A) 4.2 hrs.
B) 2.2 hrs.
C) 3.2 hrs.
D) 2.6 hrs.
Correct Answer: D
Solution :
[d] If we take the position of ship 'A' as origin then positions and velocities of both ships can be given as : |
\[{{\text{\vec{v}}}_{A}}=\left( 30\hat{i}+50\hat{j} \right)km/hr\] |
\[{{\text{\vec{v}}}_{B}}=-10\hat{i}\,km/hr\] |
\[{{\vec{r}}_{A}}=0\hat{i}+0\hat{j}\] |
\[{{\vec{r}}_{B}}=\left( 80\hat{i}+150\hat{j} \right)km\] |
Time after which distance between them will be minimum |
\[t=-\frac{{{{\vec{r}}}_{BA}}.{{{\text{\vec{v}}}}_{BA}}}{{{\left| {{{\text{\vec{v}}}}_{BA}} \right|}^{2}}};\] |
where\[{{\vec{r}}_{BA}}=\left( 80\hat{i}+150\hat{j} \right)km\] |
\[{{\text{\vec{v}}}_{BA}}=-10\hat{i}-\left( 30\hat{i}+50\hat{j} \right)\] |
\[\left( -40\hat{i}-50\hat{j} \right)km/hr\] |
\[\therefore \]\[t=-\frac{\left( 80\hat{i}+150\hat{j} \right).\left( -40\hat{i}-50\hat{j} \right)}{{{\left| -40\hat{i}-50\hat{j} \right|}^{2}}}\] |
\[=\frac{3200+7500}{4100}hr=\frac{10700}{4100}hr=2.6hrs\] |
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