Vector Addition Word Problems 2

Question

#1 Mr. McGarey sleep walks during the night and travels 45 km north of his house in his pajamas. He then turns and heads 17° north of east for 80 km. Mr. McGarey then turns directly east and walks for 20km. At the end of the 20 km, he walks into a stream and suddenly wakes astonished at his position. In what direction and how far must Mr. McGarey travel to make it back to his home?

#2 Ms. Parks travels the second floor of the high school building walking south through the hall for 20 meters. She then heads across the bridge on the second floor for 15 meters at 50° west of north. She then travels 20 meters north and turns in to the math department where she walks 5 meters at 4° north of east. What is the distance of Ms. Parks’ trip from her point of origin and the direction she traveled?

Answer 1

For #1:

The total distance north he went was 45 + 23.39 = 68.39 km and the total distance he traveled east was 76.50 + 20 = 96.50 km. Using the Pythagorean Theorem, the distance he went was sqrt(68.39² + 96.50²) = 118.3 km. To find the angle (direction), use inverse tangent (68.39/96.50) = 35.3º North of East.

Use the same process for problem #2