}}$ where $f(t)$ is position as a function of time?

Here is the full problem: I was able to prove the given expression; but the interpretation part is giving me a bit of trouble. Here is my interpretation: The average acceleration in $(a,b)$, is ...
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1answer
208 views

x-coordinate of the ball when it's velocity is perpendicular to projection velocity

We have a ball projected at 20 m/s at an angle $\pi/6$ from the x-axis. Now we have to calculate x-coordinate of the ball when it's velocity is perpendicular to projection velocity. I am thinking ...