# What is Relative velocity: Definition and 412 Discussions

The relative velocity

v

B

A

{\displaystyle {\vec {v}}_{B\mid A}}
(also

v

B
A

{\displaystyle {\vec {v}}_{BA}}
or

v

B
rel

A

{\displaystyle {\vec {v}}_{B\operatorname {rel} A}}
) is the velocity of an object or observer B in the rest frame of another object or observer A.

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1. ### Feedback on video I created on (Galilean) Relative Velocity?

I've decided to try my hand at creating youtube videos and I'd like to know what fellow PF members think. This is a community whose opinions I value. The video can basically be divided into 6 slides (about 18 minutes long in total) 1) Definition of relative velocity (verbally) 2) Definition of...
2. ### Is my work correct? (Two students running on a track)

Two students run around a 400m sport field. A goes anticlockwise (i.e., 1-2-3-4-1) while Bruns clockwise (i.e., 1-4-3-2-1). Students A and B can run 400 m in 75.0 s and 65.0 s,respectively. Students A and B should meet at some point of the run. Where do they meet? Assume the cross-over...
3. ### Calculating relative velocity -- Jumping between two moving trains

is it possible? I've given it quite some thought, and my conclusion was that it would be possible, cuz right after I jump, I'll still have the same velocity in the same direction as the running train?
4. ### Relative velocity of two objects: one on a circular path, one on a horizontal straight path

In the question I assumed the velocity of the circular object to be : $$\vec v_A= v cos( \phi + \omega t) \hat i + v sin(\phi + \omega t) \hat j$$ where $$\omega = \frac{v}{R}$$ Velocity of the other particle is $$\vec v_B = v \hat i$$ Now magnitude of relative velocity comes out on...
5. ### B How does Earth's rotation affect our movement?

How is it possible that Earth's rotation doesn't affect our relative velocity? In other words, if I walk in the opposite direction of Earth's rotation, shouldn't I reach destinations faster than if I walk in the same direction? Sorry if the terms are not that accurate, I’m an architect!
6. ### Crosswind problem (pgs. 34-35, Thinking Physics, 3rd edition)

Hi everyone, I was looking to develop my physical insight when I encountered this book by Lewis Caroll Epstein. For the crosswind problem, I couldn't understand the author's explanation; in particular, his concept of "artificial wind," and the force being larger in this case than the previous...
7. ### Relative velocity passing a ball between two soccer players

For some reason I'm having trouble understanding relative velocity problems. I know how to solve this, but I keep guessing at random methods until my answer matches the solution in the textbook. I solved it correctly by breaking the velocity of the ball into x- and y- components, then solved...
8. ### Relative Velocity and Angles of Movement (Sears & Zemansky's Exercise)

The official solution says ±25.4°, but I'm having trouble reproducing it. Here is my solution: 1) The components of the velocity of firework F with respect to the ground G in the moment of explosion are the following (Notice, I'm using sin, because the statement says 30.0° from vertical.)...
9. ### Is it possible to solve relative velocity problems without sine law?

I was able to solve this question successfully by utilizing the sine and cosine law however my instructor said I was only allowed to utilize the vector component method, I am unsure how to complete this question using the vector component method as we have two unknowns(those being the angle of...
10. ### Relative velocity Question for a Ferryboat

So far I have this: vbwx= 4.40c0s(28) = 3.88496409 vbwy= 4.40sin28 = 2.065674876 vpwx= 4.4ocos28 vpwy= 4.40sin28 +2.02 Find Square root of vpx^2 + vpy^2 = 5.43? Im confused as to whether we add the 2.02 to the sin28 or the cos28 though, did I do it right? Also, not sure how to find the...

12. ### Relative Velocity Against the Water Current

vcanoe_wrt_ground = 3 m/s + (-6) m/s = 3 m/s - 6 m/s = -3 m/s Thus, if I understand this correctly, the rower will never reach his goal 36 m away as his canoe's resultant velocity is negative (i.e., his canoe is effectively going downstream even though it is trying to go upstream). My only...
13. ### A Relativistic Relative Velocity Comp.: Bini, D. et al. (1995)

I'm trying to understand this paper (equation 2.16 specifically): Bini, D., Carini, P., & Jantzen, R. T. (1995). Relative observer kinematics in general relativity. Classical and Quantum Gravity. Am I correct in reading there is no way to express the relativistic relative velocity composition...
14. ### A new take on a relative velocity problem

I can solve this question using relative Velocity or using 2 kinematics equations. But a peer of mine, tried to do it in a different way. He substituted the above said values in the 4 equations and solved for u in terms of t and differentiated them and equated to to 0 to find a maxima. He found...
15. ### Roundtrip by Plane: Understanding Wind & Velocity Effects

The question I have is that if the aero plane is traveling in the same direction as the wind, would it not increase its velocity, as in with boats and streams? So, if by chance, ##w = v##, then the velocity of the aero plane would double. It feels weird as going by the same logic, if the speed...
16. ### Relative Velocity of a Passenger Hitting the Dashboard in a Car Crash

Where exactly have I gone wrong? I think it is the part where I assume that the person gains the deceleration of the car, but I have no other way to proceed in this case. Also please only use the equations that I have posted below, and it would help if you would not use the equation for...
17. ### Finding the velocity of a car in a different frame of reference

Here's what I did so far. The velocity of the first car is ##v = v_0 +at## Frame of reference S = the road Frame of reference S' = the second car thus, v' is the speed of the first car in the frame of reference S' and v the speed in the frame of reference S. Here's what make me doubt. The...
18. ### Doppler shift between a moving ship on the ocean and a satellite in LEO

Summary:: I would like to calculate the Doppler shift for a signal sent by a moving ship to a moving satellite. I want to calculate the frequency observed by an LEO satellite when a signal is transmitted from a moving ship. The LEO satellite has a velocity of 7120m/s and orbits at a height of...
19. ### Collision between two uniformly moving particles

Problem : The statement is given above. Here I attach the image of the problem to the right. Attempt : (1) Condition for collision : For the two particles to collide, there should be no relative velocity perpendicular to their "separation vector" ##\boldsymbol{s}##. Hence, we must have ...
20. ### What is the perceived relative velocity of these two motorcycles?

I tried to project one on top of another but I know that's incorrect since I don't know how of do this.
21. ### Swimming to and fro across a river

Problem statement : While the statement is given above, I draw the given image for the problem. Attempt : It is clear at the outset that, since the velocity of river is constant, the man will not take the same time for the forward and reverse journeys. For both journeys however, the Relevant...
22. ### Determine time after which 4 persons meet in given scenario

The point of confusion is deciding the direction each persons sets out in i.e. velocity direction of each person. Knowing this will probably help in getting the solution. At t=0, I can say that velocity of each person is as shown in diagram below.
23. ### Relativistic Relative Velocity Problem

Heres how I tried to set up the problem. I took the laboratory to be S and the frame of the particle whose speed we know to be S', so that the speed of S' relative to S is u = 0.65c. Also, by convention, S' moves to the right of S, so that S moves to the left of S'. Next, we know that the...
24. ### 2 contradicting approaches for a 1D elastic collision

So I've managed to confuse myself on this problem :) Since the problem says we can assume ##m_p << m_b##, I'm assuming that the velocity of the bowling ball will be unchanged, such that ##\vec v_{b,i} = \vec v_{b,f} = -v_{b,0} \hat i## I started out using the energy-momentum principle, ##(\vec...
25. ### To find the relative velocity of the wind as seen from a car

Could I please ask for any help with the following question: Here's my attempt: (i and j are unit vectors in the directions of east and north respectively) (apologies that LaTeX is simply not working for me, I'll label the angles in each case T and P as shown in my diagram) Let the...
26. ### To find the true velocity of wind from relative velocity

Please can I ask for help with the following as to where I'm going wrong. Book answer is 20 knots and 315 degrees My solution: In the below diagram I have sketched the two situations, k is the true speed of the wind. First question is, is my diagram correct? The velocity of the wind...
27. ### Relative velocity of the wind making a flag move

Here it is given that the flag flutters in the direction of wind w.r.t. to man. But why would the direction of fluttering of flag would change without any tangential acceleration. Is there a pseudo force acting on it. I think the direction if fluttering should remain same.
28. E

### Weirdness with this relative velocity formula when defining coordinate systems differently

Wikipedia gives, "The relative velocity ##{\displaystyle {\vec {v}}_{B\mid A}}## is the velocity of an object or observer B in the rest frame of another object or observer A." Suppose the coordinate system being used in the rest frame of ##A## is has its origin slightly displaced from ##A##...
29. ### Relative velocity in 2 dimensions

(pw is person to water, pf is person to ferry, fw is ferry to water) I get Vpw = Vpf + Vfw. Therefore Vfw = Vpw + Vpf, which is Vfw = -Vwp + Vpf. I also have that the x component of Vpw is negative. I think I'm getting confused with either the order of the formula or the negative negatives (or...
30. ### Relative velocity of a ball thrown inside a moving truck

Hi all, Not sure on how to start this question in the first place, but from what I gathered from the data given I managed to derive this from the question: ##\theta = 53.13\deg## Let inside truck be t, final position be f, and ground be g ##D_{ft} = L## ##D_{fg} = xL## Also, for velocity...
31. E

### Relative velocity of two gravitationally attracting spheres

There have been some other threads on similar problems but none address one specific point I'm confused about. The change in GPE of a body is the negative of the work done on that body by a gravitational field between two points; by this logic, since the same (but opposite) gravitational forces...
32. ### Impossible Relative Velocity Values

The answers were 1) 150 km/h 2) 200 km/h 3 )500 km/h 4) 700 km/h 5) 800 km/h (Chosen Solution) I know that values 700km/h ,100km/h ,-100km/h are possible scenarios but in what ways are 150km/h ,200km/h and 500km/h possible ?
33. ### Two body problem, velocities of two bodies, relative velocity given

When only force acting on body is a central force, angular momentum is constant and given by: L = mr^2 * w where r is distance from origin, and w is angular velocity. Angular momentum can also be written as following: L = r x mv = rmv * sin(theta) where v is tangential velocity, which is...
34. ### Unable to clearly understand relative velocity

Unable to understand why this is the case? Also, if it were in two dimensions then I am guessing the same would apply, only the 'x-co-ordinates' and 'y-coordinates' would add up separately? Lastly, does the same hold for acceleration. I am aware that this is a trivial question, many books...
35. ### Relative Velocity Of Swimmer

So I was just wondering if someone could check my method for (b) as sometimes I can have a tendency of getting the relative components wrong ect. Diagram 1 (a) Time for PY: ##T=L/c## Time for YP: ##T=L/c## Total Time:##2L/c## (b) Velocity for PY: ##c-v##...
36. ### Relative velocity between a Bus and a Car

for part 1: t= d/s = 9000/13 = 692.31s for part 2: What i am unsure about is wether or not this is after the initial observation or exactly what they are asking honestly. so i found the relative velocity of the bus to the car and vice vera and came up with: t=d/s = 9000/4 = 2250s however i don't...
37. ### Relative velocity between lift and screw

v=16m/s+4*.659s=18.636m/s (for lift) v0=16m/s-9.81*.659s=9.53m/s my question is that why 16m/s is considered for screw velocity ? it is given for lift .what does it mean 9.53m/s? If you drop something , it gets acceleration and I calculate it 6.45m for screw while falling and why should I...
38. ### Motion in 2 Dimensions & Relative velocity

Homework Statement The water in a river flows uniformly at a constant speed of 2.50 m/s between parallel banks 80.0 m apart. You are to deliver a package across the river, but you can swim only at 1.50 m/s. (c) If you choose to minimize the distance downstream that the river carries you, in...
39. ### Acceleration: 3 people walk toward each other

Homework Statement Three particles A, B, C, are situated at the vertices of equilateral triangle of side l. They approach each other with velocity v, such that A always moves toward B, B towards C and C towards A. What will be the initial acceleration? Homework EquationsThe Attempt at a...
40. ### Rigid Body Rotation relative velocity question

This is a question about the concepts behind rigid body rotation when we use relative velocity. In general, let us say that we have a rigid body and on it are two points, A and B, which are moving with velocities vA and vB respectively. These velocities are in random directions. The theory...
41. ### Contradicting solutions to a basic movement problem.

Homework Statement Hi, everyone. I came across a basic calculus problem concerning movement of 2 problems, I've attempted to solve it using vector analysis and got 1 answer, and then solved it with differentiation and got a different answer. I'll show a version of it I made which is a bit more...
42. ### I Understanding the Relative Velocity Paradox

Hi! I'm an utter novice at physics, so please bear with me if I ask a foolish question. I just learned that velocities don't purely add: 2m/s + 2m/s does not equal 4m/s, but something like 3.9999999...9 m/s, and so on. Something to do with the upper limit of c. Logic makes me assume that this...
43. ### Relative velocity and force relationship

This is something related to my job. There are two components A & B both traveling the same direction but at a different velocity. I can find out the exact velocity of both the components when they just hit each other, thus relative velocity is known. Is there a way I find out the force...
44. ### Relative velocity in special relativity

Homework Statement Imagine we are observing two aeroplaes from the ground and let their velocities be ##\mathbf{u}## and ##\mathbf{v}## respectively. Assume that the first plane has radar equipment permitting a measurement of the speed of the other plane relative to itself. The velocity so...
45. ### Calculate the relative angular velocity

Homework Statement AB is a rod of length 10 m that is leaning against the wall. Given variables are shown in the diagram. Find angular velocity of A wrt B. https://imgur.com/a/8bEdYhN I have a doubt in one step that I will highlight in "The attempt at a solution" part. Homework Equations...
46. ### River-boat problem (Relative velocity)

Homework Statement A man wishes to cross a river of width 120 m by a motorboat. His rowing speed in still water (or relative to water) is 3 m/s and his maximum walking speed is 1 m/s. The river flows with a velocity of 4 m/s. (a) Find the path which he should take to reach the point directly...
47. ### Problem using vectors and relative motion

Homework Statement A river of width 4 km flows at 5 km/h. A swimmer whose speed relative to water is 4 km/h, starts swimming from a point A on a bank. What minimum distance will the swimmer have to walk on the other bank to reach point B directly opposite to A? [/B]Homework Equations Vba = Vb...
48. ### Relative velocity of exhaust in Ideal Rocket Equation

In this derivation of the Ideal Rocket Equation (https://en.wikipedia.org/wiki/Tsiolkovsky_rocket_equation#Most_popular_derivation), they use the fact that ##V_e = V - v_e##, or that the velocity of the exhaust in the observer frame ##V_e## is the velocity of the rocket ##V## minus the speed of...
49. ### Relative velocity help -- A bird flying in a wind trying to get to its nest

Homework Statement A bird can fly in still air at 100km/h. The wind blows at 90km/h from W(x degrees)S. The bird wishes to return to its nest which is due E of its present position. In which direction, relative to the air, should it fly?My textbook says that the velocity of the bird relative to...
50. ### Relative velocity of two cars crashing into each other

So I read these two other threads: https://www.physicsforums.com/threads/relative-speed-of-two-cars.642873/ https://www.physicsforums.com/threads/two-cars-colliding.740948/ And gathered what I already thought was correct, that the relative velocities of two cars of equal mass crashing into...