Question

A motorcycle starts from rest and accelerates along a straight line at $2.2m/s^2.$ The speed of sound is 330 m/s. A siren at the starting point remains stationary. When the driver hears the frequency of the siren at 90% of when the motorcycle is stationary, the distance travelled by the motorcyclist is

• A. 123.75 m
• B. 247.5 m
• C. 495 m
• D. 990 m

Answer 1

The correct option is B 247.5 m

Let $v_m$ be the velocity of motorcyclist and v be the velocity of sound.
$V^{\prime }=\frac{90}{100}{v}_0=\frac{v_0(v-v_m)}{v}\Rightarrow 9v=10v-40v_m$
$v_m=\frac{v}{10}$
$v_m^2-0=2as=\frac{v^2}{100}$
$\therefore S=\frac{v^2}{200a}=\frac{(330{)}^2}{200\times 2.2}=247.5m$