Answer
(a) $2.18\times 10^7m/s$
(b) towards
Work Step by Step
(a) We can find the required speed of the motorist as follows:
$f^{\prime}=f(1+\frac{u}{c})$
$\implies \frac{c}{\lambda_g}=\frac{c}{\lambda_y}(1+\frac{u}{c})$
$\implies 1+\frac{u}{c}=\frac{\lambda_y}{\lambda_g}$
$\implies \frac{u}{c}=\frac{\lambda_y}{\lambda_g}-1$
We plug in the known values to obtain:
$\frac{u}{c}=\frac{590}{550}-1$
$\frac{u}{c}=\frac{40}{550}$
$u=0.072(c)$
$u=(0.072)(3\times 10^8)$
$u=2.18\times 10^7m/s$
(b) We know that $v=\frac{d}{t}$
$\implies f\lambda=\frac{d}{t}$
This equation shows that the wavelength and distance are directly proportional. Thus, when the wavelength decreases, the distance decreases as well. Hence, we conclude that the motorist should be traveling toward the traffic light.
