A) \[{{\text{h}}_{\text{1}}}\text{=}{{\text{h}}_{\text{2}}}\]
B) \[{{\text{h}}_{\text{2}}}\text{}{{\text{h}}_{\text{1}}}\]
C) \[{{\text{h}}_{\text{2}}}\text{}{{\text{h}}_{1}}\]
D) \[{{\text{h}}_{\text{2}}}\ge {{\text{h}}_{\text{1}}}\]
Correct Answer: B
Solution :
[b] \[x=3{{t}_{1}}=5{{t}_{2}}\text{ }\Rightarrow {{t}_{1}}=x/3\text{ and }{{t}_{2}}=x/5\] |
Now \[{{h}_{1}}=4{{t}_{1}}-\frac{1}{2}gt_{1}^{2}=\frac{4}{3}x-\frac{g{{x}^{2}}}{18}.\] |
and \[{{h}_{2}}=4{{t}_{2}}-\frac{1}{2}gt_{2}^{2}=\frac{4x}{5}-\frac{g{{x}^{2}}}{10}.\] |
Clearly, \[{{h}_{2}}<{{h}_{1}}.\] |
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