The largest mass is 4.7 x 10³⁰ kg and the smallest mass is 5 x 10²⁹ kg.
The given parameters;
- <em>distance between the two black holes, r = 10 AU = 1.5 x 10¹² m</em>
- <em>gravitational force between the two black holes, F = 6.9 x 10²⁵ N.</em>
- <em>combined mass of the two black holes = 5.20 x 10³⁰ kg</em>
The product of the two masses is calculated from Newton's law of universal gravitational as follows;
The sum of the two masses is given as;
m₁ + m₂ = 5.2 x 10³⁰ kg
m₂ = 5.2 x 10³⁰ kg - m₁
The first mass is calculated as follows;
m₁(5.2 x 10³⁰ - m₁) = 2.328 x 10⁶⁰
5.2 x 10³⁰m₁ - m₁² = 2.328 x 10⁶⁰
m₁² - 5.2 x 10³⁰m₁ + 2.328 x 10⁶⁰ = 0
<em>solve the quadratic equation using formula method</em>;
a = 1, b =- 5.2 x 10³⁰, c = 2.328 x 10⁶⁰
The second mass is calculated as follows;
m₂ = 5.2 x 10³⁰ kg - m₁
m₂ = 5.2 x 10³⁰ kg - 4.7 x 10³⁰ kg
m₂ = 5 x 10²⁹ kg
or
m₂ = 5.2 x 10³⁰ kg - 4.9 x 10²⁹ kg
m₂ = 4.7 x 10³⁰ kg
Thus, the largest mass is 4.7 x 10³⁰ kg and the smallest mass is 5 x 10²⁹ kg.
Learn more here:brainly.com/question/9373839
Based on the relative velocity of the man with respect to the boat and the dock:
- Distance covered in 4.0 seconds relative to the boat = 8 m
- Distance covered in 4.0 seconds relative to the dock = 56 m
<h3>What is relative velocity?</h3>
Relative velocity is the velocity of a body relative to another body which serves as a reference point.
Relative velocity is a vector.
Considering the velocity of the man and the boat:
The relative velocity of the man with respect to the boat = 2.0 m/s
Distance covered in 4.0 seconds relative to the boat = 2.0 m/s * 4.0 s
Distance moved = 8 m
Relative velocity of the man with respect to the dock = 12 + 2 = 14 m/s
Distance covered in 4.0 seconds relative to the dock = 14.0 m/s * 4.0 s
Distance moved = 56 m
In conclusion, the relative velocity is velocity with respect to a reference point.
Learn more about relative velocity at: brainly.com/question/24337516
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Answer:
VAnswer:
Step-by-step explanation:
Explanation:
Answer:
Wavelength of sound in meters = 1.348 m
Explanation:
Given
speed of sound = 34500 cm
= 345 m (since 1 cm = 0.01m)
frequency of sound = 256 Hz = 256
Wavelength of sound in meters = ?
We know that all waves have same relationship among speed s, frequency f and wavelength λ, which is given by the equation
v = fλ
Wavelength λ = v/f
= 345 m / 256
=1.348 m
Hence wavelength of sound in meters = 1.348 m
Answer:
a) L = 440 cm
Explanation:
In the open tube on one side and cowbell on the other, we have a maximum in the open part and a node in the closed part, therefore the resonance frequencies are
λ₁ = 4L fundamental
λ₃ = 4L / 3 third harmonic
λ₅ = 4L / 5 five harmonic
The violin string is a fixed cure in its two extracts, so both are nodes, their length from resonance wave are
λ₁ = 2L fundamental
λ₂ = 2L / 2 second harmonic
λ₃ = 2L / 3 third harmonic
λ₄= 2L / 4 fourth harmonic
They indicate that resonance occurs in the fourth harmonic, let's look for the frequency
v =λ f
for the fundamental
v = λ₀ f₀
V = 2L f₀
for the fourth harmonica
v = λ₄ f ’
v = L / 2 f'
2L f₀ = L / 2 f ’
f ’= 4 f₀
f ’= 4 440
f ’= 1760 Hz
for this frequency it has the resonance with the tube
f ’= 4L
L = f ’/ 4
L = 1760/4
L = 440 cm
b) let's find the frequency of the next harmonic in the tube
λ₃ = 4L / 3
λ₃ = 4 400/3
λ₃ = 586.6 cm
v = λf
f = v / λlam₃
f₃3 = 340 / 586.6
f3 = 0.579
as the minimum frequency on the violin is 440 Beam there is no way to reach this value, therefore there are no higher resonances
