Relative velocity of two speeding cars

[checkmarks]

Homework Statement

Given the following conditions, what is the relative velocity of 2 cars if their ground speeds are 80km/h for Car A and 45 km/h for Car B?
a) both cars are heading in the same direction, A behind B in the reference frame of A
b) Use the reference frame of B for part A)
c) both cars are heading towards each other. take the reference frame of A
d) use B's reference frame for part c.

Homework Equations

none. i just used simple addition + subtraction.

The Attempt at a Solution

basically the wording of this problem is really throwing me off. i don't understand what they're trying to ask me to do evne though it seems like an easy question.

im guessing that 35km/h will be the answer for A and B? because i figured if you were sitting in car B, it seems like car A is just going 35 km/h faster..?
please help. thanks

 

[basePARTICLE]

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?

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

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

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.

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.

 

[Moetasim]

I would approach this problem by first clarifying the reference frames and the direction of motion for each car. In this scenario, the reference frame is the point of view from which the motion of the cars is observed. The direction of motion is the direction in which the cars are traveling.

a) In the reference frame of car A, car B is moving in the same direction at a slower speed. Therefore, the relative velocity of car B with respect to car A is 35 km/h (80 km/h - 45 km/h).

b) In the reference frame of car B, car A is moving in the opposite direction at a faster speed. Therefore, the relative velocity of car A with respect to car B is 35 km/h (80 km/h + 45 km/h).

c) In the reference frame of car A, both cars are moving towards each other. Therefore, the relative velocity of car B with respect to car A is 125 km/h (80 km/h + 45 km/h).

d) In the reference frame of car B, both cars are moving towards each other. Therefore, the relative velocity of car A with respect to car B is 125 km/h (80 km/h + 45 km/h).

It is important to note that the relative velocity is always calculated with respect to a reference frame and the direction of motion. In this case, the relative velocity changes depending on the chosen reference frame and the direction of motion.