The two hot-air balloons in the drawing are 48.2m and 61.0 m above the ground.A person in the left balloon observes that the rig
ht balloon is 13.3 degrees above the horizontal.What is the horizontal distance x between the two balloons?
1 answer:
Answer:
The horizontal distance x between the two balloons is 54.15 m
Explanation:
The diagram described as obtained online is presented in the image attached to this solution.
Let the horizontal distance between the two balloons be x
Difference in height (vertical distance) between the two balloons = 61 - 48.2 = 12.8 m
Using trigonometric relations, it is evident that
Tan 13.3° = 12.8/x
x = 12.8/tan 13.3° = 12.8/0.2364 = 54.15 m
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Answer:
B = 38.2μT
Explanation:
By the Ampere's law you have that the magnetic field generated by a current, in a wire, is given by:
(1)
μo: magnetic permeability of vacuum = 4π*10^-7 T/A
r: distance from the center of the cylinder, in which B is calculated
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In this case, you first calculate the current Ir, by using the following relation:
J: current density
Ar: cross sectional area for r in the hollow cylinder
Ar is given by
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R2: outer radius = 26mm = 26*10^-3 m
R1: inner radius = 5 mm = 5*10^-3 m
IT: total current = 4 A
Then, the current in the wire for a distance r is:
(2)
You replace the last result of equation (2) into the equation (1):
Finally. you replace the values of all parameters:
hence, the magnitude of the magnetic field at a point 12 mm from the center of the hollow cylinder, is 38.2μT
Answer:
Explanation:
let be the mass attached, let
be the spring constant and let
be the positive damping constant.
-By Newton's second law:
where is the displacement from equilibrium position. The equation can be transformed into:
shich is the equation of motion.