Question:
Rahim drives from city A to station C at \(70\) km/h. Train leaves city B (500 km south of A) at 8:00 am toward C at \(50\) km/h. C is located between S and SW of A with AC at \(30^\circ\) to AB. Rahim must reach C at least 15 minutes before train. Latest time to leave A?
Rahim drives from city A to station C at \(70\) km/h. Train leaves city B (500 km south of A) at 8:00 am toward C at \(50\) km/h. C is located between S and SW of A with AC at \(30^\circ\) to AB. Rahim must reach C at least 15 minutes before train. Latest time to leave A?
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Relative motion problems with angled paths can be solved by breaking into components using trigonometry.
Updated On: Jul 30, 2025
- 6:15 am
- 6:30 am
- 6:45 am
- 7:00 am
- 7:15 am
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The Correct Option is B
Solution and Explanation
AC forms \(30^\circ\) with AB (500 km). Distance AC = \(500 / \cos 30^\circ \approx 577.35\) km.
Train’s path: BC = 500 km \(\tan 30^\circ \approx 288.675\) km offset → BC length from geometry.
Train speed 50 km/h, Rahim 70 km/h. Compute times to meet at C, ensuring Rahim arrives 15 min earlier.
Latest start time from A ≈ 6:30 am.
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