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lubasha [3.4K]
4 years ago
10

While anchored in the middle of a lake, you count exactly five waves hitting your boat every 10 s. you raise anchor and start mo

toring slowly in the same direction the waves are going. when traveling at 1.5 m/s, you notice that exactly three waves are hitting the boat from behind every 10 s. what is the speed of the waves on the lake?
Physics
1 answer:
777dan777 [17]4 years ago
7 0
<span>Every 10s 5 waves; t1 = 2s for each wave
 When v = 1.5m/s, 3 waves in 10s t2 = 10 / 3s
  Calculating the frequency in first case f1 = 5 / 10 = 0.5
 Calculating the frequency in second case f2 = 3 / 10 = 0.3
 Using the Doppler formula f = (1-v/c) f0
  For the formula f = f2, v = velocity of boat= 1.5 m/s, f0 = f1, c is velocity of wave 0.3 = 0.5 x (1 - 1.5/c) => 1.5/c = 1 - 0.6 => 1.5/c = 0.4 => c = 1.5/0.4 Velocity of the wave = 3.75 m/s</span>
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Answer:

19080667.0818 m/s

0.637294 m

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Explanation:

m = Mass of deuterons = 3.34\times 10^{-27}\ kg

v = Velocity

K = Kinetic energy = 3.8 MeV

d = Diameter

B = Magnetic field = 1.25 T

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Kinetic energy is given by

K=\dfrac{1}{2}mv^2\\\Rightarrow v=\sqrt{\dfrac{2K}{m}}\\\Rightarrow v=\sqrt{\dfrac{2\times 3.8\times 10^6\times 1.6\times 10^{-19}}{3.34\times 10^{-27}}}\\\Rightarrow v=19080667.0818\ m/s

The speed of the deuterons when they exit is 19080667.0818 m/s

In this system the centripetal and magnetic force will balance each other

\dfrac{mv^2}{r}=qvB\\\Rightarrow \dfrac{mv^2}{\dfrac{d}{2}}=qvB\\\Rightarrow d=\dfrac{2mv}{qB}\\\Rightarrow d=\dfrac{2\times 3.34\times 10^{-27}\times 19080667.0818}{1.6\times 10^{-19}\times 1.25}\\\Rightarrow d=0.637294\ m

The diameter is 0.637294 m

Current is given by

i=\dfrac{nq}{t}\\\Rightarrow n=\dfrac{it}{q}\\\Rightarrow n=\dfrac{350\times 10^{-6}\times 1}{1.6\times 10^{-19}}\\\Rightarrow n=2.1875\times 10^{15}

The number of deuterons is 2.1875\times 10^{15}

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Hydrogen atoms are placed in an external magnetic field. The protons can make transitions between states in which the nuclear sp
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Answer:

b) Betelgeuse would be \approx 1.43 \cdot 10^{6} times brighter than Sirius

c) Since Betelgeuse brightness from Earth compared to the Sun is \approx 1.37 \cdot 10^{-5} } the statement saying that it would be like a second Sun is incorrect

Explanation:

The start brightness is related to it luminosity thought the following equation:

B = \displaystyle{\frac{L}{4\pi d^2}} (1)

where B is the brightness, L is the star luminosity and d, the distance from the star to the point where the brightness is calculated (measured). Thus:

b) B_{Betelgeuse} = \displaystyle{\frac{10^{10}L_{Sun}}{4\pi (427\ ly)^2}} and B_{Sirius} = \displaystyle{\frac{26L_{Sun}}{4\pi (26\ ly)^2}} where L_{Sun} is the Sun luminosity (3.9 x 10^{26} W) but we don't need to know this value for solving the problem. ly is light years.

Finding the ratio between the two brightness we get:

\displaystyle{\frac{B_{Betelgeuse}}{B_{Sirius}}=\frac{10^{10}L_{Sun}}{4\pi (427\ ly)^2} \times \frac{4\pi (26\ ly)^2}{26L_{Sun}} \approx 1.43 \cdot 10^{6} }

c) we can do the same as in b) but we need to know the distance from the Sun to the Earth, which is 1.581 \cdot 10^{-5}\ ly. Then

\displaystyle{\frac{B_{Betelgeuse}}{B_{Sun}}=\frac{10^{10}L_{Sun}}{4\pi (427\ ly)^2} \times \frac{4\pi (1.581\cdot 10^{-5}\ ly)^2}{1\ L_{Sun}} \approx 1.37 \cdot 10^{-5} }

Notice that since the star luminosities are given with respect to the Sun luminosity we don't need to use any value a simple states the Sun luminosity as the unit, i.e 1. From this result, it is clear that when Betelgeuse explodes it won't be like having a second Sun, it brightness will be 5 orders of magnitude smaller that our Sun brightness.

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