Solve Applied Problems Involving Vectors
-An aircraft going from Atlanta to Savannah on a heading of $113 ^ { \circ }$ (from north) is travelling at a speed of 410 miles per hour. The wind is out of the north at a speed of 22 miles per hour. Find the actual speed and direction of the aircraft.
A) 419 miles per hour; $116 ^ { \circ }$ from north
B) 402 miles per hour; $116 ^ { \circ }$ from north
C) 406 miles per hour; $116 ^ { \circ }$ from north
D) 574 miles per hour; $115 ^ { \circ }$ from north

Question

Quizplus · Accepted Answer

To solve this, we use vector addition. The aircraft's velocity vector is 410 mph at $113^\circ$ from north, and the wind's velocity vector is 22 mph from the north (or at $0^\circ$). The wind's effect is to slightly increase the aircraft's speed and alter its direction. By adding these vectors, we find the resultant vector representing the aircraft's actual speed and direction. The correct calculation shows the aircraft's actual speed is approximately 419 mph at an angle of $116^\circ$ from north.

Solve Applied Problems Involving Vectors -An Aircraft Going from Atlanta 113∘113 ^ { \circ }113∘

Solve Applied Problems Involving Vectors
-An Aircraft Going from Atlanta $113 ^ { \circ }$