A) \[{{t}_{1}}-{{t}_{2}}\]
B) \[\frac{{{t}_{1}}+{{t}_{2}}}{2}\]
C) \[\frac{{{t}_{1}}{{t}_{2}}}{{{t}_{2}}-{{t}_{1}}}\]
D) \[\frac{{{t}_{1}}{{t}_{2}}}{{{t}_{2}}+{{t}_{1}}}\]
Correct Answer: D
Solution :
| [d] Velocity of girl w.r.t. elevator \[=\frac{d}{{{t}_{1}}}={{v}_{ge}}\] |
| Velocity of elevator w.r.t. ground \[{{v}_{eG}}=\frac{d}{{{t}_{2}}}\] then velocity of girl w.r.t. ground |
| \[\vec{v}{{=}_{gG}}={{\vec{v}}_{ge}}+{{\vec{v}}_{eG}}\] |
| i.e., \[{{v}_{gG}}={{v}_{ge}}+{{v}_{eG}}\] |
| \[\frac{d}{t}=\frac{d}{{{t}_{1}}}+\frac{d}{{{t}_{2}}}\] |
| \[\frac{1}{t}=\frac{1}{{{t}_{1}}}+\frac{1}{{{t}_{2}}}\] |
| \[t=\frac{{{t}_{1}}{{t}_{2}}}{({{t}_{1}}+{{t}_{2}})}\] |
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