The smallest particle of an element that still retains all the element's properties is a(n) _____. atom .... but many particles inside
Answer:
the googles are 5.3 m from the edge
Explanation:
Given that
depth of pool , d = 3.2 m
Now, let i be the angle of incidence
a laser pointer 0.90 m above the edge of the pool and laser beam enters the water 2.2 m from the edge
⇒tan i = 2.2/0.9
![i=arctan(2.2/.90)](https://tex.z-dn.net/?f=i%3Darctan%282.2%2F.90%29)
solving we get
i = 67.8°
Using snell's law ,
n1 ×sin(i) = n2 ×sin(r)
n1= refractive index of 1st medium= 1
n2= refractive index of 2nd medium = 1.33
r= angle of reflection
therefore,
![1\times sin(67.8) = 1.33\times sin(r)](https://tex.z-dn.net/?f=1%5Ctimes%20sin%2867.8%29%20%3D%201.33%5Ctimes%20sin%28r%29)
r = 44.1°
Now,
distance of googles = 2.2 + d×tan(r)
distance of googles = 2.2 + 3.2×tan(44.1)
distance of googles = 5.3 m
the googles are 5.3 m from the edge
Answer:
1) f= 8.6 GHz
2) t= 0.2 ms
Explanation:
1)
- Since microwaves are electromagnetic waves, they move at the same speed as the light in vacuum, i.e. 3*10⁸ m/s.
- There exists a fixed relationship between the frequency (f) , the wavelength (λ) and the propagation speed in any wave, as follows:
![v = \lambda * f (1)](https://tex.z-dn.net/?f=v%20%3D%20%5Clambda%20%2A%20f%20%281%29)
- Replacing by the givens, and solving for f, we get:
![f =\frac{c}{\lambda} =\frac{3e8m/s}{0.035m} = 8.57e9 Hz (2)](https://tex.z-dn.net/?f=f%20%3D%5Cfrac%7Bc%7D%7B%5Clambda%7D%20%3D%5Cfrac%7B3e8m%2Fs%7D%7B0.035m%7D%20%3D%208.57e9%20Hz%20%282%29)
⇒ f = 8.6 Ghz (with two significative figures)
2)
- Assuming that the microwaves travel at a constant speed in a straight line (behaving like rays) , we can apply the definition of average velocity, as follows:
where v= c= speed of light in vacuum = 3*10⁸ m/s
d= distance between mountaintops = 52 km = 52*10³ m
![t = \frac{d}{c} = \frac{52e3m}{3e8m/s} = 17.3e-5 sec = 0.173e-3 sec = 0.173 ms (4)](https://tex.z-dn.net/?f=t%20%3D%20%5Cfrac%7Bd%7D%7Bc%7D%20%3D%20%5Cfrac%7B52e3m%7D%7B3e8m%2Fs%7D%20%3D%2017.3e-5%20sec%20%3D%200.173e-3%20sec%20%3D%200.173%20ms%20%284%29)
⇒ t = 0.2 ms (with two significative figures)
Answer:
The answer is "-72 k".
Explanation:
Please find the complete question in the attached file.
Given point:
![A=(0,0,0)\\B=(0,8,0)\\C=(9,8,0)\\D=(9,0,0)](https://tex.z-dn.net/?f=A%3D%280%2C0%2C0%29%5C%5CB%3D%280%2C8%2C0%29%5C%5CC%3D%289%2C8%2C0%29%5C%5CD%3D%289%2C0%2C0%29)
![\bar{AB} = (0i+8j+0k)-(0i+0j+0k)= 8j\\\\\bar{AC} = (9i+8j+0k)-(0i+0j+0k)= 9i+8j\\\\](https://tex.z-dn.net/?f=%5Cbar%7BAB%7D%20%3D%20%280i%2B8j%2B0k%29-%280i%2B0j%2B0k%29%3D%208j%5C%5C%5C%5C%5Cbar%7BAC%7D%20%3D%20%289i%2B8j%2B0k%29-%280i%2B0j%2B0k%29%3D%209i%2B8j%5C%5C%5C%5C)
Calculating the area:
![Area=\left|\begin{array}{ccc}i&j&k\\0&8&0\\9&8&0\end{array}\right|](https://tex.z-dn.net/?f=Area%3D%5Cleft%7C%5Cbegin%7Barray%7D%7Bccc%7Di%26j%26k%5C%5C0%268%260%5C%5C9%268%260%5Cend%7Barray%7D%5Cright%7C)
![=i[8(0)-8(0)]-j[(0-0)]+k[(0-9(8))]\\\\=i[0-0]-j[(0)]+k[(0-72)]\\\\=i[0]-j[(0)]+k[(-72)]\\\\=-72 \ k](https://tex.z-dn.net/?f=%3Di%5B8%280%29-8%280%29%5D-j%5B%280-0%29%5D%2Bk%5B%280-9%288%29%29%5D%5C%5C%5C%5C%3Di%5B0-0%5D-j%5B%280%29%5D%2Bk%5B%280-72%29%5D%5C%5C%5C%5C%3Di%5B0%5D-j%5B%280%29%5D%2Bk%5B%28-72%29%5D%5C%5C%5C%5C%3D-72%20%5C%20k)
Okay so you have to find acceleration first. I used v=vo+at. Plug in the numbers and you get -11.9m/s^2 as your constant acceleration. Then plug acceleration into d=vi(t)+1/2(a)t^2
d=(40m/s)(3.34s)+1/2(-11.9m/s^2)(3.34s)^2
d=68.6m