In a car race sound signals emitted by two cars are detected by the detector on the straight track at the end point of the race. Frequency observer is 330 Hz and 360 Hz and the original frequency is 300 Hz of both cars. Race ends with the separation of 100 m between the cars. Assume both cars move with constant velocity and velocity of sound is `330(m)/(s)`. Find the time taken by wining car.

Explanation

Let the velocity of car 1 and car 2 be `V_1` and `V_2`, respectively.
Apparent frequencies of sound emitted by car 1 and car 2 as detected at end point are
`f_1=f_0(V)/(V-V_1)`,`f_2=f_0(V)/(V_V_2)`
`330=300(330)/(330-V_1)`,`360=300(330)/(330-V_2)`
`V_1=30(m)/(s)` and `V_2=55(m)/(s)`
The distance between both the cars just when the car 2 reaches end point B (as shown in fig) is