1 / 15

RELATIVE VELOCITY

RELATIVE VELOCITY. The velocity of an object with respect to another object. Notation. v A = velocity of object A with respect to a stationary object. v AG = velocity of object A with respect to ground (stationary object on the ground) v A and V AG have the same meaning.

colleen-montgomery
Download Presentation

RELATIVE VELOCITY

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. RELATIVE VELOCITY The velocity of an object with respect to another object.

  2. Notation • vA = velocity of object A with respect to a stationary object. • vAG= velocity of object A with respect to ground (stationary object on the ground) • vA and VAG have the same meaning. • vAB=velocity of object A in the frame of reference (with respect to) object B • vAB=vA-vB(velocity of object A with respect to ground - velocity of object B with respect to ground.)

  3. Relative Velocity (One Dimension) A B vA=+5.0 m/s vB=0 m/s vAB=vA-vB =+5.0 m/s – 0 m/s = +5.0 m/s vBA=vB-vA = 0-(+5.0m/s) = -5.0 m/s vAB = -vBA(Always)

  4. Relative Velocity(Two Objects Moving in Opposite Directions) • The relative velocity of two objects moving in opposite directions is the sum of the two speeds with the appropriate frame of reference direction. A B vB=+5.0 m/s vA=-10 m/s vAB=vA-vB = -10 m/s – (+5.0 m/s) = -15.0 m/s vBA = +15.0 m/s

  5. Relative Velocity(Two Objects Moving in the Same Direction) • The relative velocities of two objects moving in the same direction is the difference of the two speeds and with the appropriate frame of reference direction. A B vB=+5.0 m/s vA=+10 m/s vAB=vA-vB = +10 m/s – (+5.0 m/s) = +5.0 m/s vBA = -5.0 m/s

  6. Relative Velocity(One object moving with another object) vBC =velocity of ball with respect to car vCG=velocity of the car with respect to ground vBG=velocity of ball with respect to ground vCG=+10 m/s vBC=+20 m/s vBG=vBC+vCG vBG=+20m/s +(+10 m/s)= +30 m/s

  7. Check of Relative Velocities • vBG=vBC+vCG • vBG=(vB-vC)+(vC-vG)=vB-VG

  8. Relative Velocity(Two Dimensions) Situation 1: vA θA B A θB vB vABx=vAcosθA-vBcosθB vABy=vAsinθA-vBsinθB

  9. ` Relative Velocity in Two Dimensions Situation 2: What is the velocity of the boat in the earth’s frame of reference? vWG vWG vBW θ vBG vBW vWG= velocity of water with respect to ground vBW= velocity of boat with respect to water vBG= velocity of boat with respect to the ground. vBG=vBW+vWG θ=tan-1(vWG/vBW)

  10. Relative Velocity in Two Dimensions Situation 3: vWG vWG vBW vBG=vR vBW θ vBG=vBW+vWG θ=sin-1(vWG/vBW) vR = resultant boat speed vR The angle needed to travel directly across the stream.

  11. The angle necessary to dock a specific distance downstream: vWG Situation4: x θ d vW vB α φ What angle, α, must the boat be directed to dock a distance, x, downstream while crossing a river that is a distance, d, wide? Known: vW,,vB, x, and d. θ=tan-1(x/d) where θ=α+φ, which is the resultant angle of the boat. α= boat angle, φ=angle between boat’s aimed direction (boat angle) and actual direction. vBG=vB + vW = vR

  12. Situation 4 continued x z θ d vW z α vBG=vR vB φ vBG vR = resultant velocity from water and boat β Use law of sines. vW/vB=sin φ/sin z, solve for φ α = θ - φ

  13. Distance to dock upstream. x Situation 4a α d vW vBG vBG=vR φ θ vR = resultant velocity from water and boat vB

  14. Distance downstream docked based on specific boat direction: x Situation 5 z θ d vWG z α vBG=vR φ vBG vB vR = resultant velocity from water and boat Known: vWG, vBW, d, and α. How far will the boat aimed at an angle, α, dock downstream?

  15. Situation 5 continued x z θ d vBG=vR vBx vW vR = resultant velocity from water and boat z α = vBx φ vBG vB vRx=vW+vB(sin α) vRy = vB(cos α) θ=tan-1(vRx/vRy) tan θ=(x/d)  solve for x.

More Related