slader A jet is circling an airport control tower at a distance of 15.9 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 8.74x10-3 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.

y = 138.96 m

Explanation:

The angle subtended by the moon is the mean of the angle of the arc between the two most extreme points of the moon, we can see that the angle is very small, so we can approximate this arc to a straight line and then use the trigonometric relationships

         sin θ = y / L

where L = 15.9 10³ m and θ = 8.74 10⁻³ rad

          y = L sin θ

          y = 15.9 10³ sin (8.74 10⁻³)

         y = 15.9 10³    0.0087399

         y = 138.96 m

can be answered using momentum.

momentum = p

p1= mass1 * velocity1

p1 = p2

therefore

p1 = 6kg * 4m/s

p1 = 24kgm/s

p2=m2 * v2

24 kgm/s = 7kg * v2

v2 = 24 kgm/s / 7kg

v2= 3.42 m/s