Question

Your foot is trapped under a railway sleeper. You feel the rail vibrate and then 20s later hear a faint whistle. Estimate how much time you have to free yourself. You may assume the railway way is a straight line and: Velocity of sound in air = 0.33 km/s , The velocity of vibration along the track = 5 km/s,
Train speed: 60 km/hr, 100 km/hr and 150 km/hr

Answer 1

Explanation:

Speed of sound in air = 0.33 km/s

Speed of vibration along the track = 5 km/s

Time = Distance / Speed

$\frac{s}{0.33}-\frac{s}{5}=20\\\Rightarrow \frac{467}{165}s=20\\\Rightarrow s=20\times \frac{165}{467}\\\Rightarrow s=7.06638\ km$

When train speed: 60 km/hr

$Time=\frac{7.06638}{\frac{60}{3600}}=423.9828\ s$

Time you will have is 423.9828 s

When train speed: 100 km/hr

$Time=\frac{7.06638}{\frac{100}{3600}}=254.38968\ s$

Time you will have is 254.38968 s

When train speed: 150 km/hr

$Time=\frac{7.06638}{\frac{150}{3600}}=169.59312\ s$

Time you will have is 169.59312 s