Answer:
The longest wavelength of light is 666.7 nm
Explanation:
The general form of the grating equation is
mλ = d(sinθi + sinθr)
where;
m is third-order maximum = 3
λ is the wavelength,
d is the slit spacing (m/slit)
θi is the incident angle
θr is the diffracted angle
Note: at longest wavelength, sinθi + sinθr = 1
λ = d/m
d = 1/500 slits/mm
λ = 1 mm/(500 *3) = 1mm/1500 = 666.7 X 10⁻⁶ mm = 666.7 nm
Therefore, the longest wavelength of light is 666.7 nm
Answer:
a = 0.7267
, acceleration is positive therefore the speed is increasing
Explanation:
The definition of acceleration is
a = dv / dt
they give us the function of speed
v = - (t-1) sin (t² / 2)
a = - sin (t²/2) - (t-1) cos (t²/2) 2t / 2
a = - sin (t²/2) - t (t-1) cos (t²/2)
the acceleration for t = 4 s
a = - sin (4²/2) - 4 (4-1) cos (4²/2)
a = -sin 8 - 12 cos 8
remember that the angles are in radians
a = 0.7267
the problem does not indicate the units, but to be correct they must be m/s²
We see that the acceleration is positive therefore the speed is increasing
Tides are influenced by the force of gravity exerted by the earth, moon and the sun. The sun has a larger mass than the moon and as such has a greater gravitational pull on the earth. the moon however has greater influence over the tides because they are caused by the difference in gravity fields. This means that the moon is the dominant influence due to the fact that the fractional difference in its force across the earth is greater than that seen from the sun.
Explanation:
(a) Given:
Δx = 150 m
v₀ = 27 m/s
v = 54 m/s
Find: a
v² = v₀² + 2aΔx
(54 m/s)² = (27 m/s)² + 2a (150 m)
a = 7.29 m/s²
(b) Given:
Δx = 150 m
v₀ = 0 m/s
a = 7.29 m/s²
Find: t
Δx = v₀ t + ½ at²
150 m = (0 m/s) t + ½ (7.29 m/s²) t²
t = 6.42 s
(c) Given:
v₀ = 0 m/s
v = 27 m/s
a = 7.29 m/s²
Find: t
v = at + v₀
27 m/s = (7.29 m/s²) t + 0 m/s
t = 3.70 s
(d) Given:
v₀ = 0 m/s
v = 27 m/s
a = 7.29 m/s²
Find: Δx
v² = v₀² + 2aΔx
(27 m/s)² = (0 m/s)² + 2 (7.29 m/s²) Δx
Δx = 50 m
