# Vectors - Word Problems

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## Vectors - Word Problems Answer Key

1.

Kumar is flying a glider over the prairies. His glider constantly sinks through the air at a rate of 1 m/s. Kumar finds a thermal where the air is rising at a rate of 2.5 m/s. Compared to the glider the rising air is acting as a

- positive vector.
- neutral vector.
- negative vector.
- cross vector.

2.

Raylene is riding a sled down a hill traveling at 15 m/s. She turns around and throws a snowball back uphill at a velocity of 10 m/s. What is the ground speed of the snowball?

- 150 m/s
- 25 m/s
- 5 m/s
- 1.5 m/s

3.

Tom is on a train traveling at 17 m/s. He decides to get a snack from the rear car so he walks toward the car from the front of the train at a speed of 2 m/s. What is Tom's ground speed?

- 15 m/s
- 19 m/s
- 8.5 m/s
- 34 m/s

4.

Jose leaves home riding his bike straight east for 3 km, turns south for .5 km, then west for 5 km, and finally north for 2 km. What are the vector components from his start to finish locations?

- [math]<< -2, 1.5 >>[/math]
- [math]<< 8, 2.5 >>[/math]
- [math]<< -8, -2.5 >>[/math]
- [math]<< -2.5, 3 >>[/math]

5.

An airplane pilot follows her compass straight north and maintains an air speed of 140 mph. A wind is blowing from the west at 20 mph. After 5 hours how far west will she have traveled?

- 100 miles
- 600 miles
- -100 miles
- -600 miles

6.

An airplane pilot follows her compass straight north and maintains an air speed of 140 mph. A wind is blowing from the west at 20 mph. After 5 hours how far north will she have traveled?

- 700 miles
- 600 miles
- 707 miles
- 693 miles

7.

Two sailboats both leave the same harbor. The first one travels 16 km north and 5 km east. The second one travels 9 km west and 7 km north. How far apart are the two sailboats?

- [math]sqrt(277) \ "km" ~~ 16.6 \ "km" [/math]

8.

An airplane has an airspeed of 860 km/h, heading N30°E. The wind is blowing 60 km/h in a direction of S30°E. What is the ground speed of the airplane?

- 831.6 km/h

9.

A man needs to travel by boat from one side of the river to another in 5 minutes. The place he is going is directly across the river. If the river is 600 m wide, and there is a current of 4 m/s, how fast must the boat go and in what heading to reach the spot on time?

- He must travel at a speed of about 4.5 m/s in a direction of about 63.4° upriver from the spot he wants to go.

10.

The cruising speed of a Boeing 767 in still air is 530 mi/h. Suppose a 767 cruising directly east encounters a 80 mi/h wind blowing 40 degrees south of west.

A) Sketch the vectors described.

B) Express the vectors as ordered pairs.

C) Find the sum of the vectors.

D) Find the magnitude and direction of the vector from part C.

A) Sketch the vectors described.

B) Express the vectors as ordered pairs.

C) Find the sum of the vectors.

D) Find the magnitude and direction of the vector from part C.

- B) (530,0), (-61.3,-51.4)

C) (468.7,-51.4)

D) About 471.5 mi/h at 6.3 degrees south of east

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