## Relative Velocities and Relative Positions

Definition: If A is at position moving with velocity and B is at position moving with velocity then

1. The relative position of B relative to A is given by and the relative velocity of B relative to A is given by 2. The relative position of A relative to B is given by and the relative velocity of A relative to B is given by 3. The position of of A at any time t is given by 4. The position of of B at any time t is given by Typically we are are asked about relative velocities, relative positions and points of intersection or CRASHES!

Example A boat A started from position with speed .

a)Find the position of A at time t If boat B start from position with velocity find if boat A and B CRASH and if they do, find the position of the crash site and the distance from the origin to this position.

The position vector of B at time t is given by If they collide, at some point they are in the same place at the same time. This means that for some value of We solve: We equate the coefficients of and on both sides:  We get the same value of t from both equations hence they meet at the same place at the same time.

We can obtain the position vector of the point of collision be substituting the value t=2 into either or   The distance from the origin to is given by so distance from origin to crash site is #### Add comment Refresh