This is called the Phi Phenomenon.
This is an illusion of movement created when two or more adjacent lights blink on and off in quick succession; when two adjacent stationary lights blink on and off in quick succession; we perceive a single light moving back and forth between them. It is an optical illusion of perceiving a series of still images, when viewed in rapid succession, as continuous motion.
Answer:
A thin, taut string tied at both ends and oscillating in its third harmonic has its shape described by the equation y(x,t)=(5.60cm)sin[(0.0340rad/cm)x]sin[(50.0rad/s)t]y(x,t)=(5.60cm)sin[(0.0340rad/cm)x]sin[(50.0rad/s)t], where the origin is at the left end of the string, the x-axis is along the string, and the y-axis is perpendicular to the string. (a) Draw a sketch that shows the standing-wave pattern. (b) Find the amplitude of the two traveling waves that make up this standing wave. (c) What is the length of the string? (d) Find the wavelength, frequency, period, and speed of the traveling waves. (e) Find the maximum transverse speed of a point on the string. (f) What would be the equation y(x, t) for this string if it were vibrating in its eighth harmonic?
Answer:
(a) 
(b) 
(c) 
Explanation:
First change the units of the velocity, using these equivalents
and 

The angular acceleration
the time rate of change of the angular speed
according to:


Where
is the original velocity, in the case the velocity before starting the deceleration, and
is the final velocity, equal to zero because it has stopped.

b) To find the distance traveled in radians use the formula:


To change this result to inches, solve the angular displacement
for the distance traveled
(
is the radius).


c) The displacement is the difference between the original position and the final. But in every complete rotation of the rim, the point returns to its original position. so is needed to know how many rotations did the point in the 890.16 rad of distant traveled:

The real difference is in the 0.6667 (or 2/3) of the rotation. To find the distance between these positions imagine a triangle formed with the center of the blade (point C), the initial position (point A) and the final position (point B). The angle
is between the two sides known. Using the theorem of the cosine we can find the missing side of the the triangle(which is also the net displacement):


Answer:
The chance in distance is 25 knots
Explanation:
The distance between the two particles is given by:
(1)
Since A is traveling north and B is traveling east we can say that their displacement vector are perpendicular and therefore (1) transformed as:
(2)
Taking the differential with respect to time:
(3)
where
and
are the respective given velocities of the boats. To find
and
we make use of the given position for A,
, the Pythagoras theorem and the relation between distance and velocity for a movement with constant velocity.

with this time, we know can now calculate the distance at which B is:

and applying Pythagoras:

Now substituting all the values in (3) and solving for
we get:
