A) \[{{h}_{1}}=\frac{{{h}_{2}}}{3}=\frac{{{h}_{3}}}{5}\]
B) \[{{h}_{2}}=3{{h}_{1}}\text{ }and\text{ }{{h}_{3}}=3{{h}_{2}}\]
C) \[{{h}_{1}}={{h}_{2}}={{h}_{3}}\]
D) \[{{h}_{1}}=2{{h}_{2}}=3{{h}_{3}}\]
Correct Answer: A
Solution :
\[\therefore h=\frac{1}{2}g{{t}^{2}}\text{ }\therefore {{\text{h}}_{1}}=\frac{1}{2}g{{\left( 5 \right)}^{2}}=125\] \[{{\text{h}}_{1}}+{{\text{h}}_{2}}=\frac{1}{2}g{{\left( 10 \right)}^{2}}=500\Rightarrow {{\text{h}}_{2}}=375\] \[\therefore {{\text{h}}_{1}}+{{\text{h}}_{2}}+{{h}_{3}}=\frac{1}{2}g{{\left( 15 \right)}^{2}}=1125\] \[\Rightarrow {{h}_{3}}625\] \[{{h}_{2}}=3{{h}_{1}},{{h}_{3}}=5{{h}_{1}}\text{ or }{{\text{h}}_{1}}=\frac{{{h}_{2}}}{3}=\frac{{{h}_{3}}}{5}\]
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