Radio transmissions show observers in Houston that the International Space Station is 323 miles away, the Chi- nese space statio
n Tiangong is 462 miles away, and the angle International Space Station–Houston–Tiangong is 109 . How far apart are the two space stations?
1 answer:
Answer:
The two space stations are 644.1653 miles far apart.
Explanation:
The distance of Huston and the International Space Station is 323 miles.
The distance of Huston and the Chinese space station Tiangong is 462 miles.
Angle between the two stations = 109⁰
So, applying the law of cosines as;
c² = a² + b² - 2abcosC
From the picture shown below, a = 323 miles and b = 462 miles
So,
c² = 323² + 462² + 2(323)(462)cos109 = 104329 + 213444 - 298452cos109
cos109 = -0.3256
So,
c² = 414948.9712
<u>c = 644.1653 miles</u>
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Answer:
a) see attached, a = g sin θ
b)
c) v = √(2gL (1-cos θ))
Explanation:
In the attached we can see the forces on the sphere, which are the attention of the bar that is perpendicular to the movement and the weight of the sphere that is vertical at all times. To solve this problem, a reference system is created with one axis parallel to the bar and the other perpendicular to the rod, the weight of decomposing in this reference system and the linear acceleration is given by
Wₓ = m a
W sin θ = m a
a = g sin θ
b) The diagram is the same, the only thing that changes is the angle that is less
θ' = 9/2 θ
c) At this point the weight and the force of the bar are in the same line of action, so that at linear acceleration it is zero, even when the pendulum has velocity v, so it follows its path.
The easiest way to find linear speed is to use conservation of energy
Highest point
Em₀ = mg h = mg L (1-cos tea)
Lowest point
Emf = K = ½ m v²
Em₀ = Emf
g L (1-cos θ) = v² / 2
v = √(2gL (1-cos θ))
