Final answer:
To find the particle's velocity in reference frame C, one must add the given velocities sequentially from frame A to frame B, then to frame C, utilizing the principle of relative velocity.
Step-by-step explanation:
The question asks for the velocity of a particle in reference frame C, given its velocity in reference frame A, and the velocities of reference frames A and B relative to other frames. To solve this, we can use the principle of relative velocity: the velocity of an object in one reference frame can be found by adding the velocity of the object in another reference frame to the velocity of the second reference frame relative to the first.
The velocity of the particle in reference frame A is given as (7.0 4.0]) m/s. The velocity of reference frame A relative to reference frame B is 3.0 k m/s. The velocity of reference frame B relative to reference frame C is 7.0 j m/s. Therefore, the velocity of the particle in reference frame C can be found by first adding the velocity of reference frame A to the particle's velocity in reference frame A to find the velocity in reference frame B, and then adding the velocity of reference frame B relative to reference frame C to find the final velocity in reference frame C.