PHYSICS · Multi-part · CBSE · Physics · Motion in a Plane · Motion in a Plane
Problem
Three spacecraft—A, B, and C—coast along the same straight line far from any planets, so external forces can be neglected. Earth-based mission control measures their speeds to be 100 m/s, 60 m/s, and 20 m/s, respectively, all in the same direction.
During a synchronized data-collection interval, every crew records observations of the other two spacecraft.
(a) Construct a qualitative ranking, from greatest to least, of the magnitude of spacecraft C’s velocity as measured by the crews of spacecraft A, B, and C itself. Clearly indicate any equal magnitudes.
(b) Repeat the ranking task in part (a) for the magnitude of spacecraft A’s velocity as measured by the crews of spacecraft A, B, and C.
(c) Explain why any crew that uses its own spacecraft as the reference object must always measure that spacecraft’s velocity magnitude to be zero, regardless of what Earth-based mission control reports.
(d) Using qualitative reasoning only, formulate a general statement that predicts how the magnitude of an object’s velocity measured by two different inertial observers depends on their individual speeds relative to a third common reference. Illustrate how your statement is consistent with the specific rankings obtained in parts (a) and (b).