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prohojiy [21]
3 years ago
11

According to the rayleigh criterion, what is the shortest object we could resolve at the 25.0 cm near point with light of wavele

ngth 550 nm ?
Physics
1 answer:
Blizzard [7]3 years ago
7 0

Answer:

6.71 *10^{-5} rad

Explanation:

∅ = \frac{1.22*wavelength}{D} = \frac{1.22*550 * 10^{-9} }{25 * 10^{-2} }

∅ = 6.71 *10^{-5} rad

The minimum resolvable angle = 6.71 *10^{-5} rad

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4.) An apartment building is on fire and a guy is trapped on the fire escape ladder. There is a
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Answer:

5.3 m/s

Explanation:

First, find the time it takes for him to fall 7m.

y = y₀ + v₀ t + ½ at²

0 = 7 + (0) t + ½ (-9.8) t²

0 = 7 − 4.9 t²

t ≈ 1.20 s

Now find the velocity he needs to travel 6.3m in that time.

x = x₀ + v₀ t + ½ at²

6.3 = 0 + v₀ (1.20) + ½ (0) (1.20)²

v₀ ≈ 5.27 m/s

Rounded to two significant figures, the man must run with a speed of 5.3 m/s.

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Describe using examples how objects can be at rest and in motion simultaneously
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Will an object with more mass roll faster down a hill?
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Scientists might make a computer model of volcanic eruptions. What is the
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Mass Center Determine the coordinates (x, y) of the center of mass of the area in blue in the figure below. Answers: x=(3)/(8)a
Naya [18.7K]

Explanation:

The x and y coordinates of the center of mass are:

xcm = ∫ x dm / m = ∫ x ρ dA / ∫ ρ dA

ycm = ∫ y dm / m = ∫ y ρ dA / ∫ ρ dA

Assuming uniform density, the center of mass is also the center of area.

xcm = ∫ x dA / ∫ dA = ∫ x y dx / A

ycm = ∫ y dA / ∫ dA = ∫ ½ y² dx / A

First, let's find the area:

A = ∫ y dx

A = ∫₀ᵃ (-h/a² x² + h) dx

A = -⅓ h/a² x³ + hx |₀ᵃ

A = -⅓ h/a² (a)³ + h(a)

A = ⅔ ha

Now, let's find the x coordinate of the center of mass:

xcm = ∫ x y dx / A

xcm = ∫₀ᵃ x (-h/a² x² + h) dx / (⅔ ha)

xcm = ∫₀ᵃ (-h/a² x³ + hx) dx / (⅔ ha)

xcm = (-¼ h/a² x⁴ + ½ hx²) |₀ᵃ / (⅔ ha)

xcm = (-¼ h/a² (a)⁴ + ½ h(a)²) / (⅔ ha)

xcm = (¼ ha²) / (⅔ ha)

xcm = ⅜ a

Next, we find the y coordinate of the center of mass:

ycm = ∫ y² dx / A

ycm = ∫₀ᵃ ½ (-h/a² x² + h)² dx / (⅔ ha)

ycm = ∫₀ᵃ ½ (h²/a⁴ x⁴ − 2h²/a² x² + h²) dx / (⅔ ha)

ycm = ½ (⅕ h²/a⁴ x⁵ − ⅔ h²/a² x³ + h² x) |₀ᵃ / (⅔ ha)

ycm = ½ (⅕ h²/a⁴ (a)⁵ − ⅔ h²/a² (a)³ + h² (a)) / (⅔ ha)

ycm = ½ (⁸/₁₅ h²a) / (⅔ ha)

ycm = ⅖ h

6 0
3 years ago
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