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)

(v_c) as measured from car 1 (v_c) as measured from car 3
(c)

(v_c) as measured from car 1 (v_c) as measured from car 3
(d)

Explanation:

Step1: Analyze relative - velocity concept

The velocity of the cyclist with respect to an observer in the train is the velocity of the cyclist with respect to the ground minus the velocity of the train with respect to the ground. The train is moving east.

Step2: Consider the direction of velocities

The cyclist is moving 15° east of north with respect to the ground. When we consider the relative - velocity of the cyclist with respect to an observer in the train, we need to subtract the east - ward velocity of the train from the cyclist's velocity vector. Since \(v_CThe direction of the cyclist's velocity with respect to the ground is 15° east of north. When we find the relative velocity with respect to the train (moving east), the angle of the relative - velocity vector with respect to the north direction will increase.
For an observer in Car 1 and Car 3 (assuming they are on the train), the relative - velocity vectors should have the same general direction (because they are in the same non - accelerating frame of reference).

Answer:

A. Option Text