Question

a train is traveling east at a constant speed $v_t$, as shown in the diagram. a cyclist moving at constant speed $v_c$ heading 15° east of north with respect to the ground is also shown. if $v_c < v_t$, which of the following vectors could represent the velocity of the cyclist as measured from an observer in car 1 and from an observer in car 3?

$v_c$ as measured from car 1 $v_c$ as measured from car 3
(a)
$v_c$ as measured from car 1 $v_c$ as measured from car 3
(b)

Explanation:

Step1: Understand relative - velocity concept

The velocity of the cyclist with respect to an observer on the train ($\vec{v}_{C - T}$) is given by $\vec{v}_{C - T}=\vec{v}_{C}-\vec{v}_{T}$, where $\vec{v}_{C}$ is the velocity of the cyclist with respect to the ground and $\vec{v}_{T}$ is the velocity of the train with respect to the ground.

Step2: Analyze direction

The cyclist is moving $15^{\circ}$ east of north with respect to the ground. The train is moving east - ward. When we find the relative velocity of the cyclist with respect to the train, we subtract the velocity vector of the train from the velocity vector of the cyclist. Since $v_{C}

Step3: Consider observers in Car 1 and Car 3

Observers in Car 1 and Car 3 are in the same non - accelerating frame (the train). So, the velocity of the cyclist as measured from Car 1 and Car 3 will be the same in direction and magnitude (because the train is moving with a constant speed).

Answer:

A. Option Text, B. Option Text (Since the figure of options is not fully provided with text for B, but based on the analysis, the correct answer should have the same non - zero vectors for both measurements from Car 1 and Car 3 in the appropriate direction considering the relative - velocity subtraction. If option A has the correct equal - direction vectors, then the answer is A).