A) \[100\sqrt{3}\]
B) \[\frac{200\sqrt{3}}{3}\]
C) \[\frac{100\sqrt{3}}{3}\]
D) \[200\sqrt{3}\]
Correct Answer: B
Solution :
[b] Suppose distance travelled by car\[=x\,m\] In \[\Delta \Alpha \Beta C,\]\[\tan 30{}^\circ =\frac{100}{x+l}\] \[\Rightarrow \] \[\frac{1}{\sqrt{3}}=\frac{100}{x+l}\] \[\Rightarrow \] \[x+l=100\sqrt{3}\,m\] (i) Now, in \[\Delta ABD,\]\[\tan 60{}^\circ =\frac{100}{l}\] \[\Rightarrow \] \[\sqrt{3}=\frac{100}{l}\]\[\Rightarrow \]\[l=\frac{100}{\sqrt{3}}\,m\] On subtracting Eq. (ii) from Eq.(i), we get \[(x+l)-l=100\sqrt{3}-\frac{100}{\sqrt{3}}\] \[\Rightarrow \] \[x=100\left( \sqrt{3=\frac{1}{\sqrt{3}}} \right)\] \[\Rightarrow \] \[x=\frac{200}{\sqrt{3}}\,m\]\[\Rightarrow \]\[x=\frac{200\sqrt{3}}{3}\,m\] |
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