What is Relative velocity: Definition and 413 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. N

    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...
  2. Abhimessi10

    Difference between relative velocity and effective velocity

    Can anyone tell me the difference between concept of relative velocity and effective velocity and when to use the concept of relative velocity? For example, if a guy throws a ball from a moving object at an angle theta it undergoes projectile motion we write horizontal velocity as...
  3. O

    Energy Lost during elastic collision.

    Homework Statement . True or False:[/B] For a completely elastic collision of two isolated masses the energy lost is ½μνr2 Where μ is the reduced mass of the system and νr is the magnitude of relative velocity between the two particles. Homework EquationsThe Attempt at a Solution Elastic...
  4. M

    MHB Relative Velocity of Aircraft: Mag & Dir Before & After 16:30

    an aircraft flies horizontally at a speed 200 km hr^-1 relative to the air. its position at 15:00 is p. a wind with speed 100 km hr^-1 blows from the east from 15:00 to 16:30 . the wind then changes to a speed of 50 km hr^-1 from the south. the aircraft adjusts its heading so it maintains a...
  5. D

    Relative velocity and water skier

    Homework Statement Homework EquationsThe Attempt at a Solution The water skier makes an angle of 20 deg with the axis of the boat. I do not understand how to get the other angles.
  6. davidge

    I Relativistic relative velocity

    I'm interested in deriving the relativistic relative velocity of two particles moving near the speed of light. It turns out to be (with ##c = 1##) $$\frac{V^{(1)} - V^{(2)}}{1 - V^{(1)}V^{(2)}}$$ How should I approach to this problem? Maybe I should not think of particles at all, but instead...
  7. W

    What angle should a swimmer aim to land directly across the starting position?

    Homework Statement A swimmer who achieves a speed of of 0.75 m/s in still water swims directly across a river 72m wide. The swimmer lands on the far shore at a position 54m downstream from the starting point. Determine the direction the swimmer would have the aim to land directly across from...
  8. S

    Relative velocity during a race?

    Hello, could someone please check my answer for this problem. All of my work and equations are clearly presented in the picture attached below. (If my answer is wrong, please give me pointers on how I could obtain the correct solution). Thanks! Problem 5: On their way to play soccer in...
  9. S

    Calculating Time to Return to Starting Point in a River with Constant Current

    Hello, could someone please check my answer for this problem. All of my work and equations are clearly presented in the picture attached below. (If my answer is wrong, please give me pointers on how I could obtain the correct solution). Thanks ! Problem 3: You paddle your canoe at a...
  10. L

    Derivation of Rocket Equation Using Relative Velocity

    Based on my current understanding of the problem I do not see this following derivation as valid, although this is what was given in my course notes. Although this particular example is from an undergraduate physics course this is not a homework problem: I'm confused about the underlying...
  11. N

    Relative Velocity of Object C to Object A = 10 m/s

    Homework Statement If the relative velocity of object B to object A is 10 m/s, and the relative velocity of object C to object B is 10 m/s, what is the relative velocity of object C to object A? Homework Equations These should be vectors just to give a heads up vbs= vbw+vws vba=vab These...
  12. donaldparida

    Magnetic field when relative velocity is zero

    A current carrying conductor produces a magnetic field but what if there is an object which has the same speed as current. Will there be magnetic field by the current carrying conductor for that object?
  13. U

    Relative velocity problem with pulleys

    Homework Statement Homework Equations Vb/a = Vb - Va The Attempt at a Solution I got as far as realizing that the velocity of B depends on A so I wrote out: 2(Xa) + (Xb/a)cos15 = constant and took the derivative of that equation to get Vb/a = -16.56. I then got stuck as to how to get Vb...
  14. ChloeYip

    Angle of Rain on Earth: Investigating Relative Velocity

    Homework Statement When a cart travel to the left at v=-10m/s, the angle of rain come towards it is 50o from normal. When the cart travel to the right at v=10m/s, the angle of rain water come is perpendicular to it. What is the angle of rain come to the earth? Homework Equations relative...
  15. Jonski

    Angular Acceleration and relative velocity

    Homework Statement In the mechanism shown below, the angular velocity of link 2 is 17 rad/s CW, constant. Find the angular velocity (magnitude and direction) of link 3. The distance between A and C is 109 mm, the length of link 3 is 125 mm, and θ= 111°. Note: B is a pin-slider In the...
  16. kidgt23

    Calculating Relative Velocity: Train vs. Car Collision

    Homework Statement A person on a train watches a car approaching a railway crossing ahead on his track. It appears that the car’s driver has fallen asleep and will not slow down. The train is traveling north‐east at 100km/h while the car is going west at 80km/h. The train is 4 km and the car is...
  17. Jonski

    What is the solution for relative velocity of sliders?

    Homework Statement Homework Equations [/B] Va = Va/c + Vc Va = 0.2 + Vc Vb = Vd The Attempt at a Solution I began by finding the instant centre of rotations of AB and CD. Both of these form a right angle triangle and the length of A -> ICab = 200mm and C -> ICcd = 300mm Va/0.2 * 0.15 = Vb...
  18. A

    Relative velocity ship problem intuitively

    Homework Statement Two ships A and B are 4 km apart. A is due west of B. If A moves with uniform velocity of 8 km/hr due east and B moves with a uniform velocity of 6 km/hr due south. Calculate 1) the magnitudeof the velocity of A in relation to B 2) the closest distance apart of A and B...
  19. K

    Finding Relative Velocity in Inertial Systems

    Homework Statement An event occurs in S at x = 6 x 10^8 meters and S' at x' = 6 x 10^8 meters. Find the relative velocity of the systems. Assume that S refers to an inertial system (x,y,z,t), and S' refers to an inertial system (x',y',z',t') moving along +x axis with speed v relative to S. The...
  20. Jonski

    Velocity of a slider connect to a wheel

    Homework Statement A wheel of radius 42 mm is rolling without slipping and its centre O has a velocity 7.2 m/s in the direction shown. The slider B is driven by the link AB and A is connected to the wheel. If AC= 28.9 mm, AB= 73.9 mm and angle ACB= 73°, what is the velocity of the slider B...
  21. J

    Homework Help -- Relative Velocity

    <Moderator note: moved from technical forums, so no template> Problem: Two trains (A and B) are moving along parallel tracks at different speeds. A person sitting on train A looks out the window and sees two things happen: a firecracker explodes right outside his window, and, exactly 1.0...
  22. D

    I Relative Velocity Time Dilation: Experiments Disproving Theory?

    I have a question regarding time dilation due to relative velocity. (It's just about time dilation due to velocity not about gravitational effects.) I have seen a theory where time dilation is not relative, but always considered against an absolute frame of reference. The absolute frame of...
  23. MickeyBlue

    Relative velocity of a ball on a train

    Homework Statement A train is traveling east along a straight run of track at 72.0 km/hr. Inside, two siblings 1.9 m apart are playing catch directly across the aisle. The kid wearing a P.J.Harvey T-shirt throws the ball horizontally north. The ball crosses the train and is caught 0.75 s later...
  24. Aashish Bharat

    Relative velocity of 2 vehicles

    Two vehicles leave simultaneously from a fork in a road. Vehicle A travels at a velocity of 85 km/h north-east. Vehicle B travels at 104 km/h directly east. Calculate the velocity of vehicle A relative to the velocity of vehicle B. Answer (from memorandum): http://imgur.com/a/L0prH I do not...
  25. kipup123

    Relative Velocity (Man walking in rain question)

    Homework Statement A stationary person observes that rain is falling vertically down at 30km/hr. A cyclist is moving on the level road, at 10km/hr. In which direction the cyclist should hold his umbrella to prevent himself from the rain? 2. The attempt at a solution I used triangle law to...
  26. B

    Relative velocity of a swimmer

    Homework Statement A person decides to swim across a river 84m wide that has a current moving with a velocity of 0.40m/s[E]. The person swims 0.70m/s[N] relative to the water. In what direction should she swim if she lands at a point directly north of her starting position? Note: This is part...
  27. J

    B Understanding the Sign of Relative Velocity in Approaching Observers

    I have been told that relative velocity can be negative on this forum, so i would like to ask a few questions based on this. scenario 1) Two observers O and O' are facing each other and are approaching each other. O sees O' approaching at v=0.5c and vice versa. The vector of the velocity is...
  28. henrco

    Relativity - relative velocity

    Hi, Could i please get advice on this problem and confirm that my approach and solution are correct? Thanks in advance. 1. Homework Statement An enemy space rocket traveling at speed 0.8c towards the planet Zog fires a missile in the direction parallel to its own path. Relative to the rocket...
  29. navierstokes

    Question on relative velocity -- Find time?

    Homework Statement The distance between cities A and B it's L. An airplane flies back and forth between A and B, in a straight line, with velocity V in relation to the wind. So, calculate the total time of the flight, if the wind blows with velocity v, in a direction which forms an angle theta...
  30. D

    Need help with relative velocity problem

    Homework Statement Amy is traveling at 60mph on the highway, due North. The on-ramp nearby starts out going West, and then curves around so that eventually it is also North, parallel to the highway. A) Bob appears, traveling 40mph going West (on the onramp). What is his speed relative to Amy...
  31. D

    Relative Velocity of Ball on Moving Board

    Homework Statement A ball rolls with a velocity of 14 mm/s [W] on a board that is being pulled [E 60o N] at 20.0 mm/s. What is the velocity of the ball relative to the floor? b = ball x = board f = floor Homework Equations V_bf = V_bx + V_xf The Attempt at a Solution I tried to work through...
  32. D

    A Relative Velocity Between Colinear Free-Falling Objects | GR Answer

    Can anyone answer this question: In the context of GR, If two objects are in collinear free fall, far enough apart so that the field intensity differs for each object, and one measures the relative velocity between the objects in the coordinate system of the objects using (say) a radar system...
  33. I

    2D Relative Velocity regarding boats

    Homework Statement A boat propelled so as to travel with a speed of .5m/s in still water moves directly across a river that is 60m wide. The river flows with a speed of .3 m/s. At what angle relative to the straight across direction must the boat be pointed? How long does it take the boat to...
  34. C

    Quick Relative Velocity question

    The question asks "The kinematic equation d=vt is used in conjunction with relative velocity questions. Explain why the other kinematic equations are not useful for most relative velocity questions." I assume the answer to this is that most relative velocity questions that I deal with assume...
  35. Prof. 27

    Relative Velocity: Riverboat and Canoe

    Homework Statement A canoe has a velocity of 0.420 m/s southeast relative to the earth. The canoe is on a river that is flowing at 0.550 m/s east relative to the earth. This can't be seen in the problem statement, but the angle between the two vectors is 45 degrees. As implied by the question...
  36. L

    Advanced Vector Problem: Ships

    Homework Statement Three ships A, B, and C move with velocities \vec{v_{1}} \ \vec{v_{2}} \ \vec{u} respectively. The velocities of A and B relative to C are equal in magnitude and perpendicular. Show that \left | \vec{u} -\frac{1}{2}(\vec{v_{1}} + \vec{v_{2}}) \right |^{2} = \left |...
  37. B

    Relative Velocity of locus of curves

    Hi Folks, I am struggling to see how eqn 4.1.17 is arrived at using using eqn 4.1.10 at bottom of attachment. Its not clear to me what \frac{d \phi}{dt} is...apart from what is given in eqn 2.1.30... Any ideas? Thanks
  38. V

    Maxwell distribution of relative velocities

    I want to calculate the distribution function for the relative velocity v_r = v_1 - v_2 of two particles. Each particle velocity follows the Maxwell distribution for velocities. They have the same mass and temperature. Can I just multiplicate the Maxwell distributions of the two particles (and...
  39. B

    Relative Velocity problem: 2 pulleys riveted together

    Homework Statement As shown in the picture, two pulleys are riveted together with a known velocity. I need to find the velocity of two other points. Homework Equations V_A = VB + <ω> x <BA> V = ωr The Attempt at a Solution I've honestly been trying to figure this one out for over a...
  40. L

    Proper Acceleration In Accelerometer ?

    Hi guys, I'm working on my project with accelerometer. I know that accelerometer measure specific force or proper acceleration in general by deflection of proof mass. Proper acceleration is relative to free fall which could be analogy that proper acceleration is the relative acceleration...
  41. J

    Relative Velocity of a Grenade

    Homework Statement In an action-adventure film, the hero is supposed to throw a grenade from his car, which is going 79.0 km/h , to his enemy's car, which is going 125 km/h . The enemy's car is 15.9 m in front of the hero's when he let's go of the grenade. If the hero throws the grenade so...
  42. DanielleG

    Airplane Dropping a Package Relative Motion

    Homework Statement A Red Cross airplane is traveling horizontally east at velocity v_0 = 80.0 m/s and height h = 350 m above the ground. The plane carries emergency supplies for a village inaccessible by road. The plane will drop the package (without a parachute) into a pile of soft hay...
  43. Mr Davis 97

    Relative Velocity Problem: Finding Train Speed from Raindrop Angle

    Homework Statement A person looking out the window of a stationary train notices that rain drops are falling vertically down at a speed of 5.0 m/s relative to the ground. When the train moves at a constant velocity, the raindrops make an angle of 25° when they move past the window. How fast is...
  44. E

    Relative Velocity Boat Problem

    Homework Statement You wish to paddle a boat across an 82 m wide river and land at a boathouse that is 14 m downstream of your starting point. If the current in the river is uniform at 0.50 m/s, how fast and in what direction do you need to row to reach the boathouse in 2.0 minutes? Homework...
  45. R

    Relative Velocity moving sidewalk

    Homework Statement A "moving sidewalk" at an airport moves at 1.5m/s and is 12 m long. A person enters the sidewalk and walks at 1.8 m/s relative to the sidewalk. A)How much time is required for the person to reach the opposite end if the person walks in the same direction as the sidewalk is...
  46. R

    Kinematics in one direction - relative velocity word problem

    Homework Statement Danielle bikes at a steady rate of 4.0 m/s south along the bank of a river. Summer is rowing her kayak heading south down the river; she can row at a constant rate of 2.0 m/s in still water. There is a 5.0 meter wide bridge that spans the river and the bike trail. a) If it...
  47. S

    Understanding Relative Velocity of Runners Moving in Opposite Directions

    Homework Statement James is running west wrt the ground and Billy is running east wrt the ground, but twice as fast as James. How does the relative velocity of James wrt Billy differ if they are running toward each other or away from each other? Explain. *wrt = with relation to* Homework...
  48. K

    Question on relative velocity (High school motion)

    Homework Statement Sue rows her boat at 4.5ms. The velocity of the river flow is 2.5ms. What is sues velocity against the flow relative to the water. I can't wrap my head around the question, since sues actual velocity against the flow is 2ms. This should mean she is moving backwards 0.5ms...
  49. T

    Lift relative velocity question.

    Homework Statement From a lift moving upward with a uniform acceleration 'a', a man throws a ball vertically upward with a velocity v relative to the lift.The ball comes back to the man after a time 't' Show that a+g = 2v/t Homework Equations s=ut+1/2gt2 The Attempt at a Solution I know this...
  50. H

    Frame of reference and the varying mass problem

    Hi Friends , I had a discussion with a funny person last night. He said the following argument : Suppose there are 21 objects including the one object under consideration. Each of the 21 objects move with a velocity. Since there are 21 objects, for the object we are considering has 21...
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