AP EAMCET · PHYSICS · Motion In One Dimension
Two towns \(A\) and \(B\) are connected by a regular bus service with a bus leaving in either direction every \(T\) min. A man cycling with a speed of \(20 \mathrm{~km} / \mathrm{h}\) from \(A\) to \(B\) notices that a bus travelling in the direction of his motion goes past him every \(18 \mathrm{~min}\) and every \(6 \mathrm{~min}\) he notices a bus travelling in the opposite direction go past him. Assuming that, the buses travel with a constant speed. Find \(T\) and the constant speed of the buses.
- A \(\frac{2}{27} \mathrm{~h}\) and \(38 \mathrm{~km} / \mathrm{h}\)
- B \(\frac{5}{8} \mathrm{~h}\) and \(40 \mathrm{~km} / \mathrm{h}\)
- C \(\frac{3}{20} \mathrm{~h}\) and \(40 \mathrm{~km} / \mathrm{h}\)
- D \(\frac{2}{3} \mathrm{~h}\) and \(28 \mathrm{~km} / \mathrm{h}\)
Answer & Solution
Correct Answer
(C) \(\frac{3}{20} \mathrm{~h}\) and \(40 \mathrm{~km} / \mathrm{h}\)
Step-by-step Solution
Detailed explanation
Let, the speed of bus be \(v_B\) and that of cyclist be \(v_C\). Case 1 Bus moving from \(A\) to \(B\), Relative speed of bus \(=v_B-v_C=v_B-20\) Distance covered \(=\) Velocity \(\times\) Time \[ d=\left(v_B-20\right) \times 18...(i) \] Case 2 Bus moving from \(B\) to \(A\),…
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