An ion's position vector is initially r = 8.0 i - 4.0 j + 3.0 k, and 8.0 s later it is r = 4.0 i + 8.0 j - 6.0 k, all in meters.
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Answer:
82780.42123 m/s
14.45 days
Explanation:
m = Mass of the planet
M = Mass of the star =
r = Radius of orbit of planet =
v = Orbital speed
The kinetic and potential energy balance is given by
The orbital speed of the star is 82780.42123 m/s
The orbital period is given by
The orbital period is 14.45 days
Answer:
a) , b)
Explanation:
a) According the Archimedes' Principle, the buoyancy force is equal to the displaced weight of surrounding liquid. The mass of the coal in the barge is:
b) The submersion height is found by using the equation derived previously:
The final submersion height is:
I = V/Z
V = voltage, I = current, Z = impedance
First let's find the total impedance of the circuit.
The impedance of the resistor is:
= R
R = resistance
Given values:
R = 1200Ω
Plug in:
= 1200Ω
The impedance of the inductor is:
= j2πfL
f = source frequency, L = inductance
Given values:
f = 59Hz, L = 2.4H
Plug in:
= j2π(59)(2.4) = j889.7Ω
Add up the individual impedances to get the Z, and convert Z to polar form:
Z = +
Z = 1200 + j889.7
Z = 1494∠36.55°Ω
I = V/Z
Given values:
V = 170∠0°V (assume 0 initial phase)
Z = 1494∠36.55°Ω
I = 170∠0°/1494∠36.55°Ω
I = 0.1138∠-36.55°A
Round the magnitude of I to 2 significant figures and now you have your maximum current:
I = 0.11A