Motion in space Definition and 16 Threads

Consider a rocket with mass ##m## in space is going to move forward. In order to do so, it needs to eject mass backwards. Let the mass that is ejected has velocity ##u## relative to the rocket. What is the equation for the final velocity? It is said that after ##dt## second, the rocket will...

Hello, Can you please explain the analogy oft quoted to explain the concept of applied motion to objects in space, which goes as follows : 1. You are standing on a skateboard or sitting in a boat floating on the water, holding a bowling ball. 2. You throw the bowling ball towards the back of...

Homework Statement The system consists of a long cylindrical anode of radius a and a coaxial cylindrical cathode with radius b (b <a). On the axis of the system has a thread with a heating current I, creates in the surrounding magnetic field. Find the smallest potential difference between the...

If two particles are moving apart, how is it determined if they are moving through space or if the motion is due to the expansion of space-time? Especially if there was no other frame of reference.

This might have been answered before but it's something that has been bothering me. A rocket in space will move in a straight line. If I apply thrust, it still moves in a straight line unless I apply the thrust in a different direction. So unless I have rocket nozzles attached to the side...

Homework Statement A particle moves so that its equation of motion in vector form given is given by ##\vec{R}=((sint^-1)/2+t/2√(1-t^2))\vec{i}+1/2t^2\vec{j}## , ##0≤t<1## a)Show that particle moves with a constant speed. b)Compute ##\vec{v}## and ##\vec{a}##,and verify that...

Dear PF Forum I want to know about these questions that are still bothering me, Does the universe have preferred frame of refference? Why there's twins paradox? Motion is relative, why 1 clock experiences time dilation while the other doesn't? V = \sqrt\frac{3}{4} ≈ 86.6\% If V define ratio of...

In theory, Is it possible to have no motion at all in relative to all of space? A point in-between galaxies perhaps? Or, given enough energy, to suspend motion in absolute? If this were possible would everything rush away? We are moving through space at approx. 830 km/s.

Homework Statement The position function of objects A and B describe different motion along the same path for t >= 0. A: r(t) = cos(t)i + sin(t)j B: r(t) = cos(3t)i + sin(3t)j a) Sketch the path followed by A and B b) Find the velocity and acceleration of A and B and discuss the distance c)...

Homework Statement For V(t) = (1+t)i + (t^2-2t)j find: 1. velocity 2.Acceleration 3. speed/length 4. Unit Tangent 5. tangential component 6. normal component at t=2 Homework Equations The Attempt at a Solution 1. v'(t) = <1,2t-2> = <1, 2(t-1)> 2. a(t) = <0,2> 3. length = Square root of...

Homework Statement A 0.2 lb gear is released from rest in the position shown (Okay so this essentially a circular gear in the groves on an adjacent wall that is also circular. Think perpendicular circles with different radii. The gear is a circle, and the gear teeth are in a circular...

Hello All, Noobie question. I am using Meeus' Astronomical Algorithims to creat a spreadsheet to transform coordinates. I had no problem with precession, nutation, aberration, etc. But, I don't have as good a math background for Motion in Space. I can follow down to the final formulas for...

Homework Statement A gun has a muzzle speed of 80 meters per second. What angle of elevation should be used to hit an object 150 meters away? Neglect air resistance and use g = 9.8m/sec2 as the acceleration of gravity. Homework Equations x = (vcos//theta)t y = (vsin//theta)t - 1/2gt^2 g =...

1. A medieval city has the shape of a square and is protected by walls with length 550 m and height 16 m. You are the commander of an attacking army and the closest you can get to the wall is 100 m. Your plan is to set fire to the city by catapulting heated rocks over the wall (with an initial...

Why do things orbiting, i.e. free-falling, around Earth float away from each other? Why don't they both free fall toward Earth together? I remeber hearing once that if you let go of 2 objects while 'floating' in space they both go away from you and away from each other. Is this due to curving...

Consider a bead of mass m that is free to move on a thin, circular wire of radius r. The bead is given an initial speed v0 and there is a coefficient of kinetic friction us. The experiment is performed in a spacecraft drifting in space. Find the speed of the bead at any subsequent time t. I...