An engine approaches a hill with a constant speed. When it is at a distance of $0.9\text{ km}$, it blows a…
An engine approaches a hill with a constant speed. When it is at a distance of $0.9\text{ km}$, it blows a whistle whose echo is heard by the driver after $5\text{ s}$. If speed of sound in air is $330\text{ m/s}$, the speed of engine is
10 m/s
20 m/s
30 m/s
40 m/s
Solution
If the speed of engine is $v$, the distance travelled by engine in $5\text{ s}$ will be $5v$ and hence, the distance travelled by sound in reaching the hill and coming back to the moving driver
$= 900 + (900 - 5v) = 1800 - 5v$. So, the time interval between original sound and its echo,
$t = \frac{(1800 - 5v)}{330} = 5 \implies v = 30\text{ m/s}$