A flashlight beam is directed at a swimming pool in the dark at an angle of 46° with respect to the normal to the surface of the water. What is the angle of refraction of the beam in the water? ( The refractive index for water is 1.33.)

the angle of refraction of the beam is 33 degrees

Explanation:

Given that the

Incident angle I = 46°

Refractive index n = 1.33

According to Snell law,

Refractive index = ratio of sine of incidence to the sine of reflection.

That is

n = sin i/sin r

Substitute n and I Into the formula above.

1.33 = sin 46/sin r

Make sin r the subject of the formula

Sin r = sin 46/1.33

Sin r = 0.540

Find the sine inverse of r

r = sin^-1(0.540)

r = 32.7 degree

r = 33 degree approximately

russian is not my first language, so i'm afraid i can't write out an answer in russian, but hopefully you can find a way to do so. here's my best translation of the problem: you're given a plot of a particle's position in one-dimensional space over time, and you're asked to find either the total distance traveled by the particle after 6 seconds had elapsed, or the total displacement of the particle after 6 seconds.

if you want the total distance traveled, you would first need to determine the particle's velocity as a function of time, then integrate that over the 6-second interval. we know the position function is quadratic with roots at 0 and 6, so we have

where is unknown. because the position is parabolic, there is symmetry about the midpoint at , and we know that

so that the position function is

which means the velocity is

then the total distance traveled is

so the total distance traveled is 20 m.

on the other hand, if you want to find displacement: the particle starts at and ends at , so its displacement is 0.