Answer:
D. It is very small when compared to the universe
Explanation:
The Milky Way can be regarded galaxy which has Solar System in it. Milky way gives the description of appearance of galaxy from Earth, it is a hazy band of light that's been formed from the stars which can be visualized in the sky during the night, though it cannot be sorted by mere human eyes. Milky Way has existed for about 13.51 billion years with the radius of 52,850 light years. the Number of stars in milky way is about 100-400 billion. It should be noted that themilky way galaxy is a very large galaxy but It is very small when compared to the universe
.
Answer with Explanation:
We are given that
A=3i-3j m
B=i-4 j m
C=-2i+5j m
a.![D=A+B+C](https://tex.z-dn.net/?f=D%3DA%2BB%2BC)
![D=3i-3j+i-4j-2i+5j](https://tex.z-dn.net/?f=D%3D3i-3j%2Bi-4j-2i%2B5j)
![D=2i-2j](https://tex.z-dn.net/?f=D%3D2i-2j)
Compare with the vector r=xi+yj
We get x=2 and y=-2
Magnitude=
units
By using the formula ![\mid r\mid=\sqrt{x^2+y^2}](https://tex.z-dn.net/?f=%5Cmid%20r%5Cmid%3D%5Csqrt%7Bx%5E2%2By%5E2%7D)
Direction:![\theta=tan^{-1}\frac{y}{x}](https://tex.z-dn.net/?f=%5Ctheta%3Dtan%5E%7B-1%7D%5Cfrac%7By%7D%7Bx%7D)
By using the formula
Direction of D:![\theta=tan^{-1}(\frac{-2}{2})=tan^{-1}(-1)=tan^{-1}(-tan45^{\circ})=-45^{\circ}](https://tex.z-dn.net/?f=%5Ctheta%3Dtan%5E%7B-1%7D%28%5Cfrac%7B-2%7D%7B2%7D%29%3Dtan%5E%7B-1%7D%28-1%29%3Dtan%5E%7B-1%7D%28-tan45%5E%7B%5Ccirc%7D%29%3D-45%5E%7B%5Ccirc%7D)
b.E=-A-B+C
![E=-3i+3j-i+4j-2i+5j](https://tex.z-dn.net/?f=E%3D-3i%2B3j-i%2B4j-2i%2B5j)
![E=-6i+12j](https://tex.z-dn.net/?f=E%3D-6i%2B12j)
units
Direction of E=![\theta=tan^{-1}(\frac{12}{-6}=tan^{-1}(-2)=-63.4^{\circ}](https://tex.z-dn.net/?f=%5Ctheta%3Dtan%5E%7B-1%7D%28%5Cfrac%7B12%7D%7B-6%7D%3Dtan%5E%7B-1%7D%28-2%29%3D-63.4%5E%7B%5Ccirc%7D)
<span>they are travelling at right angles to each other.
At any given instant they form a right triangle with their starting point
</span>South bound <span>= x [mi/h]
</span> East bound <span> = x+1 [mi/h]
after five hours they will be
d=5x
and
d=5(x+1)
miles away from the starting point
(5x)^2+(5(x+1))^2=625
25x^2+(5x+5)^2=625
25x^2+25x^2+50x+25=625
50</span>x^2+50x-600=0
<span> x^2+ x - 12=0
(x+4)(x-3)=0
take the postive value
x= 3 mph the speed of south bound
4mph east bound </span>
Answer:
B) 1.5 m/s
Explanation:
The apparent frequency will be enhanced due to Doppler effect
If f be the apparent frequency , F be the real frequency , V be the velocity of sound and v be the velocity of approaching submarine then f is given by
f = F \frac{V+v}{V-v}\\
\frac{f}{F} =\frac{V+v}{V-v}\\
\frac{f}{F}-1 =\frac{V+v}{V-v}-1\\
\Delta f = \frac{2vf}{V-v}\\
200=\frac{2\times v\times 100\times 1000}{1482-v}\\
v=1.48 m/s