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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1) The equivalent resistance is
2) The voltage in the circuit is 120 V
3) The total current in the circuit is 44.0 A
Explanation:
1)
Resistors are said to be in parallel when they have the same potential difference at their terminals.
The formula to calculate the equivalent resistance for three resistors in parallel is:
where are the resistances of the three resistors.
In this problem, the resistance of each resistor is:
Substituting,
So the equivalent resistance is
2)
In this problem we are told that the three resistors are connected in parallel. This means that their terminals are connected to the same point of the circuit: therefore, this means that they also have the same potential difference across them.
Therefore, the voltage in each branch containing each resistor is the same, and it is equal to the voltage of the battery, which is
So, the voltage in the circuit is 120 V.
3)
The total current in the circuit can be found by using Ohm's law:
where
V is the voltage
R is the equivalent resistance of the circuit
I is the current
In this circuit, we have:
V = 120 V
Re-arranging the equation for I, we find the current:
Learn more about current and potential difference:
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