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A engine is approaching a hill at consta...

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.

Text Solution

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Let `v_(e)` be the speed of the engine.
Distance covered by the engine in `5s = 5 upsilon_(e)`
Distance covered by sound in reaching the hill and coming back to the moving driver
`= (900 xx 2-5 upsilon_(e) ) " "(because 0.9"km" = 900 m)`
`= 1800 -5 v_(e)`
According to the given conditions, `t = ((1800 -5 upsilon_(e) ))/(upsilon)`
As `t =5 s and v` (speed of sound) `= 340"m s"^(-1)`.
`5= (1800-5 upsilon_(e) )/(340)` or `1700 = 1800 - 5 v_(e)`
or `v_(e) = 20" ms"^(-1)`.
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