KCET · Physics · Motion In One Dimension
At a metro station, a girl walks up a stationary escalator in \(20 \mathrm{~s}\). If she remains stationary on the escalator, then the escalator take her up in \(30 \mathrm{~s}\). The time taken by her to walk up on the moving escalator will be
- A \(25 \mathrm{~s}\)
- B \(60 \mathrm{~s}\)
- C \(12 \mathrm{~s}\)
- D \(10 \mathrm{~s}\)
Answer & Solution
Correct Answer
(C) \(12 \mathrm{~s}\)
Step-by-step Solution
Detailed explanation
Let \(h\) be the height of platform, then speed of walking \(\left(v_{g}\right)=\frac{h}{20}\)
Speed of escalator \(\left(v_{e}\right)=\frac{h}{30}\)
Time taken by girl when she walk up on the moving escalator is
\(t=\frac{h}{v_{g}+v_{e}}=\frac{h}{\frac{h}{20}+\frac{h}{30}}=\frac{20 \times 30}{(30+20)}=12 \mathrm{~s}\)
Speed of escalator \(\left(v_{e}\right)=\frac{h}{30}\)
Time taken by girl when she walk up on the moving escalator is
\(t=\frac{h}{v_{g}+v_{e}}=\frac{h}{\frac{h}{20}+\frac{h}{30}}=\frac{20 \times 30}{(30+20)}=12 \mathrm{~s}\)
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