A ship A is moving westwards with a speed of 10 km h⁻¹ and a ship B, initially 100 km south of A, is moving northwards with a speed of 10 km h⁻¹. The time after which the distance between them becomes shortest is:
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Question

A ship A is moving westwards with a speed of 10 km h⁻¹ and a ship B, initially 100 km south of A, is moving northwards with a speed of 10 km h⁻¹. The time after which the distance between them becomes shortest is:

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G1 Physics · Accepted Answer

Step 1: After time t hours, ship A is 10t km west of its initial position and ship B is 100−10t km south of A's initial latitude. Step 2: Separation squared is S²=(10t)²+(100−10t)². Step 3: Minimize S²: d(S²)/dt=200t−200(100−10t)/10=0, giving t=5 h. Final answer: B.