Answer: speed of sound in air is c and as the air is also moving the velocity of sound is c+v
a
where v
a
is the speed of air
The train sounds the whistle when it is at a distance of x from the hill. Sound moving with velocity v with respect to ground, takes time t to reach the hill
t=
v
x
=
c+v
a
x
after the reflection from the sound waves travels towards the train hence now the velocity of sound is c−v
a
traveledlet the distance concerning by reflected wave be x
′
therefore time the by it t
′
=
c−v
a
x
′
the total time between echoing the whistle and its reflection t+t
′
meanwhilethe is taken, the train travels the distance x−x
′
with constant speed v
s
x−x
′
=(t+t
′
)v
s
x−x
′
=
c+v
a
v
s
x+
c−v
a
v
s
x
′
x
c+v
A
c+v
a
−v
s
=x
′
c−v
a
c−v
a
+v
s
x
′
=x
(c+v
a
)×(c−v
a
+v
s
)
(c−v
a
)×(c+v
a
−v
s
)
Step-by-step explanation: