PHYSICS · Multi-part · CBSE · Physics · Motion in a Plane · Motion in a Plane
Problem
Two research vessels, Ship M and Ship N, are conducting oceanographic surveys along the same straight line through calm waters. At noon, Ship M is 32km west of a fixed buoy and moving east toward the buoy at a constant 14kmh−1. At the same instant, Ship N is 18km east of the buoy, moving eastward away from the buoy at 10kmh−1.
At 12:30 p.m. Ship N detects an equipment malfunction and immediately reverses course, thereafter steaming west at 16kmh−1 (assume the turn is instantaneous). Ship M continues at its original speed and heading for the entire period considered.
Answer the following questions regarding the motion of the two ships.
(a) Compute the distance of each ship from the buoy at 12:30 p.m., just before Ship N reverses direction.
(b) Using the positions obtained in part (a) as new initial conditions, determine the clock time at which the two ships pass each other.
(c) Given that ocean current data are typically recorded relative to the buoy's reference frame, explain in detail why treating the buoy as the origin is advantageous for the calculations in parts (a) and (b).
(d) Suppose instead the analysis were performed in a reference frame moving east at 10kmh−1. Describe qualitatively how the ships' velocities and the computed meeting time would differ from the results found in parts (a) and (b), and account for any invariance you identify.