Explanation:
Work done by winch = kinetic energy of car
∫ T ds = ½ mv²
∫ 225s ds = ½ mv²
225/2 s² = ½ mv²
225 s² = mv²
v = 15s / √m
Given s = 10 m and m = 2500 kg:
v = 15 (10) / √2500
v = 3 m/s
Light year is the distance traveled by light in 1 year of time interval
so here we can say that the statement must have used the word light year as the distance
so we have
A) It's about 4 light-years from here to Alpha Century.
this shows the distance between two so it is correct
B) It will take me light-years to complete this homework assignment.
here it represent the light year as time so it is INCORRECT
C) A light-year is about 10 trillion kilometers.
This shows the distance so it is correct
D) It will take the Voyager spacecraft about 20,000 years to travel just 1 light-year.
It shows the distance so it is correct
E) The Milky Way Galaxy is about 100,000 light-years in diameter.
this is distance so it is also correct
Answer:
f = 200[Hz]; L=1500[km]
Explanation:
We know that frequency is the reciprocal of the period, therefore.
![f=\frac{1}{T} \\f=1/0.005\\f=200[Hz]](https://tex.z-dn.net/?f=f%3D%5Cfrac%7B1%7D%7BT%7D%20%5C%5Cf%3D1%2F0.005%5C%5Cf%3D200%5BHz%5D)
And the wavelength is determined using the following equation.
![L=\frac{c}{f} \\where:\\c = light speed = 3*10^{8}[m/s]\\ f = frecuency [Hz]\\L = wavelength [m]\\L= 3*10^{8}/ 200\\ L = 1500000[m] = 1500[km]](https://tex.z-dn.net/?f=L%3D%5Cfrac%7Bc%7D%7Bf%7D%20%5C%5Cwhere%3A%5C%5Cc%20%3D%20light%20speed%20%3D%203%2A10%5E%7B8%7D%5Bm%2Fs%5D%5C%5C%20f%20%3D%20frecuency%20%5BHz%5D%5C%5CL%20%3D%20wavelength%20%5Bm%5D%5C%5CL%3D%203%2A10%5E%7B8%7D%2F%20200%5C%5C%20L%20%3D%201500000%5Bm%5D%20%3D%201500%5Bkm%5D)
<span>It's another energy balance equation, though: energy to start with is the same as energy that you end with. Suppose that we start a distance r0 from the Earth and end a distance r1 from the Moon, then the energy balance gives:
1 v02 - G M / r0 - G m / (D - r0) = 1 v12 - G M / (D - r1) - G m / r1
...where m is the moon's mass.
One simple limit takes D ? ? and 1 v02 ? G M / r0 (the escape velocity equation), to yield:
1 v12 ? G M / r1
v1 ? ?( 2 G M / r1 ) = 2377 m/s.</span>
Answer:
![3.38\cdot 10^9 m](https://tex.z-dn.net/?f=3.38%5Ccdot%2010%5E9%20m)
Explanation:
The formula for the double-slit interference pattern is:
![y=\frac{m\lambda D}{d}](https://tex.z-dn.net/?f=y%3D%5Cfrac%7Bm%5Clambda%20D%7D%7Bd%7D)
where:
m is the order of the maximum
is the wavelength
D is the distance between the slits and the screen
d is the distance between the two slits
If we assume for instance m=5, the formula gives us the distance between the fifth maximum and the first maximum. However, this will also gives us the distance between the fifth minimum and the first minimum, as the minima fall exactly between two maxima.
Therefore, if we use:
![m=5\\d=0.22 mm=2.2\cdot 10^{-4} m\\y=59 cm=0.59 m\\D=6.3 mm=6.3\cdot 10^{-3}m](https://tex.z-dn.net/?f=m%3D5%5C%5Cd%3D0.22%20mm%3D2.2%5Ccdot%2010%5E%7B-4%7D%20m%5C%5Cy%3D59%20cm%3D0.59%20m%5C%5CD%3D6.3%20mm%3D6.3%5Ccdot%2010%5E%7B-3%7Dm)
We can find the wavelength of the light:
![\lambda=\frac{yD}{md}=\frac{(0.59 m)(6.3\cdot 10^{-3} m)}{(5)(2.2\cdot 10^{-4} m)}=3.38 m=3.38\cdot 10^9 m](https://tex.z-dn.net/?f=%5Clambda%3D%5Cfrac%7ByD%7D%7Bmd%7D%3D%5Cfrac%7B%280.59%20m%29%286.3%5Ccdot%2010%5E%7B-3%7D%20m%29%7D%7B%285%29%282.2%5Ccdot%2010%5E%7B-4%7D%20m%29%7D%3D3.38%20m%3D3.38%5Ccdot%2010%5E9%20m)