A car is initially at rest, 330 m away from a stationary observer. It begins to move towards the observer with an acceleration of `1.1 m s^(-2)` sounding its horn continuously. 20 s later, the driver stops sounding the horn. The velocity of sound in air is `330 m s^(-1)`. The observer will hear the sound of the horn for a duration of

Options

A. 20 s
B. 21 s
C. `20(2)/(3)s`
D. `19(1)/(3)s`

Answer

C

Explanation

Let the car begin to move and sound its horn at time `t_(0)`.
The sound reaches the observer in 1 s.
`therefore` The observer begins to hear the sound at time `t_(1)=t_(0)+1s`. The displacement of the car in 20 s is
`S=((1)/(2))(1.1ms^(-2))(20s)^(2)=220m`
`therefore` At time `t_(2)=t_(0)+20s`, the horn is switched off and the car is 110 m away from the observer. The sound emitted by the horn at the instant it is switched off will travel to the observer in a further time `(1//3)s`.
`therefore` The observer stops hearing the sound at time `t_(3)=t_(2)+(1)/(3)s`.
`therefore` The observer hears sound for a duration of
`t=t_(3)-t_(1)=t_(2)+(1)/(3)s-t_(1)=(t_(0)+20s)+(1)/(3)s-(t_(0)+1s)=19(1)/(3)s`