A rowboat begins at point A on the south bank of a straight river that is 300 m wide
PHYSICS · Multi-part · CBSE · Physics · Motion in a Plane · Motion in a Plane
Problem
A rowboat begins at point A on the south bank of a straight river that is 300 m wide. The river flows eastward at 2.0 m/s. The rowboat can travel at 4.0 m/s relative to the water. At the same instant the boat leaves point A, a floating log located 500 m upstream (west) of point A is carried downstream by the current.
The rower’s plan is to reach the log first and then deliver it to point B on the north bank directly opposite the log’s initial position.
Answer each part in sequence, showing all calculations and clearly stating any assumptions.
(a) Determine the heading the rower must choose to intercept the log while both are moving. Then calculate the time required to reach the log.
(b) Immediately after retrieving the log, the rower turns toward point B. Determine the new heading that will bring the boat–log system to point B with no further downstream drift.
(c) Calculate the additional time needed to travel from the interception point to point B.
(d) Compute the total elapsed time for the entire trip from leaving point A to arriving at point B with the log, and comment on whether the presence of the log significantly increased the overall travel time compared with a direct, no-log crossing.