Vector Worksheet

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:

1. blowing toward the west
2. blowing toward the east
3. blowing toward the south

 Photo by MilborneOne / CC-BY-SA 3.0

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 the plane is pointed) and its groundspeed.

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.

Photo by Petr Kratochvil / Public Domain

A. Find the distance she walked.

B. Find her displacement.

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.

Photo by Peter Griffin / Public Domain

A. Calculate the resultant velocity of the boat.

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

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 of the acceleration.

Photo by Cygtoad / CC-BY-SA 3.0