Solve the problem.
-An airplane travels at 165 km/h for 3 hr in a direction of 174° from a local airport. At the end of this time, how far east of the airport is the plane (to the nearest kilometer)?
A)4736 km
B)492 km
C)4710 km
D)52 km

Question

Quizplus · Accepted Answer

To find how far east the airplane is from the airport, we need to calculate the eastward component of its displacement. The direction of 174° from north means the plane is flying almost directly south, with a small eastward component. The eastward displacement can be calculated using the cosine of the angle from the north (since we're looking for the component parallel to the east-west axis) and the total distance traveled. The total distance is $165 \text{ km/h} \times 3 \text{ h} = 495 \text{ km}$. The angle from the east is $174° - 90° = 84°$. Thus, the eastward displacement is $495 \times \cos(84°)$. Calculating this gives a value close to 52 km, which is option D.

Solve the Problem. -An Airplane Travels at 165 Km/h for 3 Hr in 3