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Mathematics in Physics

JEE Main level, single correct, medium

32 of 121

Question 32 of 121

Ship $A$ is sailing towards north-east with velocity) $\vec{v}=30\hat{i}+50\hat{j}km{h}^{-1}$ where $\hat{i}$ points east and $\hat{j},$ north. The ship $B$ is at a distance of $80km$ east and $150km$ north of Ship $A$ and is sailing towards the west at $10km{h}^{-1}.$ $A$ will be at the minimum distance from $B$ in:

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Answer: (C) $2.6h$

{\vec{v}}_{rel}={\vec{v}}_{1}-{v}_{2}=40i+50j

{\vec{r}}_{rel}={\vec{r}}_{1}-{\vec{r}}_{2}=-80i-150j

{t}_{min}=\left|\dfrac{{\vec{v}}_{rel}\cdot {\vec{r}}_{rel}}{{\left|{\vec{v}}_{rel}\right|}^{2}}\right|=\left|\dfrac{-3200-7500}{{\left(\sqrt{{\left(40\right)}^{2}+{\left(50\right)}^{2}}\right)}^{2}}\right|

{t}_{min}=\dfrac{10700}{4100}=\dfrac{107}{41}=2.6 h

JEE Main question paper PDF

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JEE Main 2025 Apr 2 Shift 1 question paper

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