Relative velocity

what is relative velocity-

DETERMINATION OF RELATIVE VELOCITY 

• If the points P and Q be moving in the same direction with velocity u and v ( < u) then
  vPQ = u – v ( in the direction of P). 

• If the points P and Q be moving in the opposite directions, then vPQ = u + v ( in the direction of P) 

• In case the two points P, Q are moving with velocities u, v at angles α, β with x–axis, and v be the velocity of P and relative to Q inclined at an angle β to the x–axis then 

           v cosθ = u cosα – v cosβ 

            v sinθ = u sinα – v sinβ 

Example : A watchman on a light house observes two ships A and B. A sailing north at 20 km/hr and B sailing north–east at 20 km/hr. In what direction and with what speed does the ship B appear to be sailing to a person on the ship A. 

Determination of true velocity when the apparent velocity is given 

When the relative velocity of a point Q with respect to an observer P is given, as also the velocity of the observer P, the true velocity of Q is obtained by compounding these two given velocities. 

⇒

i.e  vQ = where  α is the angle between 

and tanθ = . 

Example : To a man walking due east at the rate of 4 km/hr, the wind appears to blow from the North East at 4 km/hr. Find the true velocity of the wind. 

 Hence the wind is actually blowing from north at 4 km/hr.

Check out Physics Formulas and NCERT Solutions for class 12 Physics prepared by Physics Wallah.