# 4.03 ** Vector Worksheet

**alueke2**

1. An airplane flies with an airspeed (speed relative to the air) of 215 km/h. The wind is blowing at 45.0 km/h. Find the velocity of the plane (relative to the ground) if the plane is pointed straight west and the wind is:

- blowing toward the west (3 points)
- blowing toward the east (3 points)
- blowing toward the south (4 points)
__Photo__by MilborneOne / CC-BY-SA 3.0 (For part C be sure to calculate the angle as well.)

2. If you wanted the plane in #1 to fly straight west and the wind was from the south, calculate the heading of the plane (the direction/angle the plane is pointed) and its groundspeed. *Hint: The 215 km/h will be the hypotenuse. *(10 points)

3. A teenager goes for a long walk. She travels 3.0 km north, 4.0 km east, 5.0 km south and 2.0 km west. (10 points)

__Photo__ by Petr Kratochvil / Public Domain

A. Find the distance she walked. (5points)

B. Find her displacement. (5 points)

4. A motorboat can travel at 5.0 m/s relative to the water. The motorboat is crossing a river. The river is flowing east at 3.0 m/s and the boat is pointed north. (10 points)

Here is a video that may be helpful in setting up this problem. __https://www.youtube.com/watch?v=RmxKc5m7lUU&index=7&list=PLgNbeOacocLzF1PYXt8ZWjH9OkeA4S_Pc__

__Photo__ by Peter Griffin / Public Domain

A. Calculate the resultant velocity of the boat. Remember to also give the angle. (5 points)

B. If the river is 100. m wide, how far downstream will the boat travel? (5 points)

5. A 220 kg sailboat has a force of 65 N applied to it in the southerly direction by the water and a 140 N force applied to the sail in a westerly direction. Find the acceleration of the sailboat. Accelerations are vectors, so include the direction (angle) of the acceleration. (10 points)

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