14 Problem 1 You place your ear onto a steel railroad track

(14%) Problem 1: You place your ear onto a steel railroad track and hear the sound of a distant train through the rails 1 = 4.5 seconds before you do through the air. The speed of sound in steel is v, - 6100 m/s, and and the air temperature is 27° C A Find the distance, D, to the train in meters Grade Summary Deductions Potential 0% 100% cos) cotan) asinO tan() | | ( | acosO Submissions Attempts remaining: 10 (1 % per attempt) sin) detailed view 0sinh(O atan()acotan cosh)tanh) cotanhO 0 END Degrees Radians DEL CLEAR Submit Hint I give up! Hints: 1 % deduction per hint. Hints remaining: 2 Feedback: 0% deduction per feedback

Solution

speed of sound in air
331 m/s + 0.6 m/s*C * C
331 + 0.6 (27) = 347.2 m/s
we assume that the distance is the same for both events
let time in rail be x then time in air is x+4.5
347.2 m/s (x+4.5)s = 6100 m/s (x)s
347.2 x + 1562.4 = 6100 x
5752.8x = 1562.4
x = 0.271 s time in rail
so
6100 m/s * 0.271 s = 1653.1 m or about 1653 m