Definition: If A is at position
moving with velocity
and B is at position
moving with velocity
then
-
The relative position of B relative to A is given by
and the relative velocity of B relative to A is given by
-
The relative position of A relative to B is given by
and the relative velocity of A relative to B is given by
-
The position of
of A at any time t is given by
-
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