- You go 3 m east and 4 m north in 5 s. Your friend goes 5 m at a 36.9° angle east of north in 5 s. Who has the greater average speed? Who has the greater average velocity?
 How far have you walked from your starting position if you walk 12 m north, then 18 m east, then 9 m west?
- How far east have you traveled if you ran 80 m directly northeast?
- What is the magnitude of your acceleration if your horizontal velocity changes from 10 to 13 m/s and your vertical velocity changes from 2 to 6 m/s in 4 s?
- A boat is traveling at 4 m/s north relative to the water on a river that is flowing east at 2 m/s.
- What is the boat’s velocity relative to the land?
- How far downstream does the boat drift in 10 s?
- How long does it take the boat to move 100 m across the river?
- How long does it take a car traveling 18 m/s at a 40° angle west of north to go 900 m west?
- What is the velocity of a bike with components of 8 m/s west and 15 m/s north?
- At what angle is your displacement after going 9 miles east and 15 miles north?
- What are the components of a 20 m/s velocity that is directed 10° above the horizontal?
- Your friend’s house is 4 miles away to the east and 7 miles away to the south. If you run there in a direct line, what angle does your velocity vector make relative to a line pointing straight east?
- John, at third base, throws a ball to Sam, who is at second base 90 ft away. Sam then throws it to Mike, who is at first base 90 ft away. What is the ball’s displacement?
- If a marathon (26.2 miles) follows a straight course and the winner goes 12 miles north during the race, how far west did he travel?
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- You are in the woods and use a plumb bob to determine that your line of sight to the top of a tall tree is 35º. How tall is the tree if it is 86 m away from you?
- If a compass reads a heading of 74°, what angle does this direction make with the east (x-axis)?
- A spacecraft making a course correction has a velocity of = (100, 300, 100) m/s. The spacecraft turns on its engines to create an acceleration of = (2, 5, 5) m/s2 for 5 s. What is the velocity vector of the spacecraft after the engine burn?
 A bird is flying at a velocity of 20 m/s in a direction 60º north of east.
- Calculate the bird’s velocity vector in component form.
- How long does the bird have to fly to get 100 km north?
- How far east has the bird traveled during this time?
- How much does your speed change if you start moving at (2, 4) m/s and have an acceleration of 4 m/s2 in the north direction for 8 s?
- What are the components of your velocity if you started at 10 m/s southwest and then accelerated west at 3 m/s2 for 2 s?
- A swimmer can swim 3 m/s in still water and heads directly to the opposite bank of a 30 m wide river. How far downstream will he be pushed by a perpendicular 2 m/s current?
- Calculate the x- and y-components of the two displacements shown and the resultant in component form.
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