Question

A motor cycle starts from rest and accelerates along a straight path at $2\, m/s^2$. At the starting point of the motor cycle there is a stationary electric sire. 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 $= 330 \,ms^{-1}$).

• A. $49\,m$
• B. $98\,m$
• C. $147\,m$
• D. $196\,m$

Answer 1

Answer: (B)

$98\,m$

Answer 2

Motor cycle, $u = 0, a = 2 m/s^2$ Observer is in motion and source is at rest. $\Rightarrow n'=n \frac{v-v_{O}}{v+v_{S}} \Rightarrow \frac{94}{100}n=n \frac{330-v_{O}}{330} \Rightarrow 330-v_{O}=\frac{330\times94}{100}$ $\Rightarrow v_{O}=330-\frac{94\times33}{10}=\frac{33\times6}{10}m/s$ $s=\frac{v^{2}-u^{2}}{2a}=\frac{9\times33\times33}{100}=\frac{9\times1089}{100}\approx98\,m.$