A engine is approaching a hill at constant speed. When it is at a distance of `0.9 km`, it blows a whistle, whose echo is heard by the driver after `5 s`. If the speed of sound is `340 m//s`, calculate the speed of the engine.

Explanation

(a)

Distance travelled by sound when it again meets the person
`= 900 + (900 - x)`
`= 1800 - u t_(0) = 1800 - u xx 5`
`(1800 - 5u)/(v) = 5`
`1800 - 5 u = 5v`
`1800 - 5 u = 5 xx 330`
`5 u = 150 rArr u = 30 m//s`
(ii)
`1.5 = (2x)/(v)` (i)
`2.5 = (2(d - x))/(v)` (ii)
`(i) + (ii)`
`4 = (2d)/(v)`
`d = 2v = 2 xx 332 = 664 m`

For third echo, sound reflected by one hill and then by another hill and then to person
`= (2d)/(v) = (2 xx 664)/(332) = 4 s`