(i) An engine approaches a hill with a constant speed. When it is at a distance of 0.8 km, it blows a…
(i) An engine approaches a hill with a constant speed. When it is at a distance of 0.8 km, it blows a whistle whose echo is heard by the driver after 4 s. If speed of engine in air is 330 m/s. Calculate the speed of engine. (ii) A person standing between two parallel hills fires a gun. He hears the first echo after 1.5 s and second after 2.5 s. If speed of sound is 332 m/s, calculate the distance between the hills. When will he hear the third echo?
Solution
Sol. (i) The given situation is shown in the following figure.
Distance travelled by sound when it again meets the person
= $800+(800-x)$
= $1600 - ut = 1600 - u\times 4$
Now, $\dfrac{1600-4u}{v}=4$
$\Rightarrow\;1600-4u=4v\Rightarrow\;1600-4u=4\times 330$
$4u=1600-1320$
$4u=280\Rightarrow u=70\ \mathrm{ms}^{-1}$
(ii) The given situation is shown in the following figure.
Answer: $70$ ms$^{-1}$