Two rescue boats start simultaneously from the same pier located at and head to the…

PHYSICS · Subjective · CBSE · Physics · Motion in a Plane · Motion in a Plane

Problem

Two rescue boats start simultaneously from the same pier located at

O(0,0)

and head to the distress point

D(15\,\text{km},\,12\,\text{km})

by different routes. Boat A travels first to

P(6\,\text{km},\,8\,\text{km})

and then directly to

D

. Boat B travels first to

Q(9\,\text{km},\,−4\,\text{km})

and then directly to

D

. (a) For Boat A, calculate the displacement vectors

\overrightarrow{OP}

and

\overrightarrow{PD}

and hence obtain the total displacement

\overrightarrow{OD}

. (b) Repeat the calculations of part (a) for Boat B using points

Q

and

D

. (c) Show algebraically that, despite the different paths chosen, both boats have the same resultant displacement with respect to the pier. (d) Compute and compare the total distances actually travelled by the two boats. Briefly explain why the distances differ even though the resultant displacement is identical.

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