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Two ships are 10km apart on a line running south to north. The one faster north is streaming west at 40km/hr . The other is streaming north at 40km/he. What is their distance of closet approach and how long do they to reach it?

Two ships are 10km apart on a line running south to north. The one faster north is streaming west at 40km/hr . The other is streaming north at 40km/he. What is their distance of closet approach and how long do they to reach it?

Grade:11

1 Answers

Eshan
askIITians Faculty 2095 Points
2 years ago
Dear student,

Relative velocity of second ship with respect to first one is40\sqrt{2}km/hrtowards north-east.

Hence from geometry, the distance of closes approach=\dfrac{1}{2}\dfrac{d}{cos45^{\circ}}=\dfrac{d}{\sqrt{2}}=5\sqrt{2}m

Time taken by the ship to cover this distance=\dfrac{d/\sqrt{2}}{v_{rel}}=\dfrac{5\sqrt{2}}{40\sqrt{2}}hr=0.125hr

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