The related information from Physics.
Velocity definition: Velocity is speed in a known direction.
Relative Velocity definition: The velocity of an object, A, relative to any other choosen object, B, having velocity, including stationary objects.
General calculation:
Let the velocity of object, A be equated to v1, while the velocity of object, B is equatable to v2. The relative velocity of A with respect to B is written as, Rv(v1,v2), WHEREAS, the relative velocity of B with respect to A is written as, Rv(v2,v1), which is short for Rv(+v1,+v2).
The calculation, Rv(v1,v2) is, Rv(v1,v2) = v1-v2 = (+v1) - (+v2) ;
The
resulting value can be positive (+), negative (-), or zero (0).
Because velocity is speed in a known direction, solving physics problems of this nature,
means assigning the directions of travel, in a sane, comprehensive manner. The normal
assignments for direction, starts within the frame of reference, which has been agreed
upon, as positive. Therefore Rv(v1,v2), at least means, that v1 is aligned with a positive
direction. This implies that assignments for direction are done in sequential order, and the
frame of reference is given itz direction, first, before all others.
Any object B, with velocity v2, moving in the same direction, as the direction, the frame
of reference indicates, yields a direction, identical to the frame of reference, (positive)
and the relation written Rv(+v1,+v2) which is identical to Rv(v1,v2).
Any object B, moving in the opposite direction as the direction the frame of reference
indicates, itz directional relationship to the frame of reference is, the opposite,
(negative) and the relation written Rv(+v1,-v2), which is the same as Rv(v1,-v2).
Velocity is a vector (directional) whereas speed is a scalar (non directional).
Here are the steps:
(1) From the given information construct your frame of reference (v1).
(2) Write down the equivalence relation of Rv(v1,v2)
(3) Calculate the relative velocity Rv(v1,v2) = (v1) - (v2), keeping the sign.
(4) Write your answer clearly, with direction and appropriate units.
Shall we proceed?
solving part a said:
a) both cars are heading in the same direction, A behind B in the reference frame of A
(Step 1)
<---------A (80 km/h) (+)
<----B (45 km/h) (same direction so it is positive (+))
(Step 2) Rv(+80,+45).
(Step 3) Rv(v1,v2) = v1 - v2 = 80km/h - 45km/h = 35km/h
(Step 4) The relative velocity is 35km/h
solving part b said:
b) Use the reference frame of B for part A)
(Step 1)
<----B (45 km/h) (+)
<---------A (80 km/h) (same direction so it is positive)
(Step 2) Rv(+45,+80).
(Step 3) Rv(v1,v2) = v1 - v2 = 45km/h - 80km/h = -35km/h
(Step 4) The relative velocity is -35km/h
solving part c said:
c) both cars are heading towards each other. take the reference frame of A
(Step 1)
<---------A (80 km/h) (+)
B------> (45 km/h) (opposite direction so it is negative)
(Step 2) Rv(+80,-45)
(Step 3) Rv(v1,v2) = v1 - v2 = (+80km/h) - (-45km/h) = 125km/h
(Step 4) The relative velocity is 125km/h.
solving part d said:
d) use B's reference frame for part c.
(Step 1)
<------B (45 km/h) (+)
A---------> (80 km/h) (opposite direction so it is negative)
(Step 2) Rv(+45,+80).
(Step 3) Rv(v1,v2) = v1 - v2 = (+45km/h) - (-80km/h) = 125km/h
(Step 4) The relative velocity is 125km/h.