Exercises: Solve Problems with Vectors
For magnitude computations, give exact values (simplified radicals or integers). Round to the nearest tenth only when the problem states to.
Recall / Warm-Up
Which of the following is a vector quantity?
Temperature
Mass
Force
Time
In a head-to-tail vector diagram for adding , where does the tail of go?
At the origin
At the tail of
At the tip (arrowhead) of
At any convenient point on the grid
A hiker walks 5 km north, then 5 km south, returning to the start. Which statement is correct?
Distance traveled = 0 km; displacement = 10 km
Distance traveled = 10 km; displacement = 0 km
Distance traveled = 10 km; displacement = 10 km
Distance traveled = 0 km; displacement = 0 km
Fluency Practice
Which of the following is the best example of a vector quantity in real life?
The temperature outside is 20°C.
The package weighs 3 kg.
The wind blows at 15 m/s from the northwest.
The race took 45 seconds.
A plane flies at 300 mph heading due east. A crosswind blows at 50 mph due north. How many vector quantities are described?
0 — neither is a vector
1 — only the plane's velocity is a vector
1 — only the wind is a vector
2 — both the plane's velocity and the wind velocity are vectors
A boat heads due north at 6 m/s. A river current flows due east at 8 m/s. In a head-to-tail vector diagram, which arrow is drawn first?
The river current arrow (8 m/s east)
The resultant arrow
The boat's velocity arrow (6 m/s north)
Either arrow — the order does not matter for addition
A boat travels at 6 m/s due north while a river current flows at 8 m/s due east. The two velocities are perpendicular. What is the magnitude of the resultant velocity in m/s?
A plane flies at 400 mph due east. A headwind blows at 300 mph due west (opposite direction). What is the magnitude of the plane's resultant velocity in mph?
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