Answer
$2.51\times10^8m/s$.
Work Step by Step
Use Snell’s law to find the index of refraction of the plastic.
The angles are measured from the normal to the interface.
$$n_a sin\theta_a= n_b sin\theta_b$$
$$n_b=n_a(\frac{sin \theta_a}{sin \theta_b}) $$
$$n_b=1.00(\frac{ sin62.7^{\circ}}{ sin48.1^{\circ}}) =1.194$$
Now find the speed.
$$n_b=\frac{c}{v}=1.194$$
$$v=\frac{c}{n}=\frac{3.00\times10^8m/s }{1.194 }=2.51\times10^8m/s $$
