Basic Vector Knowledge
What two things must every vector have?
Magnitude and direction
A vector has perpendicular components of 6 m and 8 m. What is the magnitude of the vector?
10 m
In SOHCAHTOA, what does TOA stand for?
Tangent = Opposite / Adjacent
When adding vectors graphically using the head-to-tail method, where should the tail of the second vector be placed?
At the head/tip of the first vector
You walk forward at 3 m/s inside a train that is moving forward at 20 m/s. What is your velocity relative to the ground?
23 m/s forward
Which of these is NOT a vector: velocity, displacement, speed, or acceleration?
Speed
A student walks 5 m east and then 12 m north. What is the magnitude of the student's displacement?
13 m
A right triangle has a hypotenuse of 20 m and an angle of 60°. Find the side adjacent to the 60° angle.
10.0 m
Vector A is 4 m east and Vector B is 3 m north. Find the magnitude and direction of the resultant.
5 m
A train travels 60 m/s east. A passenger walks 5 m/s west relative to the train. What is the passenger's velocity relative to the ground?
55 m/s east
A vector points at 225°. Which quadrant is it in?
Quadrant III
A vector has a magnitude of 13 m and one component of 5 m. What is the magnitude of the other component?
12 m
A right triangle has an adjacent side of 15 m and an opposite side of 15 m. Find the angle.
45°
Vector A is 6 m east and Vector B is 8 m south. Find the magnitude and standard direction angle of the resultant.
10 m
A bus moves forward at 2 m/s. You walk toward the front of the bus at 4 m/s relative to the bus. What is your speed relative to a person standing outside?
6 m/s forward
A student walks 8 m east, then 5 m north, then 8 m west. What is the student's resultant displacement?
5 m north
A student travels 400 m north and ends at a destination that is 800 m in a straight line from the starting point. How far east did the student travel?
692.8 m east
A vector has an x-component of 24 m and a y-component of 10 m. Find the magnitude of the vector
26 m
You walk 5 mi south, 12 mi west, 15 mi north, and then 7 mi east and then walk another 13 mi east. What is your resultant displacement?
12.8m
An airplane flies north at 1200 km/h while a wind blows east at 500 km/h. What is the airplane's speed relative to the ground?
1300 km/h
A student walks 5 mi south, 12 mi west, and then 15 mi north. In which quadrant does the student's resultant displacement point?
Quadrant II
A runner travels 500 m north and then 690 m east. What is the magnitude of the runner's displacement from the starting point?
852.1m
A vector has a magnitude of 50 m and points at an angle of 35° above the positive x-axis. Find BOTH the x-component and y-component.
x = 40.96 m, y = 28.68 m
You walk 7 mi south, 11 mi west, 23 mi north, and then 32 mi east, but then are lame and walk 4 miles south, 5 mi west, 15 mi north, and finish with 24 mi east. What is your resultant displacement?
48.3 mi
A swimmer swims north at 3 m/s across a river that is 40 m wide. The current flows east at 2 m/s. How far downstream will the swimmer travel before reaching the opposite bank?
26.67 m east