A jet is circling an airport control tower at a distance of 23.0 km. An observer in the tower watches the jet cross in front of the moon. As seen from the tower, the moon subtends an angle of 9.49 10-3 radians. Find the distance traveled (in meters) by the jet as the observer watches the nose of the jet cross from one side of the moon to the other.
To solve this problem, we can use the concept of arc length and angular size.
The angular size of an object is the angle it subtends at the observer's eye. In this case, the observer in the tower sees the jet crossing in front of the moon, so the angular size of the moon is given as 9.49 x 10^-3 radians.
The arc length formula is given by:
Arc Length = Radius × Angle
In this case, the radius is the distance between the observer and the object, which is the distance between the tower and the jet, given as 23.0 km.
Converting the distance to meters, we have:
Distance = 23.0 km × 1000 m/km = 23,000 m
Plugging in the values in the formula, we have:
Arc Length = 23,000 m × 9.49 x 10^-3 radians
Calculating the arc length, we get:
Arc Length = 218.27 meters
Therefore, the distance traveled by the jet as the observer watches the nose of the jet cross from one side of the moon to the other is approximately 218.27 meters.