A motor cycle starts from rest and accelerates along a straight path at 2 m/`s^(2)`. At the starting point of the motoer cycle there is a stationary electric siren. How far has the motor cycle gone when the driver hears the frequency of the siren at 94% of its value when the motor cycle was at rest ? (speed of sound = 330 `ms^(-1)` )

Options

A. 146 m
B. 196 m
C. 49 m
D. 98 m

Answer

D

Explanation

For observer moving away from source
` V. = ((V- v)/(V)) ` y
` (94)/(100) V = (V - v)/(V) ` V
`rArr " " 94 V = 100 V - 100 v`
`rArr " " 100v = 6 `v
100v = 6V
`v = (6 xx 330)/(100) = 19.8` m/s
Now `v^(2) - u^(2) = ` 2as
`rArr (19.8)^(2) - 0 = 2 xx 2s`
S = 96 m
`rArr ` choice (d).