A) 1 km
B) \[\sqrt{2}\,\,km\]
C) 4 km
D) \[\sqrt{7}\,\,km\]
Correct Answer: D
Solution :
Let the two roads intersect at \[A\]. If the bus and the car are at \[{{a}^{2}}+{{b}^{2}}=8{{p}^{2}}\] and \[C\] on the two roads respectively, then \[c=AB=2km,\,b=AC=3\] km. The distance between the two vehicles = \[BC=a\text{ }km\] Now \[\cos A=\cos {{60}^{o}}=\frac{{{b}^{2}}+{{c}^{2}}-{{a}^{2}}}{2bc}\] \[\Rightarrow \] \[\frac{1}{2}=\frac{{{3}^{2}}+{{2}^{2}}-{{a}^{2}}}{2\,.\,3.\,2}\Rightarrow a=\sqrt{7}\,\,km.\]
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