Answer:
D = 2.38 m
Explanation:
This exercise is a diffraction problem where we must be able to separate the license plate numbers, so we must use a criterion to know when two light sources are separated, let's use the Rayleigh criterion, according to this criterion two light sources are separated if The maximum diffraction of a point coincides with the first minimum of the second point, so we can use the diffraction equation for a slit
a sin θ = m λ
Where the first minimum occurs for m = 1, as in these experiments the angle is very small, we can approximate the sine to the angle
θ = λ / a
Also when we use a circular aperture instead of slits, we must use polar coordinates, which introduce a numerical constant
θ = 1.22 λ / D
Where D is the circular tightness
Let's apply this equation to our case
D = 1.22 λ / θ
To calculate the angles let's use trigonometry
tan θ = y / x
θ = tan⁻¹ y / x
θ = tan⁻¹ (4.30 10⁻² / 140 10³)
θ = tan⁻¹ (3.07 10⁻⁷)
θ = 3.07 10⁻⁷ rad
Let's calculate
D = 1.22 600 10⁻⁹ / 3.07 10⁻⁷
D = 2.38 m
B) gravitational to kinetic
Explanation:
The skydiver, when he is located at a certain height h above the ground, possesses gravitational potential energy, equal to:
where m is the mass of the skydiver, g is the gravitational acceleration and h is the height above the ground. As he falls, its height h decreases, while his speed v increases, so part of the gravitational potential energy is converted into kinetic energy, which is given by
so, we see that as v increases, the kinetic energy increases. Therefore the correct answer is
B) gravitational to kinetic
You could answer this right away IF you knew the length of each wave, right ?
Well, Wavelength = (speed) / (frequency).
Speed = 3 x 10⁸ m/s (the speed of light)
and
Frequency = 90.9 x 10⁶ Hertz.
So the length of each wave is 3 x 10⁸ / 90.9 x 10⁶ meters.
To answer the question, see how many pieces you have to cut
that 1.5 km into, in order for each piece to be 1 wavelength.
It'll be
(1,500 meters) divided by (3 x 10⁸ meters/sec) / (90.9 x 10⁶ Hz)
To divide by a fraction, flip the fraction and then multiply:
(1500 meters) times (90.9 x 10⁶ Hz)/(3 x 10⁸ meters/sec)
= 454.5
